Decision Support System in Aggregate Planning

Chandana Chada

Problem Report submitted

to the Benjamin M. Statler College of Engineering and Mineral Resources

at West Virginia University

in partial fulfillment of the requirements for the degree of

Master of Science in

Industrial Engineering

Bhaskaran Gopalakrishnan, Ph.D., P.E., Chair

Kenneth R. Currie, Ph.D., P.E.

Feng Yang, Ph.D.

Department of Industrial and Management Systems Engineering

Morgantown, West Virginia

2015

Keywords: Aggregate Production Planning

Copyright 2015 Chandana Chada

Abstract

Decision Support System in Aggregate Planning

Chandana Chada

Aggregate production planning is concerned with determining the quantity and timing of

production in the intermediate future, it usually covers a time period ranging from 3 to 18 months.

The main objective of aggregate planning is to minimize the total cost over the planning horizon.

One of the primary objectives of the research is to design and develop a computer program to

facilitate exploration of aggregate planning methods to obtain desirable cost attributes. The

program should consider all options and input data that a manager may use in aggregate planning.

The first phase is to design and develop a spread sheet with different cases such that each case will

use a constant strategy throughout the period for that particular case and also sensitivity analysis

is performed on the input variables with the help of macros in the spreadsheet. The second phase

is developed in such a way that there is flexibility to select different strategies for each period. The

developed methodology helps the plant operations manager and the personnel by giving them an

opportunity to take a decision and arrive at the most desirable solution.

iii

Acknowledgement

I would like to thank my advisor Dr. B. Gopalakrishnan for his continued support, guidance and

encouragement during the course of this research. Also, I wish to thank Dr. Kenneth Currie and

Dr. Feng Yang for their advice and support.

Above all, I wish to thank God, my family and friends for their constant support and blessings. I

dedicate this work to my parents, Mr. Bhaskar Reddy Chada and Mrs. Sujatha Chada, for enabling

success and happiness in all my pursuits and endeavors in life.

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Table of Contents Abstract ........................................................................................................................................... 0

Acknowledgement ......................................................................................................................... iii

List of Figures ................................................................................................................................ vi

List of tables .................................................................................................................................. vii

Chapter 1 ......................................................................................................................................... 1

Introduction ..................................................................................................................................... 1

1.1 Production Planning ......................................................................................................... 1

1.2 Importance of Production Planning and Control ............................................................. 4

1.3 Aggregate Planning .......................................................................................................... 5

1.4 Aggregate planning strategies .......................................................................................... 7

1.5 Aggregate Planning Methods ........................................................................................... 8

1.6 Need for Research ............................................................................................................ 9

1.7 Conclusion...................................................................................................................... 10

Chapter 2 ....................................................................................................................................... 11

Literature Review ......................................................................................................................... 11

2.1 Aggregate Planning Production in various fields ........................................................... 12

2.2 Researcher’s contribution to APP .................................................................................. 14

2.3 New Developments in APP ............................................................................................ 15

2.4 Production Planning in Companies ................................................................................ 17

2.5 Conclusion...................................................................................................................... 17

Chapter 3 ....................................................................................................................................... 18

Methodology ................................................................................................................................. 18

3.1 Problem Statement ......................................................................................................... 18

3.2 Description ..................................................................................................................... 18

3.3 Definitions ...................................................................................................................... 20

3.4 Theory ............................................................................................................................ 25

3.5 Conclusion...................................................................................................................... 34

Chapter 4 ....................................................................................................................................... 35

Results and Discussions ................................................................................................................ 35

4.1 Problem Description ....................................................................................................... 35

4.2 Phase- 1 .......................................................................................................................... 36

4.3 Sensitivity Analysis ........................................................................................................ 45

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4.4 Phase- 2 .......................................................................................................................... 54

Chapter 5 ....................................................................................................................................... 57

Conclusion and Future Work ........................................................................................................ 57

5.1 Conclusion...................................................................................................................... 57

5.2 Future Work ................................................................................................................... 59

References ..................................................................................................................................... 60

vi

List of Figures

Figure 1.1: Role of Production Planning in the Production Cycle ................................................. 3

Figure 1.2: Relationships of S and OP and the Aggregate Plan ..................................................... 6

Figure 3.1: Flow chart of the program .......................................................................................... 19

Figure 3.2: Strategies constant throughout the entire horizon ...................................................... 25

Figure 3.3: Sensitivity for input variables..................................................................................... 26

Figure 3.4: Strategies varying throughout the entire horizon ....................................................... 27

Figure 3.5: Initial look of the spreadsheet with input data ........................................................... 28

Figure 3.6: Case 1a- Fixed number of workers............................................................................. 29

Figure 3.7: Formula for estimating different variables ................................................................. 30

Figure 3.8: Formula for estimating costs in a period .................................................................... 30

Figure 3.9: Case 1b with subcontracting followed by overtime ................................................... 31

Figure 3.10: Case 3a- Average production rate ............................................................................ 31

Figure 3.11: Overall production costs ........................................................................................... 34

Figure 4.1: Overall Production Costs vs. Cases ............................................................................ 44

Figure 4.2: Labor hours................................................................................................................. 46

Figure 4.3: Labor hours and No. of fixed workers ....................................................................... 46

Figure 4.4: No. of fixed workers and overtime costs .................................................................... 47

Figure 4.5: Demand ...................................................................................................................... 47

Figure 4.6: Labor hours and Demand ........................................................................................... 48

Figure 4.7: Demand and subcontract cost ..................................................................................... 48

Figure 4.8: Demand and No. of fixed workers ............................................................................. 49

Figure 4.9: Overtime and Idle time costs ...................................................................................... 49

Figure 4.10: Subcontract Cost....................................................................................................... 50

Figure 4.11: No. of fixed workers and subcontract cost ............................................................... 50

Figure 4.12: Subcontract cost and idle time Cost ......................................................................... 51

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List of tables

Table 3.1: Summary of cases used in the program ....................................................................... 33

Table 4.1: Given data .................................................................................................................... 36

Table 4.2: Chase Strategy with constant workforce size .............................................................. 37

Table 4.3: Chase Strategy with varying workforce size ............................................................... 39

Table 4.4: Estimation of workers .................................................................................................. 40

Table 4.5: Breakdown of production units ................................................................................... 41

Table 4.6: Breakdown of overall production costs ....................................................................... 43

Table 4.7: Ranking ........................................................................................................................ 45

Table 4.8: Sensitivity Analysis ..................................................................................................... 52

Table 4.9: Ranking after Sensitivity Analysis .............................................................................. 53

Table 4.10: Results from phase 2 .................................................................................................. 54

Table 4.11: Plan with different Strategies throughout the horizon ............................................... 55

Table 4.12: Estimation of workers for mixed strategy ................................................................. 56

Table 5.1 Phase 1 Results ............................................................................................................. 57

Table 5.2: Results from phase 2 .................................................................................................... 58

1

Chapter 1

Introduction

In general, the product and service mix that the company pursues will be specified by the business

plans that are derived from the strategic plans, and will also indicate planned changes in market

penetration, market approaches, and other critical aspects of the business. Strategic and business

plans tend to be too general to specify resource needs and the timing of those needs, and also to

adequately coordinate action plans and resource needs of several of the key functions of the firm,

including Operations, Marketing, Finance, Information Technology, and Human Resources. A

more comprehensive planning of resources, including the type of resources, the quantity of

resources, and the timing of those resources, is accomplished by Sales and Operation Planning.

This planning activity tends to go by several names, depending on the business and the type of

production in which that business is involved. Other common names that have been used in the

past include aggregate planning, production planning, staffing planning. [1]

1.1 Production Planning

For efficient, effective and economical operation in a manufacturing unit of an organization, it is

essential to integrate the production planning and control system. Production planning is an

activity that is performed before the actual production process begins. It is the planning of

production and manufacturing processes in a company or industry. It involves determining the

schedule of production, sequence of operations, economic batch quantities, and also the

dispatching priorities for sequencing of jobs. Production control is mainly involved in

implementing production schedules and is the corollary to short-term production planning or

scheduling. Production control includes initiating production, dispatching items, progressing and

then finally reporting back to production planning. It utilizes the resource allocation of activities

of employees, materials and production capacity, in order to serve different customers [2].

Different types of production methods, such as single item manufacturing, batch production, mass

production, continuous production etc. each have their own type of production planning.

Production planning is used by companies in several different sectors, including agriculture,

manufacturing industry, amusement industry.

2

A Production plan is a plan for the future production, in which the facilities needed are determined

and arranged [3]. A production plan is made at regular intervals for a specific time period, called

the planning horizon. It would comprise of the following activities:

The required product mix and factory load are determined to satisfy demand.

Matching the required level of production to the current resources.

Scheduling and choosing the actual work to be started in the manufacturing facility.

The production orders are setup and delivered to production facilities.

In order to develop production plans, the production planner or production planning department

needs to work closely with the marketing department and sales department. They can provide sales

forecasts, or a listing of customer orders. The “work is usually selected from a variety of product

types which may require different resources and serve different customers. Therefore, the selection

must optimize customer-independent performance measures such as cycle time and customer-

dependent performance measures such as on-time delivery” [1].

As shown in Figure 1.1, the production planning takes the input from sales forecast indirectly. The

production budget is prepared using the sales forecast which in turn helps in preparing detailed

drawings. The production is authorized using this plan which also controls the production,

inspection and quality. After the goods are finished, they are dispatched. The feedback taken from

the customers is sent to sales forecast which is an input to production planning.

3

Sales Forecast

Preparation of Production

Budget

Preparation of detailed

drawings

Production planning

Authorization of

production

Production Control

Inspection and quality

control

Evaluation of

Production system

Finished goods

Dispatch to customers

Customer Management

Feedback

Figure 1.1: Role of Production Planning in the Production Cycle

4

1.2 Importance of Production Planning and Control

Better Service to Customers: Production planning and control, through proper scheduling and

expediting of work, helps in providing better services to customers in terms of better quality of

goods at reasonable prices as per promised delivery dates. Timely delivery and proper quality,

both help in winning the confidence of customers, improving relations with customers and

promoting profitable repeat orders.

Fewer Rush Orders: In an organization, where there is effective system of production planning

and control, production and operations move smoothly as per original planning and matching with

the promised delivery dates. Consequently, there will be fewer rush orders in the plant and less

overtime than in the similar manufacturing industry without adequate production planning and

control.

Better Inventory Control: A sound system of production planning and control helps in maintaining

inventory at proper levels and, thereby, minimizing investment in inventory. It requires lower

inventory of work-in-progress and less finished stock to give efficient service to customers. It also

helps in exercising better control over raw-material inventory, which contributes to more effective

purchasing.

Effective Use of Equipment: An efficient system of production planning and control makes for the

most effective use of equipment. It provides information to the management on regular basis

pertaining to the present position of all orders in process, equipment and personnel requirements

for next few weeks. The workers can be communicated well in advance if any retrenchment, lay-

offs, transfer, etc. is likely to come about. Also, unnecessary purchases of equipment and materials

can be avoided. Thus, it is possible to ensure proper utilization of equipment and other resources.

Lower Idle Time: It ensures that materials and other facilities are available to the workers in time

as per the production schedule thus ensuring lower idle times. Consequently, less man-hours are

lost, which has a positive impact on the cost of production.

Lower capital requirements: Under an efficient system of production planning and control,

everything relating to production is planned well in advance of operations. Where, when and what

is required in the form of input is known before the actual production process starts. Inputs are

made available as per schedule which ensures even flow of production without any bottlenecks.

5

Facilities are used more effectively and inventory levels are kept as per schedule neither more nor

less. Thus, helps in minimizing capital investment in equipment and inventories.

Good public image: A proper system of production planning and control is helpful in keeping

systematized operations in an organization. Such an organization is in a position to meet its orders

in time to the satisfaction of its customers. Customer satisfaction leads to increased sales, increased

profits, industrial harmony and ultimately good public image of the enterprise.

Improved Plant Morale: It co-ordinates the activities of all the departments involved in the

production activity. It ensures even flow of work and avoids rush orders. It maintains healthy

working environment in the plant thus, improving plant morale as a by-product.

1.3 Aggregate Planning

The output of Sales and Operation Planning is called an Aggregate plan. Aggregate production

planning is concerned with determining the quantity and timing of production in the intermediate

future, it usually covers a time period ranging from 3 to 18 months [4]. The aggregate plan is built

in such a way that it satisfies forecast demand by adjusting production rates, workforce size,

inventory levels, overtime work, subcontracting work, and other controllable variables like hiring,

layoffs etc. These plans are the job of the operations manager, working with other functional areas

of the firm. It gives an idea to the management as to what quantity of materials and other resources

are to be procured and when, so that the total cost of operations of the organization is kept to a

minimum over that period. Normally, the physical resources of the firm are assumed to be fixed

during the planning horizon of interest and the planning effort is oriented toward the best utilization

of those resources, given the external demand requirements. Aggregate production planning has a

strong need when a demand pattern is highly seasonal.

The main objective of aggregate planning is to minimize the total cost over the planning horizon.

Maximizing customer service, utilization of plant and equipment and minimizing inventory

investment, changes in workforce levels, production rates should also be considered. Good

intermediate planning requires the coordination of demand forecasts with functional areas of a firm

and its supply chain. The coordination can be difficult as each functional part of a firm and the

6

supply chain has its own limitations and constraints. This coordination planning effort has evolved

into a process known as Sales and Operation Planning (S and OP).

As shown in the Figure 1.2, S and OP receives input from a variety of sources both internal and

external to the frim. S and OP takes into account the process planning and capacity decisions,

demand forecasts, workforce size, supply chain support, on-hand inventory and external capacity.

Market demand and research contribute to product decisions which is further contributed towards

process planning and capacity decisions. An aggregate plan is developed based on S and OP.

Product Decisions

Process planning and

capacity decisions

Master production

schedule and MRP

External

Capacity

Demand

Forecasts,

Orders

Workforce

Inventory on

hand

Market PlaceResearch &

Technology

Supply Chain

support

Detailed work schedules

Aggregate Plan

Sales & Operations

planning

Figure 1.2: Relationships of S and OP and the Aggregate Plan

7

1.4 Aggregate planning strategies

When generating an aggregate plan strategy, the operations manager can consider changing the

inventories which is used to absorb changes in the demand during the planning period, varying the

workforce size, varying the production rates, use of subcontracting or changing the price of the

product. All these strategies involve manipulation of inventory, production rates, workforce size,

capacity and other controllable variables. A firm can develop a plan by choosing the capacity

options which do not try to change demand but attempt to absorb demand fluctuations, or choose

the demand options through which firms try to smooth out changes in the demand pattern over the

planning period.

The different capacity options are:

Changing the inventory levels by increasing the inventory during periods of low demand

to meet high demand in future periods which further increases costs associated with

storage, insurance, handling, capital etc.

Varying the workforce size by hiring and laying off production workers to match

production rates which includes costs related to training, hiring and layoff.

Varying production rates through overtime by keeping a constant workforce while varying

number of working hours, of course there is a limit to overtime as it results in worker

fatigue.

Subcontracting is another possible option to satisfy the demand during peak demand

periods but finding a subcontracting supplier is always an issue and there is a loss of quality

control.

The basic demand options are:

Influencing the demand through different forms of advertising, promotion, selling, price

cuts etc.

Back ordering during high demand periods but this involves a risk of lost sales and the

customer must be willing to wait.

8

A widely used technique is to develop a product mix of counter seasonal items but this

requires skills and is tough finding products with opposite demand patterns.

A combination of different capacity options can be used to develop plans to arrive at the most

desirable production cost. This gives rise to two extremes, one being chase strategy and the other

is level strategy.

Chase strategy attempts to achieve output rates for each period to match the demand

forecast for that period. It can be accomplished in a variety of ways. For example, varying

the workforce level to vary production rates by hiring, laying off, overtime or

subcontracting.

Level strategy tries to maintain a constant work force or production rate over the planning

horizon. A combination of chase and level strategies can also be used to come up with a

new strategy called mixed strategy.

1.5 Aggregate Planning Methods

There are many techniques that operations managers use to develop aggregate plans. The popular

one among them is graphical & charting technique which is a trial & error approach and the other

ones are mathematical approaches like transportation method of linear programming, dynamic

programming, goal programming, differential calculus, heuristics approach and search decision

rule [5].

The graphical technique is easy to understand and use, but might not give the optimal production

plan. These plans work with a few controllable variables allowing planners to compare the

production costs for each strategy and choose the best optimal production plan, which is

acceptable. In this method the demand is forecasted for each period, capacity of regular time,

overtime, subcontracting, labor costs, hiring and layoff costs, inventory holding costs are to be

determined to compute calculations and develop alternative plans. Operations managers can come

up with different plans by changing the set of variables or permutations of the set of variables in

each plan.

9

One possible strategy is to maintain constant workforce throughout the planning period by

maintaining a constant rate of production or varying it accordingly. The other possible strategies

could be by maintaining a constant workforce at a level necessary to meet the lowest or average

demand and to meet all demand above this level by either subcontracting, overtime, or both.

Overtime usually has a limit as excess will lead to worker fatigue. Subcontracting can also be

limited. Operations managers could develop strategies where the workforce level varies as per the

monthly requirements. In these strategies the monthly demand is satisfied by hiring and laying off

workers as per requirement. It can also use a combination of subcontracting, overtime, hiring and

layoff.

1.6 Need for Research

In aggregate planning, calculation of different costs associated with production by using different

strategies like chase, level and mixed strategies is a very tedious process. In an extremely dynamic

manufacturing sector, production people very often face a roadblock in analyzing the different

strategies of aggregate planning due to the computational complexity involved in the above

mentioned strategies. Apart from the time consuming manual calculation methods, there are no

rules of thumb to recommend which aggregate planning method has to be selected for analysis.

This issue becomes even more complex as the number of variables that need to be considered for

evaluating a particular method. These issues result in a need for computer program in which the

aggregate planning strategies are automated such that the user has the flexibility to choose the

method of choice easily. Also, a computer application will speed up the planning process and thus

saves expensive engineering hours.

Hence the primary objectives of this research are to:

Design and develop a spreadsheet based computer program to facilitate exploration of

aggregate planning methods to obtain desirable cost attributes.

Perform sensitivity analysis of various options with respect to cost allowing the operations

manager to arrive at the most desirable plan.

In order to illustrate the functionality of the developed program, a fundamental scenario is taken

from the book “Operations management” by Jay Heizer and Barry Render. A specific problem is

10

taken for which different cases are evaluated using the strategies discussed above. This allows the

operations manager to arrive at the most desirable cost plan. As this is user friendly, all levels of

management can access the program. Implementing and following this program will give a good

estimate to the operations manager and helps in reducing the overall production costs.

1.7 Conclusion

The chapter is an introduction to the topic of production planning. It helps in understanding the

importance of production planning, control and aggregate planning. Also, it helps in understanding

different types of strategies like chase strategy, level strategy and methods in aggregate production

planning. This research work will give the plant operations manager a basic idea about various

plans with different strategies and their respective production costs. It will help them to arrive at

the most desirable solution by giving them the flexibility to vary the input variables and see the

overall effects on the production costs before actually coming to a conclusion about the final plan

for the entire horizon.

11

Chapter 2

Literature Review

Spreadsheets are the most common software tool managers use to analyze data and model

quantitative problems. The reasons for the popularity of spreadsheets are many, but we could

highlight the following: they are widespread, user-friendly, flexible, and allow the analysis of

multiple scenarios. Therefore, many companies and education centers have found spreadsheets to

be an easy method for business modeling as they offer a wide set of tools ranging from formulas

—whether easy ones or more complex ones— to simulation of different scenarios, macros, charts,

etc. [6]

The consideration of uncertainty in manufacturing systems supposes a great advance. Models for

production planning which do not recognize the uncertainty can be expected to generate inferior

planning decisions as compared to models that explicitly account for the uncertainty. [7]

Traditional aggregate production planning models are applicable in a stable economic

environment, with low rates of change. Consequently, factories can operate in a relatively stable

manner, with capacity and mix changes being made infrequently. However, in the last decade, we

have seen rapid changes in many process industry sectors usually brought about by competition

within the sector and by economic growth in emerging economies, with the consequent increases

in demand. In such situations, raw material availability and processing capacity can both be

significant constraints. Here, the traditional aggregate production planning formulations are not

able to capture the competition in the production tier for the raw material, nor the competitive

interactions between producers on variables such as production quantities, capacity constraints,

raw material availability and price. [8]

The planning of production, inventories and work-force at an aggregate level in response to a

known demand schedule has received substantial treatment in the literature since the early fifties.

Several models have been proposed with Silver and Bowman giving very good review of these

models. Lee and Khumwala have tested these models in an implementation methodology through

simulation technique. However, the linear decision rules of Holt, Modigliani, Muth and Simon and

the linear programming model of Manssman and Smith are the most widely used. Application of

12

linear programming for aggregate production planning are also reported by Eisseman and Young

in a study of a textile mill, by Fabian in a study of blast furnace operations and by Wai-Hing Chin

in a study of the packing industry. Explicit determination of the demand in terms of products is

therefore of little use since it fails to give the projected load on the production facilities. It is

therefore important that the demand be determined in such a way as to give a clearer picture of the

actual production load. [9]

2.1 Aggregate Planning Production in various fields

Demand for many industrial products, including food industry products, presents highly seasonal

patterns, which makes the production and materials management a difficult task. Aggregate

Production Planning (APP) is a middle term planning concerned with the determination of

production, inventory, and work force levels to meet such a fluctuating demand requirements over

a planning horizon typically of one year. The goal is to meet the seasonal forecasted product

demand in a cost-effective manner. [10]

In hierarchical production planning (HPP) systems, aggregate production planning (APP) is meant

to balance capacity requirements and production quantities for medium term planning horizons.

Aggregate plans provide the basic input for further planning steps. [11]

“Our model integrates production capacity planning and workforce flexibility planning. In contrast

to traditional approaches, it considers discrete capacity adaptations which originate from technical

characteristics of assembly lines as well as from work regulations and shift planning. In particular,

our approach takes change costs into account and explicitly represents a working time account via

a linear approximation. A solution framework containing different primal heuristics and

preprocessing techniques is embedded into a decision support system”. [12]

Aggregate production planning (APP) plays a critical role in supply chain management (SCM).

This paper investigates multiproduct, multi period APP problems with several distinct types of

fuzzy uncertainties. In contrast to the existing studies, the modelling in this work conserves the

fuzziness such that the obtained APP is more effective. [13]

13

A production plan concerns the allocation of resources of the company to meet the demand forecast

over a certain planning horizon and a distribution plan involves the management of warehouse

storage assignments, transport routings and inventory management issues. A production–

distribution plan integrates the decisions in production, transport and warehousing as well as

inventory management. The overall performance of a supply-chain is influenced significantly by

the decisions taken in its production–distribution plan and hence one key issue in the performance

evaluation of a supply chain is the modelling and optimization of the production–distribution plan

considering its actual complexity. [14]

Efficient long-term capacity management is vital to any manufacturing firm. It has implications

on competitive performance in terms of cost, delivery speed, dependability and flexibility. In a

manufacturing strategy, capacity is a structural decision category, dealing with dynamic capacity

expansion and reduction relative to the long-term changes in demand levels. Within the S and OP,

resource planning is used for determining the appropriate capacity levels in order to support the

production plan. Manufacturing strategy and sales and operations planning provide two

perspectives on long-term capacity management, raising and treating different issues. [15]

Depending upon the assumptions made and the modelling approach used, aggregate production

planning (APP) problems can be quite complex and large scale. [16]

“The aim of this paper is to formulate a model that integrates production planning and order

acceptance decisions while taking into account demand uncertainty and capturing the effects of

congestion. Orders/customers are classified into classes based on their marginal revenue and their

level of variability in order quantity (demand variance). The proposed integrated model provides

the flexibility to decide on the fraction of demand to be satisfied from each customer class, giving

the planner the choice of selecting among the highly profitable yet risky orders or less profitable

but possibly more stable orders”. [17]

This study investigates on integration of lateral transshipment to aggregate production–distribution

planning (APDP) problems. Inventory holding, backordering and additional capacity options

including overtime and changing workforce level are considered as possible strategies to meet the

14

fluctuating and dynamic demand. In multi-site manufacturing environment, all the manufacturing

sites are interconnected through a lateral transshipment strategy to serve each other. [18]

In Manufacturing-to-Order or Engineering-to-Order systems producing complex and highly

customized items, each item has its own characteristics that are often tailored for a specific

customer. Project scheduling approaches are suitable for production planning in such

environments. However, when we consider the production of complex items, the distinct

production operations are often aggregated into activities representing whole production phases.

In such cases, the planning and scheduling problem works on the aggregate activities, considering

that, in most cases, such activities also have to be manually executed. Moreover, simple finish-to-

start precedence relations no longer correctly represent the real production process, but

overlapping among activities should be allowed. [19]

2.2 Researcher’s contribution to APP

Jain et al. [20] introduced a model for a manufacturing scenario where dissimilar machines perform

similar operations with different cycle times and production rates, and they proposed

configuration-based formulation instead of resource-based formulation to solve aggregate

planning problems using several heuristics. Wang and Fang [21] discussed the multi-objective

problem with fuzzy linear programming (FLP) and concluded that FLP approach is effective than

non-fuzzy problem formulation in real scenarios. The researchers [22] devised heuristics and

mathematical relationships based on tabu search method to solve the multi-variable problem of

sawmill operations for APP. Wang and Liang [23] presented possibilistic linear programming

(PLP) model to minimize the overall cost and to help in multi-criterion decision making.

Kumar and Haq [24] analyzed the effectiveness of ant colony algorithm in combination with

genetic algorithm for aggregate production planning. Agrawal [25] reported a case study of

furniture manufacturing for the aggregate planning and accessed various approaches effectiveness.

Gomes et al. [26] developed a multiple criteria mixed integer linear programming model for the

construction material manufacturing firm and also proposed a decision support system to find out

the better solutions of APP problems. Authors [27] investigated that fuzzy models are more

suitable than the stochastic and deterministic approaches for aggregate production distribution

15

planning (APDP) and they improved their fuzzy model by integrating it with genetic algorithm to

make it applicable to the more complex problems.

Jamalnia et al. [28] devised a hybrid fuzzy multi-objective non-linear programming model which

attempts to maximize the profit and to minimize the total cost regarding different variables and

this model is also synchronized with genetic algorithm. Researchers [29] proposed multi-objective

linear as well as non-linear programming models of APP for the supply chain management and

these multi-objective models had been optimized using genetic algorithm. The authors [30]

evaluated a model for the cost of being flexible in a manufacturing environment with respect to

existing capacity and the model was used in combination with decision support system for mid-

term capacity planning. Wang and Yeh [31] found that modified particle swarm optimization

(MPSO) is more effective than standard particle swarm optimization (SPSO) for complex

problems of APP by introducing the idea of sub-particles and coding. The above discussed

literatures generally provide a better solution to the aggregate planning of discrete type of

manufacturing firms.

2.3 New Developments in APP

A reformulation of the aggregate planning problem - This will more closely agree with situations

frequently encountered in practice. The proposed reformulation assumes that a firm’s production

planners want to determine the expected service and inventory levels for a given production profile

in the face of uncertain seasonal demand. By using several different production profiles which are

each consistent with the firm’s staffing, subcontracting, and overtime policies, it is possible to pick

the profile that best meets the firm’s preferences for service level and inventory turns. Actually,

the trade-offs between inventory and service level are examined so that an informed choice can be

made by all those concerned. [32]

Production decision framework – a heuristic method - It is a dynamic model proposed to assist the

manager in the planning process. Emphasis was placed on developing a logical, understandable,

and straightforward model. The development phase utilizes a ratio, named RPCC, which represents

the relative value of the cost of changing the production level to the cost of carrying inventory.

This ratio is used to determine the length of an effective planning horizon. Two indicators, the

16

current period ratio and the planning horizon ratio, are calculated to reflect the demand to current

production rate over different time periods. Based on the joint values of these indicators, the

planning problem is subdivided into one of nine mutually exclusive and exhaustive states. A set

of action statements, representing logical responses to each of the sub problems, is formulated.

A discrete production-switching rule – This was developed to accommodate discrete production

environments which rely on crew loading. Inventory costs are estimated using an interval approach

rather than traditional point estimates. The model allows incorporation of overtime options and is

interactive in nature. Decision variables from the model can be disaggregated and linked directly

to lower-level planning activities. [32]

Improved hierarchical production planning - The hierarchical approach, by partitioning the

problem into a series of sub problems, is able to reduce the complexity of the solution process,

trading off mathematical optimality for good, feasible solutions with reduced costs. Such an

approach is desirable in practice. The improved hierarchical production-planning model consists

of four modules: (1) forecasting; (2) aggregate production planning; (3) disaggregate production

planning; (4) sequencing. When no forecasts for individual products are provided, the improved

hierarchical production-planning model overcomes this weakness by appending a front-end

forecasting module. In addition to reducing direct costs, this model provides efficient tools to aid

managers in their decision making process. It is not confined to one decision level; in fact, middle

management, production-planning personnel, schedulers, etc. can all benefit from the use of the

various modules within the hierarchical production-planning system. [32]

In hierarchical production planning system, Aggregate Production Planning (APP) falls between

the broad decisions of long-range planning and the highly specific and detailed short-range

planning decisions. The proposed approach attempts to minimize total costs with reference to

inventory levels, labor levels, overtime, subcontracting and backordering levels, and labor,

machine and warehouse capacity. Here several genetic algorithm parameters are considered for

solving NP-hard problem (APP problem) and their relative comparisons are focused to choose the

most auspicious combination for solving multiple objective problems. An industrial case

demonstrates the feasibility of applying the proposed approach to real APP decision problems.

[33]

17

2.4 Production Planning in Companies

On discussing with the operations manager during the energy audit visits to the two plants, it is

understood that the production planning is done on a weekly and monthly basis accordingly. The

manufacturing plant 1 bases its daily production on 3 weeks of forecast and 4 months of long term

planning. Every week the daily requirement is released which is based on the demand in the market

which helps in developing weekly buckets. They use Material Requirements Planning (MRP) to

plan the production requirements. They always try to maintain a constant workforce with varying

production levels. If maintaining the constant workforce doesn’t satisfy the demand, then they

outsource the remaining production needed. They always try to satisfy the customer demand

irrespective of the available production.

The operations manager of the manufacturing plant 2 stated that they always try meet the demand

and satisfy the customer requirements. They create a production requirements plan 6-8 weeks

ahead and this might change according to the situation. The lead time is usually 8 weeks and they

produce 2 weeks ahead or sometimes 1 week. They use a constant workforce size, but might use

overtime production to satisfy the demand.

Using this spreadsheet the operations managers of these companies will be able to use their

available data to look into the various possible options. This will give them the flexibility to

explore different strategies available and implement the most feasible one according to their

companies’ policy.

2.5 Conclusion

This chapter started with the importance of spreadsheets in the real world, which is followed by

history of aggregate planning and its traditional methods. Also, various fields benefited by

aggregate production planning are discussed. Later the contributions of various researchers to

Aggregate Production Planning (APP) is discussed. New developments in APP are also discussed

followed by production planning in two manufacturing plants and how they are benefited by this

research work. The later chapters of this work provide the methodology in order to generate

different production planning cases which helps the operations manager and concerned personnel.

18

Chapter 3

Methodology

3.1 Problem Statement

The main objective of this work is to develop a program which will allow the operations manager

to find alternate solutions easily based on his understanding. This research is based on a

fundamental scenario taken from the book “Operations management” by Jay Heizer and Barry

Render. A specific problem is taken from the book for which different methods are evaluated using

the strategies discussed in chapter 1.

The program considers all variables as input to the program that an operations manager uses in

aggregate planning as given in the book. A user friendly program is to be developed which will

allow easy changes to the variables and to come up with different strategies which uses a number

of combinations of variables. This program would give the manager a clear idea as to which plan

gives the optimal solution, which plan is most feasible among the ones developed and a comparison

can be made among the solutions obtained to see variations in input parameters. Also, the program

allows to perform sensitivity analysis of various options with respect to cost. This allows the

operations manager to arrive at the most desirable plan. As it is user friendly, the higher and lower

levels of management can easily access the program.

3.2 Description

The first phase of the research is to design and develop a spreadsheet based computer program

which will perform sensitivity analysis on input variables using a constant strategy throughout the

planning period for that particular case. The second phase is allowing the strategies to differ

keeping the input variables constant. The graphical technique discussed in chapter 1 is used to

evaluate different strategies. All the capacity options are used to develop plans with different sets

of options, these are analyzed by comparing the overall production costs and the optimal plan is

selected accordingly. The spreadsheet is developed to compute overall production costs and graphs

are plotted to evaluate these strategies.

19

Satisfy the demand by

overtime first followed

by subcontracting

Satisfy the demand by

subcontracting first

followed by overtime

Compute production

costs

Cases 1-3a, 4,5-6a,7 Cases 1-3b, 5-6b

Start

Input

data

Any limits on input

data?

Input the

limits into

the

program

Assume

reasonable

limits

Yes

If OC < SC

No

NoYes

Phase 1 Phase 2

End

Figure 3.1: Flow chart of the program

20

The flow chart shown in Figure 3.1 explains how the data is input to the program. The overtime

and subcontracting production is constrained if there are any limits imposed as per the policies of

the company. Also, there might be a limit on holding capacity because of the size restrictions.

After entering all the input data, the overall production costs are estimated for all the cases.

3.3 Definitions

The inputs to the program are to be determined. They are:

Demand forecast (Monthly) - The forecasted demand for all the periods over the planning

horizon is to be determined through various types of forecast approaches. These can

include qualitative methods like Jury of Executive Opinion, Delphi Method etc. and

quantitative methods like Naïve Approach, Moving Averages, Exponential Smoothing,

Trend Projection and Linear Regression.

Production days- The number of working days that accounts for production in that period.

It excludes the regular holidays, holidays accounted for unusual shut downs etc.

Daily Demand- The demand forecast over the production days gives us the daily demand.

𝐷𝑎𝑖𝑙𝑦 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 =𝑇𝑜𝑡𝑎𝑙 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑑𝑎𝑦𝑠

Working hours/day- Number of hours of work for an employee in a day. It usually is 8

hours as defined by U.S. Department of Labor.

Production units- Number of units required to be produced in a period to satisfy the

customer demand.

Labor hours/unit- Number of hours of required labor to produce a unit of production.

Regular/Fixed workers- Number of workers available for each production day which is

fixed. These workers are not affected by demand fluctuations.

21

Regular production costs- The costs related to the regular time labor are regular production

costs.

Inventory limit- The warehouses cannot hold too much inventory. Usually there is a limit

on its holding capacity.

Inventory costs- The costs incurred to hold production units for a particular period of time

or the additional costs involved in storing and maintaining a piece of inventory over the

course of a period.

Initial Inventory- The inventory at the end of the previous time period or the current number

of inventory units in the warehouse.

Overtime pay- According to U.S. Department of Labor, if an employee works for more

than 40 hours in a week, the employer must pay him an overtime cost. This cost is well

above the regular labor costs.

Overtime limit- keeping in mind the health of a worker, he shouldn’t be allowed to work

over a certain limit of hours. It usually varies from one organization to another.

Subcontract pay- A subcontractor is a person hired by a general contractor to perform a

specific task as part of the project. The costs incurred to hire these subcontractors gives

rise to subcontract pay.

Subcontract limit- There is a limit on the subcontract production. It varies same as above.

Shortage costs- Consequences of not being able to meet the demand from the production

and inventory leads to lost sales giving rise to stock out costs or shortage costs.

Idle time costs- Whenever the inventory reaches its maximum limit and cannot hold further

capacity, the plant is kept idle or the excess quantity produced might have to be scrapped.

The costs incurred due to this accounts for the idle time costs.

Hiring costs- Costs incurred to hire extra number of workers to satisfy the demand

requirement for the current period.

22

Layoff costs- Costs incurred to lay off workers because of the fluctuations in the demand.

Previous Demand- The demand during the previous period.

Production rate- It is the number of production units to be produced daily. It is given by the

equation as follows:

𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐹𝑖𝑥𝑒𝑑 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑥 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑖𝑛𝑔

ℎ𝑜𝑢𝑟𝑠𝑑𝑎𝑦

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑏𝑜𝑟ℎ𝑜𝑢𝑟𝑠𝑢𝑛𝑖𝑡

Regular time production is the quantity produced by the fixed workers in a regular interval of time.

𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑥 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑑𝑎𝑦𝑠

Beginning Inventory for each period is the number of inventory units the warehouse holds initially

or the inventory units that the warehouse holds at the end of previous period that is carried out to

the current period. Whichever case applies.

Ending Inventory for each period is the number of units available at the end of each period after

the demand is satisfied.

𝐸𝑛𝑑𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

= 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

+ 𝑆𝑈𝑀 (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 + 𝑆𝑢𝑏𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 + 𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒) 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

− 𝐷𝑒𝑚𝑎𝑛𝑑 𝑓𝑜𝑟 𝑡ℎ𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑

Overtime production is the quantity produced by the fixed workers during extra hours/overtime.

To satisfy the demand, a company might use a supplier or a subcontractor to produce the extra

quantity needed, this is termed as subcontract production.

Case 1- If Overtime cost is less than Subcontracting cost

𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

= 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑 − (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 + 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦)

23

𝑆𝑢𝑏𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

= 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑 − (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 + 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

+ 𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛)

Case 2- If Overtime cost is greater than Subcontracting cost

𝑆𝑢𝑏𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

= 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑 − (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 + 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦)

𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

= 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑 − (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 + 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

+ 𝑆𝑢𝑏𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛)

Number of required workers- The number of workers required for a particular period can be

determined as follows:

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 = 𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑥 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑏𝑜𝑟

ℎ𝑜𝑢𝑟𝑠𝑢𝑛𝑖𝑡

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑖𝑛𝑔ℎ𝑜𝑢𝑟𝑠

𝑑𝑎𝑦 𝑥 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑑𝑎𝑦𝑠

Inventory/Holding- The number of units the warehouse is holding at the end of each period that is

carried out to next period.

Shortage units- The number of units that are lost due to shortage in production and inventory.

𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒 𝑢𝑛𝑖𝑡𝑠

= 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 + 𝑆𝑈𝑀 (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 + 𝑆𝑢𝑏𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 + 𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒) 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

− 𝐷𝑒𝑚𝑎𝑛𝑑

Idle time units- When the Inventory limit reaches its maximum, the plant is kept idle or excess

quantity is scrapped.

24

𝐼𝑑𝑙𝑒 𝑡𝑖𝑚𝑒 𝑢𝑛𝑖𝑡𝑠

= 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 + 𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 − 𝐷𝑒𝑚𝑎𝑛𝑑

− 𝐸𝑛𝑑𝑖𝑛𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

Hired workers- The difference between the numbers of workers required for the current and

previous period.

Laid-off workers- The difference between the numbers of workers required for the previous and

current period.

If number of workers required for current period > previous period

𝐻𝑖𝑟𝑒𝑑 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 (𝑐𝑢𝑟𝑟𝑒𝑛𝑡 − 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠) 𝑝𝑒𝑟𝑖𝑜𝑑

If number of workers required for current period < previous period

𝐿𝑎𝑖𝑑 − 𝑜𝑓𝑓 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 (𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡) 𝑝𝑒𝑟𝑖𝑜𝑑

Units produced by hiring- The units produced by the hired workers.

𝑈𝑛𝑖𝑡𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑

=𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐻𝑖𝑟𝑒𝑑 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑥 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑖𝑛𝑔

ℎ𝑜𝑢𝑟𝑠𝑑𝑎𝑦

𝑥 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐷𝑎𝑦𝑠

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑏𝑜𝑟ℎ𝑜𝑢𝑟𝑠𝑢𝑛𝑖𝑡

Units accounted for laying off - The units the laid-off workers would have produced.

𝑈𝑛𝑖𝑡𝑠

=𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐿𝑎𝑖𝑑 − 𝑜𝑓𝑓 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑥 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑖𝑛𝑔

ℎ𝑜𝑢𝑟𝑠𝑑𝑎𝑦

𝑥 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐷𝑎𝑦𝑠

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑏𝑜𝑟ℎ𝑜𝑢𝑟𝑠𝑢𝑛𝑖𝑡

Total Costs- The sum of all the costs incurred due to production, inventory, shortage, hiring & lay-

off, idle time.

25

𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝑠 = 𝑆𝑈𝑀 (𝑅𝑒𝑔𝑢𝑙𝑎𝑟 + 𝑆𝑢𝑏𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 + 𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒) 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠

+ 𝐻𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡𝑠 + 𝑆𝑡𝑜𝑐𝑘𝑜𝑢𝑡 𝑐𝑜𝑠𝑡𝑠 + 𝐼𝑑𝑙𝑒𝑡𝑖𝑚𝑒 𝑐𝑜𝑠𝑡𝑠

+ 𝐻𝑖𝑟𝑖𝑛𝑔 𝑜𝑟 𝐿𝑎𝑦𝑜𝑓𝑓 𝑐𝑜𝑠𝑡𝑠

3.4 Theory

A mix of different capacity options and strategies are used to generate logical plans with different

sets of options. For convenience, these strategies and options are termed as “cases” in this program.

In all of these plans, production units, number of workers employed and overall production costs

are computed. These plans are compared using the plots generated for overall production costs of

each plan. Based on this, an optimal plan is selected accordingly. Further, sensitivity analysis is

done on the plans using the two different phases which are described below.

Phase 1

The first phase considers constant strategy which is employed throughout the entire

planning horizon changing the input variables by say up to ± 20%. The input variables and a

combination of up to two variables are plotted to see their effect on the production costs. The

variables and the combinations which have a significant effect on the production costs are analyzed

to see if there is any change in the optimum plan selected above.

As shown in Figure 3.2, a constant strategy is used for all the periods in the planning horizon.

Figure 3.2: Strategies constant throughout the entire horizon

26

The sensitivity analysis is done in the first phase with various input variables as shown in the

Figure 3.3.

Figure 3.3: Sensitivity for input variables

Phase 2

The second case uses different strategies for each period across the entire horizon by

keeping the input variables constant throughout the problem. A thorough understanding of the

input variables, production rates and their effect on the overall production costs will help in

coming up with an optimal plan. Obtaining an optimal plan is tedious with this process because

it involves lot of trial and error instances. These instances will give the productions planning

personnel a flexibility to play with different combinations of strategies.

The Figure 3.4 shows the phase 2 of the program which uses mixed strategies/cases for all the

periods in the planning horizon.

27

Figure 3.4: Strategies varying throughout the entire horizon

The five plans generated in the first phase of the program use a chase strategy which are discussed

below in detail. There are no hiring and layoff costs as this method uses a chase strategy with

constant workforce size throughout the entire planning horizon.

The first plan uses a constant rate of daily production. The production rate is determined using the

fixed number of workers, which is considered to be constant throughout the entire planning period.

Regular production is computed using the production rate determined above. To satisfy the further

demand, the overtime or subcontracting is employed as follows:-

If overtime pay rate is less than subcontracting pay, then the demand is satisfied using the

overtime production. Further, if the overtime production cannot satisfy the total demand in

that period, the required units are produced through subcontracting.

If overtime pay rate is greater than subcontracting, then the demand is first satisfied through

subcontract production followed by overtime depending upon the customer’s demand.

Initially a spreadsheet is developed with information for all the input variables, demand, number

of production days. Using this data, daily demand is calculated as shown in Figure 3.5. As we can

see there are limits on Overtime, Subcontracting, and Holding capacity which act as constraints in

the cases that are to be developed. This sheet is named as “Option1”.

28

Figure 3.5: Initial look of the spreadsheet with input data

Usually there is a limit on overtime as excess overtime leads to worker fatigue. The subcontracting

can also be limited depending upon the policy of the organization. In this case, there might be a

chance of lost sales if the demand is not satisfied by regular, overtime and subcontract production.

The beginning and ending inventories are computed using the equations discussed in the previous

sections. The total number of units in the warehouse at the end of each period are also computed.

Idle time units are determined if the holding reaches its maximum capacity.

Another sheet is developed for case 1a as shown in the Figure 3.6, where the required demand is

satisfied by regular production followed by overtime followed by subcontracting. The formula for

production rate, regular, overtime, subcontract production and beginning inventory are shown in

the figure below. Similar sheets are developed for all other cases 1-3a, 4, 5-6a, and 7, also they use

the same formula to estimate the overall production needed to satisfy the demand. The formula

takes reference from a sheet named “Option1” which has the input data.

29

Figure 3.6: Case 1a- Fixed number of workers

The second and third plans also use a constant rate of daily production. The production rate for

the second plan is taken as the minimum value of the daily demand whereas it is the average value

for the third plan. The daily demand is computed for each period by dividing the monthly demand

over number of production days in that period. Regular production followed by overtime and

subcontracting or vice versa is computed in a way similar to the first plan. Beginning & ending

inventories, inventory units, idle time and shortage units are calculated similarly. The number of

workers required for each period will be a constant number as the production rate is constant. This

is calculated using the equations discussed in the previous sections.

In the Figure 3.7, the formulas for calculating variables like ending inventory, holding capacity,

number of shortage units, number of idle time units on a machine and number of workers employed

for each period are shown. The formula takes reference from a sheet named “Option1” which has

the input data.

30

Figure 3.7: Formula for estimating different variables

In the Figure 3.8, the formula for calculating the total costs related to all types of production,

inventory, shortage and idle time are shown for a particular period. The formula takes reference

from a sheet named “Option1” which has the input data.

Figure 3.8: Formula for estimating costs in a period

As shown in the Figure 3.9 for case 1b, where overtime cost is greater than subcontracting cost,

subcontracting is given the first preference over overtime production. The formula shown below

is used to carry out the calculations for both types of production. The formula takes reference from

a sheet named “Option1” which has the input data.

31

Figure 3.9: Case 1b with subcontracting followed by overtime

The Figure 3.10 for case 3a shows the formula used to estimate the costs incurred due to regular

type of production. Similar formulas are used for other type of cases. The formula takes reference

from a sheet named “Option1” which has the input data.

Figure 3.10: Case 3a- Average production rate

The fourth plan uses the maximum rate of daily demand as the constant rate of daily production.

As it is using the maximum rate, the demand for each period is satisfied by the regular production.

In this case usually the holding costs will be higher when compared to the previous plans discussed

32

above. If there is a limit on holding, then the idle time costs will rise as excess quantity will have

to be scrapped because excess quantity is produced when compared to the other plans.

The fifth plan uses a constant production rate which is computed on the basis of average number

of workers employed for the second and third plan. It is based on a logical conclusion that the

optimal number of workers employed will be a value somewhere between the number of workers

employed in second and third plans which use a minimum and average rate of daily demand

respectively. Regular, overtime, subcontracting, inventory units, beginning and ending

inventories, shortage, and idle time are computed similar to the previous plans.

A chase strategy with varying workforce size is used for the last two plans. The rate of production

varies in this strategy which results in the fluctuation of the work force size. Hiring and Layoff

costs are incurred due to these fluctuations.

The sixth plan’s regular time production will be same as the previous period’s demand. To produce

the desired amount of regular production, workers must be either hired or laid off accordingly.

Further demand is satisfied by overtime followed by subcontracting or vice versa, whichever case

is applicable as discussed in the previous plans. If the overtime production is limited then it is

satisfied by both types of production i.e. overtime and subcontracting. If both types of production

are limited and the customers demand is not yet met, then this gives rise to the stock out costs. If

the demand is satisfied and excess quantity is produced, the excess units would have to be scrapped

due to limitation of the holding capacity. All other computations like inventories, etc. are

determined as discussed above.

The seventh plan is similar to the previous plan which also uses a chase strategy with varying

workforce size. Here the production rate will be same as the current period’s demand rate. As it is

using the current period demand, there will be no need for overtime and subcontract production.

To consume the load of demand workforce size should be changed accordingly by either hiring or

laying off. There will not be any shortage, idle time or inventory units as only the required quantity

is produced. All other computations are determined as discussed in the previous plans.

33

All the plans or cases used in the spreadsheet are summarized in the Table 3.1 as shown below:

Table 3.1: Summary of cases used in the program

Cases/Plans Regular Production

Rate

Further

demand Workforce size Hiring/Layoff

1a Fixed number of

workers

Overtime first Constant

-

1b Subcontract first -

2a Minimum value of daily

demand Overtime first

Constant -

2b Subcontract first -

3a Average value of daily

demand Overtime first

Constant -

3b Subcontract first -

4 Maximum value of daily

demand - Constant -

5a Average value of

number of workers used

in case 3 and case 4

Overtime first

Constant

-

5b Subcontract first -

6a Previous period’s

demand

Overtime first Varies Yes

6b Subcontract first

7 Current period’s

demand - Varies Yes

The regular production rate for case 1 is based on the fixed number of workers as given above.

Similarly, the production rate varies from case to case. Further demand is satisfied by overtime

followed by subcontracting for cases ‘a’, where as it is vice versa for cases ‘b’. Workforce size is

constant for cases 1a-5b. It varies for cases 6a-7 which gives rise to hiring and layoff .

All the plans are developed using the strategies/cases as discussed above. The overall production

costs are calculated for each plan and are summarized in the tabulated form as shown in Figure

3.11.

34

Figure 3.11: Overall production costs

A graph is plotted to see the range of costs for all these plans. Further, the results can be analyzed

by performing a sensitivity analysis on controllable variables like number of labor hours per unit,

limit on overtime production, subcontracting, inventory capacity, number of fixed workers, costs

for different types of labor, shortage costs, idle time costs, etc.

3.5 Conclusion

The program is developed by using the above methodology. It addresses various issues the

production planner is likely to encounter in real-time scenarios. This program can be used by all

levels of management dealing with production planning because of its user friendliness. It will

give them the flexibility to play with various input variables and strategies developed so that they

could choose an optimal strategy.

35

Chapter 4

Results and Discussions

4.1 Problem Description

Based on the above mentioned methodology, the program is developed with two different phases.

A specific problem is taken from the book “Operations management” by Jay Heizer and Barry

Render. Based on the data given in the problem, each case’s total production cost is estimated. The

problem is described below:-

The Sales and Operation at Kansas Furniture has received the following estimates of demand

requirements.

Month July August September October November December

Demand 1,000 1,200 1,400 1,800 1,800 1,800

Production

days 22 18 21 21 22 20

Assuming the stock out costs for lost sales of $100 per unit, inventory carrying costs of $25 per

unit per month, 300 units of beginning and zero units of ending inventory. Additional units are

produced by either subcontracting at $60 per unit premium cost, or hiring additional workers at

$30 per unit and cost of laying off is $60 per unit cut back, or permitting a maximum of 20%

overtime at a premium of $40 per unit. The firm produced 1,300 units in June. Assuming that

warehouse limitations permit no more than a 180-unit carryover from month to month. Any time

inventories reach 180, the plant is kept idle. Idle time per unit is $60. Assuming the labor hours

per unit produced is 1.6 and number of fixed workers to be 12. The number of working hours per

day is 8.

36

4.2 Phase- 1

Firstly, the daily demand is calculated according to the equation discussed in the previous chapter.

It is the value of demand over number of production days in that period. Table 4.1gives the values

of the daily demand.

Table 4.1: Given data

Period Production days Demand (D) Daily Demand (=D/days)

1 22 1,000 45.45

2 18 1,200 66.67

3 21 1,400 66.67

4 21 1,800 85.71

5 22 1,800 81.82

6 20 1,800 90.00

Total 124 9,000 436.32

After the daily demand is calculated, production rate is decided for each case as discussed in

previous chapter.

Let us take an example of a case which uses minimum value of the daily demand as the production

rate. The minimum value that can be found from the table 4.1 is 45.45. Regular production is the

product of production rate and number of production days. Since the beginning inventory has 300

units, the demand is satisfied by using this completely. The excess demand is satisfied by overtime

followed by subcontracting as cost for overtime is less than subcontracting. The excess production

is stored in inventory which can hold up to a maximum of 180 units. All the excess units are

scrapped or the machines are kept idle. If the demand cannot be satisfied with the production, this

will give rise to stock out costs. Table 4.2 summarizes all the values discussed above. This uses a

chase strategy with constant workforce size.

37

Production rate (R) = 45.45

Table 4.2: Chase Strategy with constant workforce size

Period Demand

(D)

Production

days

Regular

Production

(RP= R *

Days)

Beginning

Inventory

(BI)

Production

needed**

(D–RP–BI)

Overtime

Production***

(OP= D-RP-

BI)

Subcontract

Production

(SP= D-RP-

BI-OP)

Shortage

(S=D-RP-

BI-OP-

SP)

Ending

Inventory

****

(EI=BI+R

P+OP+SP

-D)

Idle time

(IT=RP+

BI-D-EI)

1 1,000 22 1,000 300 0 0 0 0 180 120

2 1,200 18 818 180 202 202 0 0 0 0

3 1,400 21 954 0 446 280 166 0 0 0

4 1,800 21 954 0 846 360 486 0 0 0

5 1,800 22 1,000 0 800 360 440 0 0 0

6 1,800 20 909 0 891 360 531 0 0 0

Total 9,000 124 5,635 480 3,185 1,562 1,623 0 180 120

** The value is always greater than or equal to zero.

*** If the production needed exceeds zero, overtime comes into effect. It is permitted up to 20% of the demand.

**** It is limited to 180. Excess is discarded or plant is kept idle.

38

Also, let us take an example of a case which uses a chase strategy with varying workforce size.

The regular production for the current period is the demand for previous period. Since it uses

previous period’s demand, the values of forecasting for June are given. The following month’s

units are estimated based on the June’s month forecast. Since the beginning inventory has 300

units, the demand is satisfied by using this completely. The excess demand is satisfied by overtime

followed by subcontracting as cost for overtime is less than subcontracting. The excess production

is stored in inventory which can hold up to a maximum of 180 units. All the excess units are

scrapped or the machines are kept idle. If the demand cannot be satisfied with the production, this

will give rise to stock out costs. All these are tabulated in table 4.3.

39

Production rate (R) = Previous period’s demand

Table 4.3: Chase Strategy with varying workforce size

Period Demand

(Di)

Regular

Production

(RPi= Di-1)

Beginning

Inventory

(BIi)

Production

needed**

(D–RP–BI)i

Overtime

Production***

(OP= D-RP-BI)i

Subcontract

Production

(SP= D-RP-

BI-OP)i

Shortage

(S=D-RP-

BI-OP-SP)i

Ending

Inventory****

(EI=BI+RP+OP+

SP-D)i

Idle time

(IT=RP+BI-

D-EI)i

0 1,300

1 1,000 1,300 300 0 0 0 0 180 420

2 1,200 1,000 180 20 20 0 0 0 0

3 1,400 1,200 0 200 200 0 0 0 0

4 1,800 1,400 0 400 360 40 0 0 0

5 1,800 1,800 0 0 0 0 0 0 0

6 1,800 1,800 0 0 0 0 0 0 0

Total 10,300 8,500 480 620 580 40 0 180 420

** The value is always greater than or equal to zero.

*** If the production needed exceeds zero, overtime comes into effect. It is permitted up to 20% of the demand.

**** It is limited to 180. Excess is discarded or plant is kept idle.

40

The regular production in table 4.3 is maintained by hiring or laying off additional workers. The

number of additional units required by hiring or additional units laid off are given in table 4.4. It

also includes the number of additional workers hired or laid off to produce the required number of

units.

Number of labor hours/ production unit is taken as 1.6 (LH).

Number of working hours/day is taken as 8 (WH).

Table 4.4: Estimation of workers

Period Production

days

Regular

Production

(RP)

Number of

workers (W =

RP*LH

/(WH*days))

Hiring

(workers)

Layoff

(workers)

Hiring (units)

(= extra

workers*days*

WH/LH)

Layoff

(units)

1 22 1,300 12 0 0 0 0

2 18 1,000 11 0 1 0 90

3 21 1,200 11 0 0 0 0

4 21 1,400 13 2 0 210 0

5 22 1,800 16 3 0 330 0

6 20 1,800 18 2 0 200 0

Total 124 8,500 81 7 1 740 90

Similarly, all the case’s units like regular, overtime, subcontracting etc., are estimated and

tabulated as shown in Table 4.5. Companies always try to satisfy the requirements, so there might

not be any stock out units. There are no additional hiring and lay off units as the first five cases

use a chase strategy with constant workforce size. Table 4.5 gives the breakdown of all types of

units. It can be seen that case 4 has the highest number of idle time units which can be explained

by the value of the daily rate it uses.

41

Table 4.5: Breakdown of production units

Case

Production units Inventory units Shortage

units

Idle

time

units

Number

of

workers Regular Overtime Subcontract Hiring Layoff Beginning Ending

1a 7,440

1,160 540 0 0 540 240 0 440 72

1b 0 1,700

2a 5,635

1,562 1,623 0 0 480 180 0 120 54

2b 377 2,808

3a 9,000

647 0 0 0 840 540 0 947 90

3b 0 647

4 11,160 0 0 0 0 1,200 1,080 0 2,280 108

5a 7,440

1,160 540 0 0 540 240 0 440 72

5b 0 1,700

6a 8,500

580 40 740 90 480 180 0 420 81

6b 0 620

7 9,000 0 0 980 110 1,200 1,080 0 120 86

42

The various types of costs incurred due to regular, overtime and subcontracting production,

inventory, shortage and idle time are estimated and tabulated as shown in Table 4.6. It can be seen

that there are no stock out costs as companies always try to satisfy the demand requirements. There

are no additional hiring and lay off costs as the first five cases use a chase strategy with constant

workforce size but the last two cases have these costs because they use a chase strategy with

varying workforce size. Table 4.6 gives the breakdown of all types of costs. It can be seen that

case 7 has the lowest production cost followed by case 6a. The overall costs for case 1a and case

5a are about the same. The highest cost is 65% more than lowest one.

43

Table 4.6: Breakdown of overall production costs

Case

Production Costs ($) Holding

Costs, HC

($)

Shortage

Costs ($)

Idle time

Costs, IC

($)

Total

Costs ($) Regular

(RC)

Overtime

(OC)

Subcontract

(SC) Hiring Layoff

1a

148,800 46,400 32,400

0 0 6,000 0 26,400 260,000

1b 0 102,000 283,200

2a 112,700

62,480 97,380

0 0 4,500 0 7,200 284,260

2b 15,080 168,480 307,960

3a 180,000

25,880 0

0 0 13,500 0 56,820 276,200

3b 0 38,820 289,140

4 223,200 0 0 0 0 27,000 0 136,800 387,000

5a 148,800

46,400 32,400

0 0 6,000 0 26,400 260,000

5b 0 102,000 283,200

6a 170,000

23,200 2,400 22,200 5,400 4,500 0 25,200

252,900

6b 0 37,200 264,500

7 180,000 0 0 29,400 6,600 27,000 0 7,200 250,200

44

A graph is plotted with strategies against overall production costs which is shown in Figure 4.1. It

shows that the least cost is observed for case 7 and the highest cost is for case 4. All other costs

for this specific problem taken from the book has values in the range 240,000 and 320,000 except

for case 4.

Figure 4.1: Overall Production Costs vs. Cases

All these cases are arranged in an ascending order of overall production costs to see which are

among the lowest and highest ranked. These are shown in table 4.7. As we can see, case 7 using a

chase strategy with varying workforce size has the least cost. Case 6a, which also uses a chase

strategy with varying workforce size, is the second least. Case 1a and 5a both are of the same cost

which bases its production on fixed number of workers and average number of workers. The costs

for cases 3b, 2b and 4 which use average, minimum and maximum rate of production stand high

among all the other types of strategies followed.

1a

1b 2a

2b

3a3b

4

5a

5b

6a6b

7

$200,000

$240,000

$280,000

$320,000

$360,000

$400,000

1a 1b 2a 2b 3a 3b 4 5a 5b 6a 6b 7

Tota

l Pro

du

ctio

n C

ost

s

Cases

Phase 1- Basic Total Cost

45

Table 4.7: Ranking

Cases Production Costs ($) Rank

1a 260,000 3.5

1b 283,200 7.5

2a 284,260 9

2b 307,960 11

3a 276,200 6

3b 289,140 10

4 387,000 12

5a 260,000 3.5

5b 283,200 7.5

6a 252,900 2

6b 264,500 5

7 250,200 1

4.3 Sensitivity Analysis

In phase 1 of the problem, the entire horizon period uses a constant strategy. Input variables are

changed ± 5% to ± 20% to see which has the most effect on the overall production costs and also

the ranking. All the graphs are plotted against production costs with the variables, which are most

effective, on the horizontal axis. For simplicity, the variables and the combination of two variables

are taken into consideration.

In Figure 4.2, a graph is plotted for labor hours per production unit vs. overall costs. Irrespective

of the number of labor hours per production unit, the costs for cases 2a, 2b, 3a, 3b, and 4 turn out

to be constant, so these are not shown in the graph for simplicity. But the other case’s costs are

effected by varying it from -5% to +20% as shown.

46

Figure 4.2: Labor hours

In the Figure 4.3 below, a graph is plotted for the combination of labor hours per production unit

and number of fixed workers against overall costs. It is found out that, by varying the labor hours

per production unit along with the number of fixed workers has no effect on the cases 1a, 1b, 2a,

3a, 3b and 4, so these are not shown in the graph for simplicity. All the other cases were effected

by changing this combination of variables.

Figure 4.3: Labor hours and No. of fixed workers

230,000

240,000

250,000

260,000

270,000

280,000

290,000

300,000

310,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Labor hours per production unit

1a 1b 5a 5b 6a 6b 7

230,000

240,000

250,000

260,000

270,000

280,000

290,000

300,000

310,000

320,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Labor hours per production unit and No. of fixed workers

2b 5a 5b 6a 6b 7

47

In the Figure 4.4, number of fixed workers and overtime costs are varied simultaneously and a

graph is plotted against overall costs. It is found out that the cases 3b, 4, 5b, 6b, and 7 are not at

all effected by varying this combination of input variables, so these are not shown in the graph for

simplicity.

Figure 4.4: No. of fixed workers and overtime costs

Figure 4.5 shows that the demand is directly proportional to the production costs. A steady increase

or decrease is observed in the graph as the demand is increased or decreased respectively.

Figure 4.5: Demand

240,000

250,000

260,000

270,000

280,000

290,000

300,000

310,000

320,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

No. of fixed workers and Overtime Cost

1a 1b 2a 2b 3a 5a 6a

200,000

250,000

300,000

350,000

400,000

450,000

500,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Demand1a 1b 2a 2b 3a 3b

4 5a 5b 6a 6b 7

48

A graph is plotted for the combination of labor hours per production unit and demand against

overall costs in the Figure 4.6. Cases 3a, 3b, 4, 5a, and 6a increased steadily by increasing this

variable combination and vice versa.

Figure 4.6: Labor hours and Demand

In the Figure 4.7 below, a graph is plotted for the combination of demand and subcontract cost

against overall costs. The costs for cases 2a, 3a, 3b, 4, 5a, and 5b are directly proportional to this

combination.

Figure 4.7: Demand and subcontract cost

200,000

250,000

300,000

350,000

400,000

450,000

500,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Labor hours per production unit and Demand1a 1b 2a 2b 3a 3b

4 5a 5b 6a 6b 7

200,000

250,000

300,000

350,000

400,000

450,000

500,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Demand and Subcontract Cost1a 1b 2a 2b 3a 3b

4 5a 5b 6a 6b 7

49

The next combination is demand and number of fixed workers against overall costs as shown in

Figure 4.8. The costs for the cases 1b, 3a, 3b, 4, 5a are directly proportional whereas the remaining

cases are exponential to the variable combination.

Figure 4.8: Demand and No. of fixed workers

The effect of varying overtime and idle time costs are very minimal for all the cases except case

4. A gradual increase can be observed by increasing the combination and vice versa in Figure 4.9

Figure 4.9: Overtime and Idle time costs

200,000

250,000

300,000

350,000

400,000

450,000

500,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Demand and No. of fixed workers1a 1b 2a 2b 3a 3b

4 5a 5b 6a 6b 7

240,000

260,000

280,000

300,000

320,000

340,000

360,000

380,000

400,000

420,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Overtime Cost and Idle time Cost1a 1b 2a 2b 3a 3b

4 5a 5b 6a 6b 7

50

Varying the subcontract cost as shown in Figure 4.10 has no effect on cases 3a, 4, 6a and 7, so

these are not shown in the graph for simplicity. Case 2b is effected most and all the remaining

cases have a minimal effect.

Figure 4.10: Subcontract Cost

When subcontract cost along with the number of fixed workers are varied as shown in Figure 4.11,

the cost for cases 3a, 4, 6a and 7 are not affected, so these are not shown in the graph for simplicity.

All other cases have a minimal effect except case 2b.

Figure 4.11: No. of fixed workers and subcontract cost

240,000

260,000

280,000

300,000

320,000

340,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Subcontract Cost

1a 1b 2a 2b 3b 5a 5b 6b

240,000

260,000

280,000

300,000

320,000

340,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

No. of fixed workers and Subcontract Cost1a 1b 2a 2b

3b 5a 5b 6b

51

When subcontract cost along with idle time cost are varied as shown in Figure 4.12, the cost for

all the cases increase. A steady increase is found for case 2a, 3b, 4, and 5b.

Figure 4.12: Subcontract cost and idle time Cost

For convenience, number of fixed workers is abbreviated as FW. Demand as D, Labor hours as

LH, Subcontract cost as SC, Overtime cost as OC, Idle time cost as IC.

From Figures 4.2-4.12, it can be observed that Demand alone, also when combined with other

variables like labor hours per unit production and number of fixed workers had an effect on the

overall production costs. Idle time costs when combined with overtime and subcontracting costs

also effected the production costs for all the cases. These are summarized in the table 4.8.

240,000

260,000

280,000

300,000

320,000

340,000

360,000

380,000

400,000

420,000

440,000

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Co

sts

Subcontract Cost and Idle time Cost

1a 1b 2a 2b 3a 3b

4 5a 5b 6a 6b 7

52

Table 4.8: Sensitivity Analysis

Cases LH D SC LH+D LH+FW D+FW D+SC FW+OC FW+SC OC+IC SC+IC

1a

1b

2a

2b

3a

3b

4

5a

5b

6a

6b

7

After the sensitivity analysis is performed, cases are ranked based on the ascending order of the

overall production costs. Input variables with significant percentage change are taken into

consideration. For example, 5% increase in labor hours per production unit changed the ranking

of the case as shown in table 4.9. Similarly, other variable percent changes are summarized below.

53

Table 4.9: Ranking after Sensitivity Analysis

Cases Basic

Variations in input variables up to ± 5% to ± 20%

LH

(+5%)

D

(+5%)

SC

(+10%)

LH+D

(-5%)

LH+FW

(+10%)

D+FW

(-15%)

D+SC

(-20%)

FW+OC

(-15%)

FW+SC

(+10%)

OC+IC

(-15%)

SC+IC

(-15%)

1a 3.5 4 5 3.5 2 3 2 8 5 3 2.5 3.5

1b 7.5 8 9 8.5 5 7 5 9 10 7 8.5 6.5

2a 9 7 8 10 8 8 6 4 7 10 7 9

2b 11 11 11 11 11 11 11 5 11 11 11 11

3a 6 6 6 6 6 6 4 6 6 6 6 8

3b 10 9 10 7 9 10 9 7 9 8 10 10

4 12 12 12 12 12 12 12 12 12 12 12 12

5a 3.5 5 4 3.5 7 4 3 1 3 4 2.5 3.5

5b 7.5 10 7 8.5 10 9 7 3 8 9 8.5 6.5

6a 2 1 1 2 3 2 8 10 1 2 1 1

6b 5 3 3 5 4 5 10 11 4 5 5 5

7 1 2 2 1 1 1 1 2 2 1 4 2

54

4.4 Phase- 2

This phase involves a case with different strategies throughout the entire horizon. A program is

developed in such a way that the operations manager is given a flexibility to use a different strategy

during each period based on his understanding of aggregate planning production variables. Trial

and error method is used to come up with combinations in such a way that the total cost is less

than the least value obtained in case 1. Table 4.10 summarizes few combinations with values less

than the one obtained in phase 1.

Table 4.10: Results from phase 2

Period Case

1 7 7 7 7 2a

2 7 6a 6b 5a 5a

3 7 7 7 5b 7

4 7 6a 6a 4 6a

5 7 7 5a 4 4

6 7 6a 6b 7 6a

Total cost

($) 250,200 224,900 246,000 241,850 238,250

The following table 4.11 summarizes all the production units and the corresponding costs with

different cases for the six period planning horizon. For example, consider cases 2a, 5a, 7, 6a, 4 and

6a are used in the six period plan as shown in the last column as given in table 4.10.

55

Table 4.11: Plan with different Strategies throughout the horizon

Period Case Demand

(D)

Production

Beginning

Inventory

(BI)

Production Ending

Inventory****

(EI=BI+RP+OP

+SP-D)

Idle time

(IT=RP+B

I-D-EI)

Days Rate Regular

(RP)

Needed**

(D–RP–

BI)

Overtime***

(OP= D-RP-

BI)

Subcontract

(SP= D-RP-

BI-OP)

1 2a 1,000 22 45.45 1,000 300 0 0 0 180 120

2 5a 1,200 18 60 1,080 180 0 0 0 60 0

3 7 1,400 21 66.67 1,400 60 0 0 0 60 0

4 6a 1,800 21 66.67 1,400 60 340 340 0 0 0

5 4 1,800 22 90 1,980 0 0 0 0 180 0

6 6a 1,800 20 81.82 1,800 180 0 0 0 180 0

Total 9,000 124 8,660 780 340 340 0 660 120

Costs($) 173,200 13,600 16,500 7,200

** The value is always greater than or equal to zero.

*** If the production needed exceeds zero, overtime comes into effect. It is permitted up to 20% of the demand.

**** It is limited to 180. Excess is discarded or plant is kept idle.

56

Table 4.12 summarizes the number of workers used for the planning horizon discussed above.

Also, it includes the additional number of units or workers hired and laid off.

Number of labor hours/ production unit is taken as 1.6 (LH).

Number of working hours/day is taken as 8 (WH).

Table 4.12: Estimation of workers for mixed strategy

Period Production

days

Regular

Production

(RP)

Number of

workers (W =

RP*LH

/(WH*days))

Hiring

(workers)

Layoff

(workers)

Hiring (units)

(= extra

workers*days*

WH/LH)

Layoff

(units)

1 22 1,000 9 0 0 0 0

2 18 1,080 12 3 0 270 0

3 21 1,400 13 1 0 105 0

4 21 1,400 13 0 0 0 0

5 22 1,980 18 5 0 550 0

6 20 1,800 18 0 0 0 0

Total 124 8,660 83 9 0 925 0

57

Chapter 5

Conclusion and Future Work

5.1 Conclusion

The Excel program for two phases are developed for the specific problem given in the book and

sensitivity analysis is performed as discussed in the previous chapter. In the first phase, twelve

cases were developed with a combination of chase and level strategies. Sensitivity analysis was

performed on the input variables. The least cost was obtained for case 7 which used a chase strategy

with varying workforce size. The results are summarized in the table 5.1.

Table 5.1 Phase 1 Results

Cases Overall Production Costs ($) Order

7 250,200 1

6a 252,900 2

1a 260,000 3.5

5a 260,000 3.5

6b 264,500 5

3a 276,200 6

1b 283,200 7.5

5b 283,200 7.5

2a 284,260 9

3b 289,140 10

2b 307,960 11

4 387,000 12

Sensitivity analysis is performed for all the input variables. The variables which have a significant

effect on overall costs are labor hours per production unit, demand, subcontract cost, labor hours

along with fixed number of workers, demand along with fixed number of workers and subcontract

cost, fixed number of workers along with overtime cost and subcontract cost, idle time cost along

58

with subcontract cost and overtime cost. The effect of variables in the descending order are given

below,

Demand Demand +

Fixed Workers

Demand +

Labor Hours

Demand +

Subcontract Cost

Idle time Cost +

Overtime Cost

Idle time Cost +

Subcontract Cost

Subcontract Cost Subcontract Cost + Fixed Workers

Labor Hours Fixed Workers + Overtime Cost

Labor Hours + Fixed Workers

Phase 2 uses different strategies throughout the entire horizon. By trial and error method few

combinations are listed below in such a way that these costs are less than the least cost obtained in

phase 1.

Table 5.2: Results from phase 2

Period Case

1 7 7 7 7 2a

2 7 6a 6b 5a 5a

3 7 7 7 5b 7

4 7 6a 6a 4 6a

5 7 7 5a 4 4

6 7 6a 6b 7 6a

Total cost

($) 250,200 224,900 246,000 241,850 238,250

59

5.2 Future Work

The Excel program developed can help an operations manager to deal with aggregate production

planning in developing a plan for the horizon period. Because of its simplicity, the lower levels of

management can also access this program based on their experience with production planning.

This program gives different types of plans with different strategies which may not guarantee an

optimal cost. Further research can be done to obtain optimal costs.

Several other variables which might affect the overall production costs can be taken into

consideration. Electricity can be included as a parameter as energy consumption is directly

proportional to amount of production. Further the peak electrical demand can be reduced by

producing in off-peak season which reduces large penalties and electrical demand charges. Also,

the peak production demand can be reduced by the shifting a part of it to subcontracting.

As the input variables are deterministic in the program developed, further research can be done to

include the potential for stochastic variability of input variables which can be represented in terms

of confidence interval.

Several mathematical techniques can be used to arrive at the most desirable plan in order to

minimize the overall production costs. Demand forecast plays an important role in aggregate

production planning. It has a strong need when a demand pattern is highly seasonal. As the plan is

based on the demand forecast, changes in forecasting methodology can have several effects on the

plan. This program can be extended to multiproduct type as this was developed for a single product.

Multiproduct makes it very complex but it’s quite helpful in the real time scenario.

60

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