CHAPTER THIRTEEN INVENTORY MANAGEMENT Chapter 13 Inventory Management.

CHAPTER THIRTEENINVENTORY MANAGEMENT

Chapter 13

Inventory Management


MTSU Management 362 13-2

Independent Demand(Chapter 13)

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand(Chapter 14)

Independent demand is uncertain. Dependent demand is certain.



Types of Inventories (1 of 2)

• Raw materials & purchased parts

• Partially completed goods called work in progress

• Finished-goods inventories

– (manufacturing firms) or merchandise (retail stores)



Types of Inventories (2 of 2)

• Replacement parts, tools, & supplies

• Goods-in-transit (pipeline) to warehouses or customers



Supplier – Production – Distribution SystemSupplier Distribution

Inventories

Raw materialin-transit

Sub-assemblyparts in-transit

Maintenance,repair, and operating

supplies in-transit

Raw MaterialInventory

Work-in-processInventory

FactoryFinishedGoods

InventoryComponentInventory

MROInventory

Purchasing

Production andInventory Control

Shipping andTraffic

RetailerInventory

Orders

WarehouseInventory

Production Inventories

Customer DistributionInventories

Orders

Supplier



Functions of Inventory

• Meet anticipated demand• Smooth production requirements• Decouple components (areas) of the production-

distribution• Protect against stock-outs• Take advantage of order cycles• Help hedge against price increases or to take

advantage of quantity discounts• Permit operations (operation lead time)



Concerns of Inventory Control• Level of customer service

– have the right goods, in sufficient quantities, in the right place, at the right time

– in other words, the customer gets what ever he/she wants when he/she wants it

• Inventory-related costs – ordering costs– carrying costs



Objectives of Inventory Management (1 of 2)

• Achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds

• Two fundamental decisions

– how much to order

– when to place the order



• Possible performance measures

– customer satisfaction• number of backorders/lost sales• number of customer complaints

– inventory turnover• ratio of annual cost of goods sold to average inventory

investment

– days of inventory• expected number of days of sales that can be supplied

from existing inventory

Objectives of Inventory Management (2 of 2)



Requirements forEffective Inventory Management

• A system to keep track of the inventory on hand and on order

• A classification system for inventory items• A reliable forecast of demand that includes an

measure of forecast error• Reasonable estimates of inventory holding costs,

ordering costs, and shortage costs• Knowledge of lead times and lead time variability



Inventory Counting Systems (1 of 2)

• Perpetual Inventory (Continual) System

– Keeps track of removals from and receipts into inventory continuously

• Cycle counting - taking physical counts of items and reconciling

with records on a continual

rotating basis



0

214800 232087768

Inventory Counting Systems (2 of 2)

• Universal Product Code - Bar code printed on a label that hasinformation about the item to which it is attached

• Periodic System

– Physical count of items made at periodic intervals



ABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly

AA - very important

BB - mod. important

CC - least important

Figure 13-1

Annual $ volume of items

AA

BB

CC

High

Low

Few ManyNumber of Items



Demand Forecast andLead Time Information

• Reliable estimates of the amount and timing of demand

• Lead time - time interval between ordering and receiving the order

• Extent of variability in demand and lead time



The Typical Procurement Cycle

Internal Order CycleOrder Request/RequisitionAuthorization signatures obtainedVerification by inventory controlPurchasing researches vendors, obtains quotes, etc.Order transferred to vendor

Internal Order CycleOrder Request/RequisitionAuthorization signatures obtainedVerification by inventory controlPurchasing researches vendors, obtains quotes, etc.Order transferred to vendor

Vendor CycleReceives and enters orderManufactures or “picks” orderShips order

Vendor CycleReceives and enters orderManufactures or “picks” orderShips order

Internal Receiving CycleReceivingIncoming inspectionInventory control receives order, updates records, and notifies department

Internal Receiving CycleReceivingIncoming inspectionInventory control receives order, updates records, and notifies department



Cost Information• Holding or carrying costs

• Ordering costs



Holding or Carrying Costs• Cost to carry a unit in inventory for a

length of time

• Includes interest (opportunity cost), insurance, taxes, depreciation, obsolescence, deterioration

• May be expressed as a percentage of unit price or as a dollar amount per unit



Ordering Costs• Cost of ordering and receiving inventory

• Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality

• Generally expressed as a fixed dollar amount, regardless of order size



Shortage Costs• Result when demand exceeds the inventory

on hand

• Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime

• Difficult to measure, thus may have be subjectively estimated



Basic Systems for Independent Demand• Fixed-order-quantity systems

– basic economic order quantity (EOQ) model [purchasing model]

– basic economic order quantity model with incremental or noninstantaneous replenishment [production order quantity]

– quantity discount model• Fixed-order-interval systems



Only one product is involvedAnnual demand requirements are knownDemand is spread evenly throughout the year

so that the demand rate is reasonable constantLead time does not varyEach order is received in a single deliveryThere are no quantity discounts, i.e., the price

is constant

Basic EOQ ModelAssumptions



How the Basic Fixed-Order-Quantity Model Works

Profile of Inventory Level Over Time

Quantityon hand

Time

Figure 13-2



Total Annual Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

Q2

H DQ

STC = +



Cost Minimization Goal

Order Quantity (Q)

An

nu

al C

os

tFigure 13-4



Minimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Alternatively we can use calculus by taking the first derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Q = 2DS

H =

2(Annual Demand )(Order or Setup Cost )

Annual Holding CostOPT



Basic Fixed Order Quantity ModelWith Incremental Replenishment

• Used to determine the order size, production lot, if an item is produced at one stage of production and then sent to the next stage or the customer

• Differs from the basic model because orders are assumed to be supplied or produced at a uniform rate (p) rather than the order being received all at once





Quantityon hand

Q

Start toreceive order

Placeorder


Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

TimeFinishreceiving order

Production rate- usage rate





Quantityon hand

Q


Placeorder


Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

TimeFinishreceiving order

Production rate- usage rate




• It is also assumed that the supply rate, p, is greater than the usage rate, u

• Figure 13-6, page 573, shows the difference between the basic EOQ model and this model

• The change in maximum inventory level requires modification of the TC equation

SQ

D H

p

u-p

2

Q TC

O

O




• The optimization results in

u-p

p

H

2DS QO



Quantity Discount Model (1 of 4)

• This model differs from the basic model because the price per unit (P) may vary with the quantity ordered

• The supplier offers a lower unit price if larger quantities are ordered at one time

• This is presented as a price or discount schedule, i.e., a certain unit price covers a certain order quantity range



Quantity Discount (2 of 4)

• Under this condition, annual product cost becomes an incremental cost and must be considered in the determination of the EOQ

• The total annual costs (TC) = Annual holding cost + annual setup cost + annual product cost

TC = (Q/2)H + (D/Q)S + DP



Costs FunctionsUnder Quantity Discount

Order Quantity

$ co

st




To find the EOQ, the following procedure is used

Compute the basic EOQ using the lowest unit price and H=IP where I is an interest rate. If the resulting EOQ is feasible, i.e., that quantity can be purchased at the price used, it is optimal. Otherwise, go on to Step 2




Using the EOQ from Step 1 and the discount schedule, find the price that should have been used and compute a new EOQ using this price. This new EOQ should be feasible.

Compute the TC for the EOQ found in Step 2Compute the TC for all quantities greater than

Step 2’s EOQ where a discount begins. Select the quantity with the lowest TC as the EOQ



Basis for Setting the Reorder Point

• In the fixed quantity system, the ordering process is triggered when the inventory level drops to a critical point, the reorder point (ROP)

• This starts all activities associated with placing, filling and receiving the order, or the lead time for the item




• During the lead time, customers continue to draw down the inventory level

• It is during this period that the inventory is vulnerable to stockout (run out of inventory)

• When the demand during the lead time is not known or not constant, a certain amount of inventory above the average or expected demand is carried; this is safety stock


MTSU Management 362 13-38LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Reorder Point




• Determinants of the reorder point

– The rate and distribution of demand

– The distribution of lead time

– The degree of stockout risk acceptable to management, customer service level

• Reorder point (ROP) = Expected demand during lead time + safety stock




• Customer service level

– order cycle service level is the probability that demand will not exceed supply during the lead time

– annual service level is the percentage of demand filled directly from inventory


MTSU Management 362 13-41LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Reorder Point



Lead Time Demand

ROP

Place order

safetystock

Distribution oflead time demand

Service level

Risk of shortageDistributions of daily demand with mean of and a standard deviation ofd d



ROP

Risk ofa stockout

Service level

Probability ofno stockout

Mean or expected demand =

Safetystock

0 z

Quantity

z-scale

Figure 13-13

Distribution of Lead Time Demand

LT dStandard deviation = dLT



ROP = +

Risk ofa stockout

Service level

Probability ofno stockout

Mean or expected demand =

Safetystock

Quantity

Distribution of Lead Time Demand

LT dStandard deviation = dLT

LT d dLTz



Administration of the System• Using the perpetual counting system, a signal is given when

the records indicate that the inventory reaches the ROP

• Using the periodic counting system, a two-bin system could be used– two bins of inventory

– bin A holds an amount equal to the reorder point

– bin B holds the remainder of the order

– customers are supplied out of bin B

– when bin B is empty, it is time to reorder

– customers are then supplied out of bin A until the order arrives


Fixed-Order-Interval Model



Basic Fixed-Order-Interval SystemInventory Level Over Time

Time

Inve

nto

ry L

evel

Target Maximum

Minimum Inventory

OrderQuantity

OI

OrderQuantity

OrderQuantity

OrderQuantity

OI OI OI

When to order

How muchto order



Operation of Fixed-Order-Interval Systems• As demand for the inventoried item occurs, the

inventory level drops• When a prescribed period of time has elapsed,

the ordering process is triggered, i.e., the time between orders is fixed or constant

• At that time the order quantity is determined using order quantity = target maximum level - current inventory level



• After the lead time elapses, the ordered quantity is received, and the inventory level increases

• The maximum inventory level is expected demand during protection interval + safety stock, or

Operation of Fixed-Order-Interval Systems

LTOIz LTOId d



Administration of the System• Using the periodic counting system, the

inventory is reviewed (counted) at the end of each order interval

• Using the perpetual counting system, an item’s inventory level is checked in the inventory at the end of each order internal



Reasons to Use

• Supplier’s policy might encourage use

• Some situations do not lend themselves to continuous monitoring

• Used where it is desirable to physically count inventory each time an order is placed



Benefits/Advantages• Benefits

– results in tight control needed for A items in a A-B-C classification

– grouping ordering to one supplier may result in savings

• Disadvantages– larger amount of safety stock needed for the

same service level– cost of periodic reviews


Single-Period Model



Single-Period Model• Used to handle ordering of perishables

and items with a limited useful life

• Focuses on two costs

– shortage cost - unrealized profit per unit = revenue per unit minus cost per unit

– excess cost - purchase cost minus salvage value

sC

eC



Optimal Stocking Level

In the case where the distribution of demand is continuous, find the order quantity that provides the area under the distribution and to the left equal to the optimal service level

In the case where the distribution of demand is discrete, choose the order quantity so that provides the optimal service level is equaled or exceeded

es

s

C C

C level Service

CHAPTER THIRTEEN INVENTORY MANAGEMENT Chapter 13 Inventory Management.

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