BIZ2121-04 Production & Operations...

BIZ2121-04 Production & Operations Management

Process Capacity

Sung Joo Bae, Assistant Professor

Yonsei University School of Business

Sharp’s Capacity Problem

Planning Capacity Capacity is the maximum rate of output of a process or

system

Without enough capacity, what will happen to the organization? ◦ Missing opportunities

◦ Late response leading to overinvestment

◦ Disrupted cashflow and loosing dominant position in the market

◦ Takes long time to recover from those missing opportunities

◦ Acquisition of new capacity can take some time (e.g. semiconductor, nuclear power plants)

◦ The influence of new product development can be reduced (e.g. Apple’s iPhone)

Planning Capacity Accounting, finance, marketing, operations, purchasing, and human

resources all need capacity information to make decisions

◦ Accounting: provides cost information needed to evaluate expansion decisions

◦ Finance: performs financial analysis of the proposed capacity expansion investment and raises funds to support them

◦ Marketing: provides demand forecast (e.g. airline, cruise ship, IT products)

Capacity planning is done in the long-term and the short-term

◦ Factors related to the long-term decisions Firm’s economies (or diseconomies) of scale

Capacity cushions

Timing and sizing strategies How much of a cushion is needed to handle variable/uncertain demand? (Size of cushion)

Should we expand capacity ahead of demand, or wait until demand is more certain? (Timing)

Supply chain readiness

Planning Capacity

Capacity planning (long-term)

Economies and diseconomies of scale

Capacity timing and sizing strategies

Systematic approach to capacity decisions

Constraint management (short-term)

Identification and management of bottlenecks

Product mix decisions using bottlenecks

Managing constraints in a line process

Capacity management

Measures of Capacity Utilization

Output measures of capacity ◦ Adequate for individual processes within the firm, or the firm

with relatively small number of standardized products and services

◦ With high level of customization and variety in product mix, measuring only output is not very useful

◦ e.g. the number of cars produced per day

Input measures of capacity ◦ Adequate for low volume, flexible processes

◦ e.g. the number of workstations, the number of workers

◦ Input-output conversion is necessary since demand is met by output

Utilization

Utilization = 100% Average output rate

Maximum capacity

Measures of Capacity Utilization

Utilization

◦ The degree to which a resource (equipment, space, or workforce) is currently being used

◦ Too high add extra capacity

◦ Too low eliminate unneeded capacity

◦ A process can be operated above its capacity level

Overtime, extra shifts, temporarily reduced maintenance activities, overstaffing, subcontracting

But these are temporary solutions quality can be affected

Utilization = 100% Average output rate

Maximum capacity

Capacity and Scale

Economies of scale

◦ The average unit cost of a service or good can be

reduced by increasing its output rate

Fixed costs are spread over more units

Some maintenance cost, manager’s salaries, depreciation of plant

and equipment, etc.

Reducing construction costs

Costs are same whether it is small or large facilities: building

permits, architect’s fees, rental fee of building equipment

Cutting costs of purchased materials

Bargaining power and volume discount (Walmart, Toys”R”Us)

Finding process advantages

Shifting to line processes, more specialized equipment, learning

effect, lowering inventory, reducing the number of changeovers, etc.

Capacity and Scale

Diseconomies of scale

◦ Complexity

Communication, organizational structure, organization

of factory floor

◦ Loss of focus

Compared to the smaller, more agile organizations

◦ Inefficiencies

Lots of inefficiencies related to the large production

Increased inventories, transportation within the production

floor, etc.

Capacity and Scale

Figure 6.1 – Economies and Diseconomies of Scale

250-bed hospital

500-bed hospital

750-bed hospital

Output rate (patients per week)

Average unit cost

(dollars per patient)

Economies of scale

Diseconomies of scale

One size doesn’t fit all!

Capacity Timing and Sizing Sizing capacity cushions: Important decisions regarding the

tradeoffs between efficiency and customer satisfaction

Capacity cushions are the amount of reserve capacity a process uses to handle sudden changes

Appropriate cushion varies by industry

◦ Paper industry (capital-intensive): well under 10%

◦ Hotel: 30 to 40% (customer service problems under 20%)

◦ Cruise ship industry: 5%

◦ Demand variability in volume: cushion should be large enough to handle the peak hours otherwise prompt customer service is not possible (e.g. groceries busy during the weekends)

◦ Demand variability in product mix: Workstation shift: problematic if workers are not trained for different stations

Supply uncertainty

◦ Cushions necessary for employee absenteeism, vacations, holidays, etc.

Capacity cushion = 100% – Average Utilization rate (%)

Capacity Timing and Sizing

Decision related to when to adjust

capacity levels and by how much

◦ Expansionist strategy

◦ Wait-and-see strategy

◦ Combination strategy


Planned unused capacity

Time

Cap

acit

y

Forecast of capacity required

Time between increments

Capacity increment

(a) Expansionist strategy: • Economies of scale & learning effect Cost efficiency • Excess capacity with too much cushion at first • Preemptive marketing (Chicken Game in Semiconductor):

:By making large capacity expansion or announcing that one is imminent, the firm can preempt the expansion of other firms

Time

Cap

acit

y

(b) Wait-and-see strategy • Reduced risk of overexpansion • Possibility of preemption or incapability to meet the high demand surge

Planned use of short-term options

(overtime, temporary workers, subcontractors, etc.)

Time between increments

Capacity increment


Forecast of capacity required

Linking Capacity

Capacity decisions should be linked to processes and supply chains throughout the organization

Important issues are competitive priorities, quality, and process design

◦ Higher level of capacity cushion Competitive priorities on fast delivery (competitive priorities)

Higher level of the service quality (quality)

Larger investment in capital intensive equipment or higher level of worker flexibility (process design)

Systematic Approach

1. Estimate future capacity requirements

2. Identify gaps by comparing requirements

with available capacity

3. Develop alternative plans for reducing the

gaps

4. Evaluate each alternative, both qualitatively

and quantitatively, and make a final choice

Systematic Approach

Step 1 is to determine the capacity required to meet future demand using an appropriate planning horizon

Capacity requirement: capacity required for some future time period to meet the demand

◦ Demand forecast, productivity, competition, and technological change in consideration

Output measures based on rates of production

Input measures may be used when

◦ Product variety and process divergence is high

◦ The product or service mix is changing

◦ Productivity rates are expected to change

◦ Significant learning effects are expected

◦ e.g. the number of employees, machines, trucks, etc.

Systematic Approach

For one service or product processed at one

operation with a one year time period, the

capacity requirement, M, is

Capacity requirement

= Processing hours required for year’s demand

Hours available from a single capacity unit (such as an employee or machine) per year,

after deducting desired cushion

M = Dp

N[1 – (C/100)]

where

D = demand forecast for the year (number of customers serviced or units of product)

p = processing time (in hours per customer served or unit produced)

N = total number of hours per year during which the process operates

C = desired capacity cushion (expressed as a percent)

Systematic Approach

Setup (changeover) times may be required if

multiple products are produced

Capacity requiremen

t

=

Processing and setup hours required for year’s demand, summed over all services

or products

Hours available from a single capacity unit per year, after deducting desired cushion

M =

[Dp + (D/Q)s]product 1 + [Dp + (D/Q)s]product 1 + … + [Dp + (D/Q)s]product n

N[1 – (C/100)]

where

Q = number of units in each lot

s = setup time (in hours) per lot

D/Q = number of lots

Estimating Capacity Requirements

EXAMPLE 6.1

A copy center in an office building prepares bound reports for two clients.

The center makes multiple copies (the lot size) of each report. The

processing time to run, collate, and bind each copy depends on, among

other factors, the number of pages. The center operates 250 days per year,

with one 8-hour shift. Management believes that a capacity cushion of 15

percent (beyond the allowance built into time standards) is best. It

currently has three copy machines. Based on the following table of

information, determine how many machines are needed at the copy center.

Item Client X Client Y

Annual demand forecast (copies) 2,000 6,000

Standard processing time (hour/copy) 0.5 0.7

Average lot size (copies per report) 20 30

Standard setup time (hours) 0.25 0.40

Estimating Capacity Requirements SOLUTION

M = [Dp + (D/Q)s]product 1 + [Dp + (D/Q)s]product 1 + … + [Dp + (D/Q)s]product n

N[1 – (C/100)]

= [2,000(0.5) + (2,000/20)(0.25)]client X + [6,000(0.7) + (6,000/30)(0.40)]client Y

[(250 day/year)(1 shift/day)(8 hours/shift)][1.0 - (15/100)]

= = 3.12 5,305

1,700

Rounding up to the next integer gives a requirement of four machines.

Systematic Approach

Step 2 is to identify gaps between projected capacity requirements (M) and current capacity

◦ Complicated by multiple operations and resource inputs

Step 3 is to develop alternatives

Base case is to do nothing and suffer the consequences

Many different alternatives are possible: base case, long-term expansion, short-term remedies

Systematic Approach

Step 4 is to evaluate the alternatives

◦ Qualitative concerns include strategic fit and

various uncertainty (demand, competition,

technological change, cost estimates)

◦ Quantitative concerns may include cash flows and

other quantitative measures

Evaluating the Alternatives EXAMPLE 6.2

A restaurant is experiencing a boom in business. The owner expects to

serve 80,000 meals this year. Although the kitchen is operating at 100

percent capacity, the dining room can handle 105,000 diners per year.

Forecasted demand for the next five years is 90,000 meals for next year,

followed by a 10,000-meal increase in each of the succeeding years. One

alternative is to expand both the kitchen and the dining room now,

bringing their capacities up to 130,000 meals per year. The initial

investment would be $200,000, made at the end of this year (year 0). The

average meal is priced at $10, and the before-tax profit margin is 20

percent. The 20 percent figure was arrived at by determining that, for each

$10 meal, $8 covers variable costs and the remaining $2 goes to pretax

profit.

What are the pretax cash flows from this project for the next five years

compared to those of the base case of doing nothing?

Evaluating the Alternatives SOLUTION

Recall that the base case of doing nothing results in losing all potential

sales beyond 80,000 meals. With the new capacity, the cash flow would

equal the extra meals served by having a 130,000-meal capacity, multiplied

by a profit of $2 per meal. In year 0, the only cash flow is –$200,000 for the

initial investment. In year 1, the 90,000-meal demand will be completely

satisfied by the expanded capacity, so the incremental cash flow is (90,000

– 80,000)($2) = $20,000. For subsequent years, the figures are as follows:

Year 2: Demand = 100,000; Cash flow = (100,000 – 80,000)$2 = $40,000




Evaluating the Alternatives

If the new capacity were smaller than the expected demand in any year, we

would subtract the base case capacity from the new capacity (rather than

the demand). The owner should account for the time value of money,

applying such techniques as the net present value or internal rate of return

methods. For instance, the net present value (NPV) of this project at a

discount rate of 10 percent is calculated here, and equals $13,051.76.

NPV = –200,000 + [(20,000/1.1)] + [40,000/(1.1)2] +

[60,000/(1.1)3] + [80,000/(1.1)4] + [100,000/(1.1)5]

= –$200,000 + $18,181.82 + $33,057.85 + $45,078.89 +

$54,641.07 + $62,092.13

= $13,051.76

Tools for Capacity Planning

Waiting-line models

◦ Useful in high customer-contact processes

Simulation

Can be used when models are too complex for waiting-line analysis

Decision trees

Useful when demand is uncertain and sequential decisions are involved

Decision Trees

1

Low demand [0.40]

High demand [0.60]

Low demand [0.40]

High demand [0.60]

$70,000

$220,000

$40,000

$135,000

$90,000 Don’t expand

Expand

2

Figure 6.4 – A Decision Tree for Capacity Expansion

$135,000

$109,000

$148,000

$148,000

Are schematic models of available alternatives and possible consequences

Are useful with probabilistic events and sequential decisions

Decision Trees

Square nodes represent decisions

Circular nodes represent events

Events leaving a chance node are collectively exhaustive

Conditional payoffs for each possible alternative-event combination shown at the end of each combination

Draw the decision tree from left to right

Calculate expected payoff to solve the decision tree from right to left

Decision Trees

Payoff 1

Payoff 2

Payoff 3

Alternative 3

Alternative 4

Alternative 5

Payoff 1

Payoff 2

Payoff 3

E1 & Probability

E2 & Probability

E3 & Probability

E2 & Probability

E3 & Probability

Payoff 1

Payoff 2

1st decision

1

Possible 2nd decision

2

Decision Trees

= Event node

= Decision node

Ei = Event i

P(Ei) = Probability of event i FIGURE A.4 – A Decision Tree Model

Decision Trees

After drawing a decision tree, we solve it by

working from right to left, calculating the

expected payoff for each of its possible paths

1. For an event node, we multiply the payoff of each event branch by the event’s probability and add these products to get the event node’s expected payoff

2. For a decision node, we pick the alternative that has the best expected payoff

Analyzing a Decision Tree EXAMPLE A.8

A retailer will build a small or a large facility at a new location

Demand can be either small or large, with probabilities estimated to be 0.4 and 0.6, respectively

For a small facility and high demand, not expanding will have a payoff of $223,000 and a payoff of $270,000 with expansion

For a small facility and low demand the payoff is $200,000

For a large facility and low demand, doing nothing has a payoff of $40,000

The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively

For a modest response the payoff is $20,000 and $220,000 if the response is sizable

For a large facility and high demand the payoff is $800,000

Analyzing a Decision Tree

SOLUTION

The decision tree in Figure A.5 shows the event probability and the payoff for each of the seven alternative-event combinations. The first decision is whether to build a small or a large facility. Its node is shown first, to the left, because it is the decision the retailer must make now. The second decision node is reached only if a small facility is built and demand turns out to be high. Finally, the third decision point is reached only if the retailer builds a large facility and demand turns out to be low.

Analyzing a Decision Tree $200

$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2

FIGURE A.5 – Decision Tree for Retailer (in $000)

High demand [0.6]

3

Do nothing

Advertise

Modest response [0.3]

Sizable response [0.7]

1


$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2


High demand [0.6]

3

Do nothing

Advertise



1 0.3 x $20 = $6

0.7 x $220 = $154

$6 + $154 = $160


$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2


High demand [0.6]

3

Do nothing

Advertise



1

$160

$160


$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2


High demand [0.6]

3

Do nothing

Advertise



1

$160

$160

$270


$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2


High demand [0.6]

3

Do nothing

Advertise



1

$160

$160

$270

x 0.4 = $80

x 0.6 = $162

$80 + $162 = $242


$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2


High demand [0.6]

3

Do nothing

Advertise



1

$160

$160

$270

$242

x 0.6 = $480

0.4 x $160 = $64

$544


$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

2


High demand [0.6]

3

Do nothing

Advertise



1

$160

$160

$270

$242

$544

$544

Application A.6

Fletcher (a realist), Cooper (a pessimist), and Wainwright (an optimist) are joint owners in a company. They must decide whether to make Arrows, Barrels, or Wagons. The government is about to issue a policy and recommendation on pioneer travel that depends on whether certain treaties are obtained. The policy is expected to affect demand for the products; however it is impossible at this time to assess the probability of these policy “events.” The following data are available:

a. Draw the decision tree for the Fletcher, Cooper, and Wainwright using the following table

b. What is the expected payoff for the best alternative in the decision tree below?

Alternative

Land routes,

No Treaty

(0.50)

Land Routes,

Treaty Only

(0.30)

Sea routes,

Only (0.20)

Arrows 840,000 440,000 190,000

Barrels 370,000 220,000 670,000

Wagons 25,000 1,150,000 -25,000

Application A.6

Decision Trees

1

Low demand [0.40]

High demand [0.60]

Low demand [0.40]

High demand [0.60]

$70,000

$220,000

$40,000

$135,000

$90,000 Don’t expand

Expand

2

Figure 6.4 – A Decision Tree for Capacity Expansion

$135,000

$109,000

$148,000

$148,000

Solved Problem 1

Solved Problem 2

SOLUTION

Table 6.1 shows the cash inflows and outflows. The year 3 cash flow is

unusual in two respects. First, the cash inflow from sales is $50,000

rather than $60,000. The increase in sales over the base is 25,000

meals (105,000 – 10,000) instead of 30,000 meals (110,000 – 80,000)

because the restaurant’s capacity falls somewhat short of demand.

Second, a cash outflow of $170,000 occurs at the end of year 3, when

the second-stage expansion occurs.

The net cash flow for year 3 is $50,000 – $170,000 = –$120,000.

Solved Problem 2

The base case for Grandmother’s Chicken Restaurant (see Example 6.2) is

to do nothing. The capacity of the kitchen in the base case is 80,000 meals

per year. A capacity alternative for Grandmother’s Chicken Restaurant is a

two-stage expansion. This alternative expands the kitchen at the end of

year 0, raising its capacity from 80,000 meals per year to that of the dining

area (105,000 meals per year). If sales in year 1 and 2 live up to

expectations, the capacities of both the kitchen and the dining room will be

expanded at the end of year 3 to 130,000 meals per year. This upgraded

capacity level should suffice up through year 5. The initial investment would

be $80,000 at the end of year 0 and an additional investment of $170,000

at the end of year 3. The pretax profit is $2 per meal. What are the pretax

cash flows for this alternative through year 5, compared with the base

case?

Solved Problem 2

TABLE 6.1 | CASH FLOWS FOR TWO-STAGE EXPANSION AT GRANDMOTHER’S CHICKEN RESTAURANT

Year

Projected Demand

(meals/yr)

Projected Capacity

(meals/yr)

Calculation of Incremental Cash Flow

Compared to Base Case

(80,000 meals/yr)

Cash Inflow

(outflow)

0 80,000 80,000 Increase kitchen capacity to 105,000 meals = ($80,000)

1 90,000 105,000 90,000 – 80,000 = (10,000 meals)($2/meal) = $20,000

2 100,000 105,000 100,000 – 80,000 = (20,000 meals)($2/meal) = $40,000

3 110,000 105,000 105,000 – 80,000 = (25,000 meals)($2/meal) = $50,000

Increase total capacity to 130,000 meals = ($170,000)

($120,000)

4 120,000 130,000 120,000 – 80,000 = (40,000 meals)($2/meal) = $80,000

5 130,000 130,000 130,000 – 80,000 = (50,000 meals)($2/meal) = $100,000

Solved Problem 2

NPV = –80,000 + (20,000/1.1) + [40,000/(1.1)2] – [120,000/(1.1)3] +

[80,000/(1.1)4] + [100,000/(1.1)5]

= –$80,000 + $18,181.82 + $33,057.85 – $90,157.77 + $54,641.07

+ $62,092.13

= –$2,184.90

For comparison purposes, the NPV of this project at a discount rate of 10 percent is calculated as follows, and equals negative $2,184.90.

On a purely monetary basis, a single-stage expansion seems to be a better alternative than this two-stage expansion. However, other qualitative factors as mentioned earlier must be considered as well.

End of Process Quality Session

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