MD 021 - Management and Operations
Capacity Planning and Decision Theory
§ Measures of capacity
§ Bottlenecks
§ Capacity strategies
§ A systematic approach to capacity decisions
§ Make or Buy Problem
§ Decision Making Under Uncertainty and Risk, Decision Trees
Capacity Planning
Capacity is the maximum rate of output for a facility.
Capacity planning considers questions such as:
· Should we have one large facility or several small ones?
· Should we expand capacity before the demand is there or wait until demand is more certain?
Measuring Capacity
Measurement Type
· Output measure for product focus
· Input measure for process focus
Utilization =
Efficiency =
Effective Capacity = Design Capacity (maximum output rate) – Allowances (e.g. personal time, maintenance, and scrap)
Sizing Capacity Cushion
Cushion: the amount of the reserved capacity that a firm maintains to handle sudden increase in demand or temporary losses of production capacity
Capacity cushion =1 - Utilization
Pressures for Large Cushion
· Uneven demand
· Uncertain demand
· Changing product mix
· Capacity comes in large increments
· Uncertain supply
Pressure for Small Cushion
· Capital costs
Links with Other Areas
Other Choice / Cushion· Faster delivery times / · Larger
· Smaller yield losses / · Smaller
· Higher capital intensity / · Smaller
· Less worker flexibility / · Larger
· Lower inventories / · Larger
· More stable schedules / · Smaller
A Systematic Approach to Capacity Decisions
1. Estimate capacity requirements
2. Identify gaps
3. Develop alternatives
4. Evaluate the alternatives
Estimate Capacity Requirements
1. One type of product
where D = number of units (customers) forecast per year
p = processing time (in hours per unit or customer)
N = total number of hours per year during which the process operates
C = desired capacity cushion rate (%)
2. More than one type of product: n types of products
Q = number of units in each lot
s = setup time (in hours) per lot
Note: Always round up the fractional part for the number of machines required.
8
Capacity Planning Problem
You have been asked to put together a capacity plan for a critical bottleneck operation at the Surefoot Sandal Company. Your capacity measure is number of machines. Three products (men’s women’s, and kid’s sandals) are manufactured. The time standards (processing and setup), lot sizes, and demand forecasts are given in the following table. The firm operates two 8-hour shifts, 5 days per week, 50 weeks per year. Experience shows that a capacity cushion of 5 percent is sufficient.
Time StandardsProduct / Processing
(hr/pair) / Setup
(hr/lot) / Lot Size
(pairs/lot) / Demand Forecast
(pairs/yr)
Men’s sandals / 0.05 / 0.5 / 240 / 80,000
Women’s sandals / 0.10 / 2.2 / 180 / 60,000
Kid’s sandals / 0.02 / 3.8 / 360 / 120,000
a. How many machines are needed at the bottleneck?
b. If the operation currently has two machines, what is the capacity gap?
c. If the operation can not buy any more machines, which products can be made?
d. If the operation currently has five machines, what is the utilization?
Capacity Planning Problem
Solution
Total time available per machine per year:
(2 shifts/day)(8 hours/shift)(5 days/week)(50 weeks/year)
= 4000 hours/machine/year
With a 5% capacity cushion, the hours/machine/year that are available are:
4000(1-0.05) = 3800 hours/machine/year
Total time to produce the yearly demand of each product:
(This is equal to the processing time plus the setup time.)
Men’s =(0.05)(80,000)+(80,000/240)(0.5)= 4167 hrs
Women’s =(0.10)(60,000)+(60,000/180)(2.2)= 6733 hrs
Kid’s =(0.02)(120,000)+(120,000/360)(3.8)= 3667 hrs
Total time for all products =4167+6733+3667= 14567 hrs
a. Machines needed = (14,567/3800) = 3.83 = 4 machines
b. Capacity gap is 4 - 2 = 2 machines
c. With two machines, we have (3800)(2) = 7600 hours of machine capacity. We can make all of the women’s sandals (6733 hours) and some of the men’s sandals, for example.
d. With five machines, (5)(4000) = 20,000 machine-hours/yr are available. The total number of machine-hours/yr needed for production are 14,567.
Utilization = (14,567/20,000)(100%) = 73%. Thus, the capacity cushion is (100% - 73%) = 27%.
Vertical Integration Problem: Make or Buy
Hahn Manufacturing has been purchasing a key component of one of its products from a local supplier. The current purchase price is $1,500 per unit. Efforts to standardize parts have succeeded to the point that this same component can now be used in five different products. Annual component usage should increase from 150 to 750 units. Management wonders whether it is time to make the component in-house, rather than to continue buying it from the supplier. Fixed costs would increase by about $40,000 per year for the new equipment and tooling needed. The cost of raw materials and variable overhead would be about $1,100 per unit, and labor costs would go up by another $300 per unit produced.
a. Should Hahn make rather than buy?
b. What is the break-even quantity?
c. What other considerations might be important?
8
Decision Making Under Uncertainty
Decision Rules
Maximin: Choose the alternative that is the “best of the worst.”
Maximax: Choose the alternative that is the “best of the best.”
Laplace: Choose the alternative with the best weighted payoff.
Minimax regret: Choose the alternative with the best “worst regret” (i.e.,
opportunity losses).
Decision Making Under Uncertainty
Event 1 (Low demand) / Event 2 (High demand)
Alternative 1 (Small facility) / $300 / $200
Alternative 2 (Large facility) / $50 / $400
Decision rules:
Maximin:
Maximax:
Laplace:
Minimax regret:
Decision Making Under Risk
Event 1 (Low demand)
Probability = 0.3 / Event 2 (High demand)
Probability = 0.7
Alternative 1 (Small facility) / $300 / $200
Alternative 2 (Large facility) / $50 / $400
Use the expected value decision rule:
8