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Chapter 3: Strategic Capacity Management

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We will discuss … What is capacity? The concept of process capacity Capacity utilization Economies and diseconomies of scale Capacity balance Little's law äRelating inventory, flow time, and flow rate Batch sizes and capacity Decision Trees

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Strategic Capacity Planning Capacity äthe ability to hold, receive, store, or accommodate. ämeasures can (as opposed to does) Strategic capacity planning äapproach for determining the overall capacity level of capital intensive resources, including facilities, equipment, and overall labor force size. Examples??

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Two Ways to Improve a Process Reduce excess capacity at some step in the process äLower the cost for the same output Use the capacity at an underutilized process step to increase the capacity at a bottleneck äIncrease the output at the same cost A bottleneck is the weakest link Process capacity = minimum {Res 1 capacity,. Res 2 capacity, …)

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Capacity Utilization Capacity used ä rate of output actually achieved Best operating level ä capacity for which the process was designed Capacity utilization rate = Capacity used / Best operating level Underutilization Best Operating Level Avg unit cost of output Volume Overutilization

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Example of Capacity Utilization During one week of production, a plant produced 83 units of a product. Its historic highest or best utilization recorded was 120 units per week. What is this plants capacity utilization rate? Answer: Capacity utilization rate = Capacity used. Best operating level = 83/120 =0.69 or 69% Answer: Capacity utilization rate = Capacity used. Best operating level = 83/120 =0.69 or 69%

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Economies & Diseconomies of Scale 100-unit plant 200-unit plant 300-unit plant 400-unit plant Volume Average unit cost of output Economies of Scale and the Experience Curve working Diseconomies of Scale start working

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Other Issues Capacity Focus The concept of the focused factory holds that production facilities work best when they focus on a fairly limited set of production objectives Plants Within Plants (PWP) äExtend focus concept to operating level Capacity Flexibility Flexible processes Flexible workers Flexible plants

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Capacity Planning: Balance Stage 1Stage 2Stage 3 Units per month 6,0007,0005,000 Unbalanced stages of production Stage 1Stage 2Stage 3 Units per month 6,000 Balanced stages of production Maintaining System Balance: Output of one stage is the exact input requirements for the next stage

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What it is: Inventory (I) = Flow Rate (R) * Flow Time (T) Implications: Out of the three performance measures (I,R,T), two can be chosen by management, the other is GIVEN by nature Hold throughput (flow rate) constant: Reducing inventory = reducing flow time Littles Law 7:008:009:0010:0011:0012:0013:0014:0015:0016:0017:0018: Flow Time Inventory Inventory=Cumulative Inflow – Cumulative Outflow Cumulative Inflow Cumulative Outflow Time Patients Can be used in analyzing capacity issues!

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Examples Suppose that from 12 to 1 p.m. 200 students per hour enter the GQ and each student is in the system for an average of 45 minutes. What is the average number of students in the GQ? äInventory = Flow Rate * Flow Time ä= 200 per hour * 45 minutes (= 0.75 hours) ä= 150 students If ten students on average are waiting in line for sandwiches and each is in line for five minutes, on average, how many students are arrive each hour for sandwiches? äFlow Rate = Inventory / Flow Time = 10 Students / 5 minutes = hour ä= 120 students per hour Airline check-in data indicate from 9 to 10 a.m. 255 passengers checked in. Moreover, based on the number waiting in line, airport management found that on average, 35 people were waiting to check in. How long did the average passenger have to wait? äFlow Time = Inventory / Flow Rate = 35 passengers / 255 passengers per hour = hours ä= 8.24 minutes

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Batch of 12 Batch of 60 Batch of 120 Batch of 300 Time [minutes] Set-up from Part A to Part B Set-up from Part B to Part A Produce Part A (1 box corresponds to 24 units = 12 scooters) Produce Part B (1 box corresponds to 12 units = 12 scooters) Production cycle The Impact of Batch Size on Capacity

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Capacity calculation: Note: Capacity increases with batch size: Note further: … and so does inventory Batch Size Set-up time + Batch-size*Time per unit Capacity given Batch Size= (in units/time) Capacity Analysis with Batching

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Data about set-up times and batching Set-up time, S Process 1Assembly process 120 minutes - Per unit time, p2 minutes/unit3 minutes/unit Capacity (B=12) units/min0.33 units/minute Capacity (B=300) units/min0.33 units/minute

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B/[S+B*p] = k implies that B = S*k / (1 – p*k)

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Problem Part a: What is the capacity for a batch size = 50? Part b: For a batch size of 10, what is the bottleneck What batch size should be chosen to smooth the flow?

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Process Utilization and Capacity Utilization Process Utilization = Flow Rate / Process Capacity äExample: Tom can process 100 forms per day and he actually processes 70 forms. äProcess utilization = ?? Utilization of resource = Flow rate / Capacity of resource äProcess 400 items per hour äCapacities of resources (items/hour): äResource 1: 500 implies utilization of 80% äResource 2: 450 implies utilization of 89% äResource 3: 600 implies utilization of 67% äBottleneck is the resource with the lowest capacity and the highest utilization äBottleneck is ??

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Decision Trees Used to structure complex decision problems Use expected return criteria Consider probabilities of occurrence of events Use: ächance nodes (denoted by circles ) ädecision (or choice) nodes (denoted by squares) Use a concept of folding back to arrive at the best policy

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Example of a Decision Tree Problem A glass factory specializing in crystal is experiencing a substantial backlog, and the firm's management is considering three courses of action: A) Arrange for subcontracting B) Construct new facilities C) Do nothing (no change) The correct choice depends largely upon demand, which may be low, medium, or high. By consensus, management estimates the respective demand probabilities as 0.1, 0.5, and 0.4. A glass factory specializing in crystal is experiencing a substantial backlog, and the firm's management is considering three courses of action: A) Arrange for subcontracting B) Construct new facilities C) Do nothing (no change) The correct choice depends largely upon demand, which may be low, medium, or high. By consensus, management estimates the respective demand probabilities as 0.1, 0.5, and 0.4.

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Example of a Decision Tree Problem (Continued): The Payoff Table The management also estimates the profits when choosing from the three alternatives (A, B, and C) under the differing probable levels of demand. These profits, in thousands of dollars are presented in the table below: LowMediumHigh A B C204060

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Example of a Decision Tree Problem (Continued): Step 1. We start by drawing the three decisions A B C

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Example of Decision Tree Problem (Continued): Step 2. Add our possible states of nature, probabilities, and payoffs A B C High demand (0.4) Medium demand (0.5) Low demand (0.1) $90k $50k $10k High demand (0.4) Medium demand (0.5) Low demand (0.1) $200k $25k -$120k High demand (0.4) Medium demand (0.5) Low demand (0.1) $60k $40k $20k

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Example of Decision Tree Problem (Continued): Step 3. Determine the expected value of each decision High demand (0.4) Medium demand (0.5) Low demand (0.1) A A $90k $50k $10k EV A =0.4(90)+0.5(50)+0.1(10)=$62k $62k

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Example of Decision Tree Problem (Continued): Step 4. Make decision High demand (0.4) Medium demand (0.5) Low demand (0.1) High demand (0.4) Medium demand (0.5) Low demand (0.1) A B C High demand (0.4) Medium demand (0.5) Low demand (0.1) $90k $50k $10k $200k $25k -$120k $60k $40k $20k $62k $80.5k $46k Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility

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Problem 2 Owner of a small firm wants to purchase a PC for billing, payroll, client records Need small systems now -- larger maybe later Alternatives: äSmall: No expansion $4000 äSmall: äLarger $9000 After 3 years small systems can äbe traded in for a larger $7500 $4000 äFuture demand is Likelihood of needing larger system later is 0.80 What system should he buy?

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Problem 2 L:.89,000 S:.29,000 10,000 Large10,000 Exp Need largeTrade-in13,500 9,000 ExpL:.8 S:.26,000 9,200 Small11,500 Trade-in11,500 Need large L:.8 S:.24,000 10,000

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