Chapter 3: Strategic Capacity Management

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

Strategic Capacity Planning the ability to hold, receive, store, or accommodate. measures can (as opposed to does) Strategic capacity planning approach for determining the overall capacity level of capital intensive resources, including facilities, equipment, and overall labor force size. Examples?? 3

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

Capacity Utilization Capacity utilization rate = Capacity used / Best operating level Capacity used rate of output actually achieved Best operating level capacity for which the process was designed Underutilization Best Operating Level Avg unit cost of output Volume Overutilization 5

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 plant’s capacity utilization rate? Answer: Capacity utilization rate = Capacity used . Best operating level = 83/120 =0.69 or 69% 6

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

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) Extend focus concept to operating level Capacity Flexibility Flexible processes Flexible workers Flexible plants 10

Capacity Planning: Balance Unbalanced stages of production Units per month Stage 1 Stage 2 Stage 3 6,000 7,000 5,000 Maintaining System Balance: Output of one stage is the exact input requirements for the next stage Balanced stages of production Units per month Stage 1 Stage 2 Stage 3 6,000 6,000 6,000 12

Little’s Law Can be used in analyzing capacity issues! 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 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 11 10 9 8 7 6 5 4 3 2 1 Flow Time Inventory Inventory=Cumulative Inflow – Cumulative Outflow Cumulative Inflow Outflow Time Patients Can be used in analyzing capacity issues!

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? Inventory = Flow Rate * Flow Time = 200 per hour * 45 minutes (= 0.75 hours) = 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? Flow Rate = Inventory / Flow Time = 10 Students / 5 minutes = 0.083 hour = 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? Flow Time = Inventory / Flow Rate = 35 passengers / 255 passengers per hour = 0.137 hours = 8.24 minutes

The Impact of Batch Size on Capacity Production cycle Batch of 12 Production cycle Batch of 60 Batch of 120 Batch of 300 60 120 180 240 300 Time [minutes] Produce Part B (1 box corresponds to 12 units = 12 scooters) Set-up from Part A to Part B Produce Part A (1 box corresponds to 24 units = 12 scooters) Set-up from Part B to Part A

Capacity Analysis with Batching 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 1/p 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 50 90 130 170 210 250 290 330 370 410 450 490 530 570 610 650 Batch Size

Data about set-up times and batching Process 1 Assembly process 120 minutes - Per unit time, p 2 minutes/unit 3 minutes/unit Capacity (B=12) 0.0833 units/min 0.33 units/minute Capacity (B=300) 0.4166 units/min

B/[S+B*p] = k implies that B = S*k / (1 – p*k) Figure : Choosing a “good” batch size Batch size is too small, process capacity could be increased (set-up step is at the bottleneck) Batch size is too large, could be reduced with no negative impact on process capacity (set-up is not at the bottleneck) Capacity 1/p 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 50 90 130 170 210 250 290 330 370 410 450 490 530 570 610 650 Batch Size Capacity of slowest step other than the one requiring set-up B/[S+B*p] = k implies that B = S*k / (1 – p*k)

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?

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

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

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. 20

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: 0.1 0.5 0.4 Low Medium High A 10 50 90 B -120 25 200 C 20 40 60 21

Example of a Decision Tree Problem (Continued): Step 1 Example of a Decision Tree Problem (Continued): Step 1. We start by drawing the three decisions A B C 22

$90k $50k $10k A $200k $25k B -$120k C $60k $40k $20k 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 $200k $25k -$120k $60k $40k $20k 23

Example of Decision Tree Problem (Continued): Step 3 Example of Decision Tree Problem (Continued): Step 3. Determine the expected value of each decision $90k High demand (0.4) Medium demand (0.5) Low demand (0.1) $50k $62k $10k A EVA=0.4(90)+0.5(50)+0.1(10)=$62k 24

Example of Decision Tree Problem (Continued): Step 4. Make decision High demand (0.4) Medium demand (0.5) Low demand (0.1) A B C $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 25

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: Small: No expansion capabilities @ $4000 Small: expansion @6000 Larger system @ $9000 After 3 years small systems can be traded in for a larger one @ $7500 Expanded @ $4000 Future demand is Likelihood of needing larger system later is 0.80 What system should he buy?

Problem 2 L: .8 9,000 S: .2 10,000 Large Exp Need large Trade-in 13,500 6,000 9,200 Small 11,500 4,000