Announcement-exam rules

• Bring a calculator to the exam-no use of mobile phones allowed

• Bring your own pencil and eraser• Formulas will be provided-know what

notation means

2

Capacity Management

• First check if average capacity is enough: is there a perpetual queue? If not, increase capacity

• Capacity may be enough on average but badly distributed over time periods experiencing demand fluctuations: check if there is a predictable queue, do proper scheduling; you may need more people to accommodate scheduling constraints

• Find sources of variability and try to reduce them: these create the stochastic queue

3

Example

• Consider the Migros on campus• Do a capacity analysis for the check out

process of Migros.

4

Multi-stage processes• Theoretical flow time

– Length of critical path (longest) determines flow time– Does not include waiting time between stages– Can be reduced by working faster, smarter, or by moving

work off the critical path• Average flow time

– Includes processing as well as waiting times on longest path

– Measured or simulated– Waiting between stages can be reduced by better

balancing the stages, finding ways to reduce resource interference, and by reducing variability in arrivals and processing times

5

Multi-stage processes

• Capacity/throughput rate– The stage that has the lowest capacity determines

the capacity of the entire process– Only speeding-up the bottleneck or increasing the

resources devoted to the bottleneck stage can improve capacity

– If we improve the bottleneck capacity a lot, the bottleneck will shift to another stage at some point

6

Example: process analysis

8 min/unit3 min/unit 5 min/unit

•What is the flowtime? Throughput rate?

•How long will it take you to fill a rush order of one unit?

•How long will it take to finish an order of 5 units?

•How many orders can you fill in an hour?

•What are the utilizations of the workers?

7

Example: process analysis

8 min/unit3 min/unit 5 min/unit

•What is the flowtime? Throughput rate?

•How long will it take you to fill a rush order of one unit?

•How long will it take to finish an order of 5 units?

•How many orders can you fill in an hour?

•What are the utilizations of the workers?

You are the manager of a widget factory. Production of a widget is currently a two-stage process. The first stage (cutting and planing) takes 3 minutes per unit of input. The output of the first stage is then finished in the second stage, which takes 4 minutes. Assume demand is very high, and all of production can be sold at a mark-up (over costs) of $3.00 per unit. Sam the supervisor is considering an upgrade to an NC (numerical control) machine that can flexibly do all these tasks (cutting, planing and finishing); moreover, this machine will take just 5 minutes to produce one unit of a widget.

As a result of the upgrade, monthly margin generated by the factory will:

IncreaseDecrease Remain unchanged

• A mail order company has one department for taking customer orders and another for handling complaints. Currently each has a separate phone number. Each department has 7 phone lines. Calls arrive at an average rate of 1 per minute and are served at 1.5 per minute. Management is thinking of combining the departments into a single one with a single phone number and 14 phone lines.

• Average flow time experienced by customers will….?

A bank would like to improve its drive-in service by reducing waiting and transaction times. Average rate of customer arrivals is 30/hour. Customers form a single queue and are served by 4 windows in a FCFS manner. Each transaction is completed in 6 minutes on average. The bank is considering to lease a high speed information retrieval and communication equipment that would cost 30 YTL per hour. The facility would reduce each teller’s transaction time to 4 minutes per customer.a. If our manager estimates customer cost of waiting in queue to be 20 YTL per customer per hour, can she justify leasing this equipment?b. The competitor provides service in 8 minutes on average. If the bank wants to meet this standard, should it lease the new equipment?

Category Product 1 Product 2 Product 3Profit/unit $30 $50 $20Machine 1 time/unit 0.5 2.0 0.75Machine 2 time/unit 1.0 1.0 0.5

Better Products, Inc., manufactures three products on two machines (each product needs to be processed on both machines). In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows:  

Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2 time. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced. Formulate a linear programming model that can be used to determine the number of units of each product to produce to maximize the total profit contribution