Part B Methods: Question per preamble:

Preamble: Nico Case is an industrial engineer working in Vancouver, BC. Ms. Case is

responsible for the design and development of a new warehousing operation for a

national manufacturer of yoga clothing. Nico has several design alternatives available,

each with differing types of equipment, production strategy, cost, and potential

throughput. Accordingly, Ms. Case has decided to build a simulation model to guide her analysis. The following questions relate to this study.

Q 1a. Ms. Case is interested in setting the warm up period for her model. She has run a pilot run of her simulation and output hourly throughput for her system. She receives the following data:

Time	Rep 1	Rep 2	Rep 3
1	3	5	4
2	49	40	37
3	20	19	19
4	22	24	24
5	24	20	20
6	22	25	25
7	25	20	22
8	25	21	24
9	21	20	24
10	21	24	25

a) Define what is meant by "transient" as opposed to steady-state" for a simulation model.

b) Why is it important to identify a warm up period for a simulation model?

c) Using Welch's technique and a moving window with w = 1, estimate the warm up

period for this model.

Q 2a. Ms. Case must determine a replication length and run time strategy for her simulation. She believes that a 30-day period, after the identification of the transient, is sufficient for her purposes and makes some sense, given the historical data she has available for a similar system that was installed by the Ontario Liquor Control Board in their warehouse in Whitby, Ontario.

Nico has completed a pilot run of 10 replications of 30 simulated days, using the run

strategy of batch means. She receives the following output:

Rep	Throughput
1	3500
2	3851
3	4522
4	4756
5	4872
6	4020
7	4618
8	4968
9	4632
10	4548

a) Use the data from the pilot runs to prove to Nico that a 30-day replication length is insufficient.

b) Provide an algorithm (and advice) for determining a proper run length for this model.

c) Compare the run strategies of "batch means" and "replication/deletion". How are these implemented? What are the advantages/disadvantages of each?

d) Assume that Ms. Case wishes to get around the problem in part (a) by implementing a "replication/deletion" strategy with a run length of 30 days. Would this solve the problem? Why or why not?

Q 3a. After determining an appropriate warm up period, run length, and run strategy, Nico Case conducts a set of experiments with her model.

a.) In the first set of experiments, she runs her model for 5 replications of one-year, following a 30 day warm up, under the strategy of batch means. Assume that a one-year period is sufficient for statistical purposes. The monthly throughput from her model is 6,000 units/month and the standard deviation is 50. Approximately how many replications are required if Ms. Case wants her experiments to be powered to detect a difference in monthly throughput of 15 units, 19 times out of 20?

b.) Assume that Ms. Case has run her model for 5 replications of 30 days, following a 30-day warm up period. The average monthly throughput from her model is N (6104, 70). The system vendor indicates that a similar system installed in Whitby, ON is known to have a monthly throughput of 6053 units. No standard deviation is provided by the vendor. What can you say about Nico's model, with relation to the vendor estimates?

c.) As a final test of validity, Ms. Case adjusts her model to make it representative of her firm's current warehouse layout and logistics. She runs her model for 6 replications of one year and calculates the monthly throughput. She also obtains a sample of data from her firm's warehouse for the previous 6 months.

	Simulation	Warehouse
Month 1	4040	4060
Month 2	4020	4060
Month 3	4005	4051
Month 4	4001	4024
Month 5	4046	4028
Month 6	3977	4061

Is there any evidence that the simulation is representative of the existing warehouse?