Reference no: EM131436046

Question 1. A simulation model of a job shop was developed to investigate different scheduling rates. To validate the model, the scheduling rule currently used was incorporated into the model and the resulting output was compared against observed system behavior. By searching the previous year's database records, it was estimated that the average number of jobs in the shop was 21.70 (7) on a given day. Seven independent replications of the model were run, each for duration of 30 days, with the following results for average n

Replication (i)	Avg. Number of Jobs (Yi)
1	18.9
2	22.0
3	19.4
4	22.1
5	19.8
6	21.9
7	20.2

a) Develop and conduct a t-test to evaluate whether model output is consistent with system behavior. Use a level of significance (α) of 0.05.

b) What is the power of this test? (Use α = 0.05)

c) Suppose that you would like to reject the null hypothesis (model validity) with probability at least 0.80 if the true difference between the model and the actual system is 1 job. What sample size is needed to guarantee a power of 0L80 or higher? (Use α = 0.05)

Question 2. A simulation model of a production facility was developed to investigate the effect of new machining centers on daily throughput. To validate the model, the current process with the old technology was incorporated into the model and the following output was captured.

Replication (i)	Throughput (Yi)
1	120
2	116
3	110
4	130
5	128
6	140
7	103
8	125
9	115
10	127

Historical data shows the average daily throughput to be 125 units.

Develop a 95% confidence interval on the throughput data collected to assess the validity of the simulation model. Use ε = 2 units.

Question 3. An airport will soon be designated as an international airport. Of course, a number of international flights will arrive and require immigration and customs. The airport would like to examine the customs staffing and establish a policy on the number of passengers who should have bags searched and the staffing of the customs facility. Table 1 shows the arrival schedule of international flights per hour arriving to the airport (and the immigration and customs area).

Table 1: Arrival Schedule
Time Period	Planes Per Hour
6am-1am	1
7am-8am	2
8am-9am	3
9am-1pm	4
1pm-6pm	3
6pm-10pm	2

The number of passengers who arrive on each international flight is uniformly distributed between 250 and 300.

An airport systems analyst has developed a probabilistic method to decide which customers will have their bags searched. The decision is made when the passengers are about to enter the normal customs queue. The decision process is as follows. A number is first generated from a Poisson distribution with a mean of 7. This number is increased byl to avoid getting a zero. This successively generated random number will serve as an -unlucky" number for a passenger. A passenger count is also started. When the count reaches the generated "unlucky' number, that unlucky passenger is sent to another line to have his or her bags searched. A new "unlucky" number is then generated and the process repeats.

In the customs area, the service time of passengers that have their bags searched is a function of the number of bags to be searched. Table 2 displays information for the number of bags per "searched" passenger.

Table 2: Number of Batas per Passenger
Number of Bags	Probability
1	25
2	50
3	25

The service time (i.e., search time) is expo(1.5) minutes per bag. Additionally, "searched" passengers that have 3 bags require two customs agents for processing. -Searched" passengers that possess 1 or 2 bags require a single customs agent. For passengers that do not have their bags searched, the service time to be processed in the customs area is expo(0..55) minute.

Work To Do -

Develop a simulation model for this proposed system and perform 100 replications. The simulation is to run until the last passenger on the last Wane of the day has been completely processed. Airport officials have stated the goal of "searched" passengers spending an average of 50 minutes and "non-searched" passengers spending an average of 17 minutes in the customs area. Using your simulation model, you should determine the number of customs agents in the search and non-search areas, respectively, to achieve the stated goal. You will need to develop 55% confidence intervals on the time in system based on passenger type (searched vs. nom-searched) to determine proper staffing levels.

You must use the Process Analyzer to perform the analysis of the staffing levels.

Exercise Requirements -

Provide a short report (2-3 pages max) that contains:

1. A discussion of your simulation model. State any assumptions that you make.

2. Table showing the results from the process analyzer (Le. staffing levels and time in system values).

3. Presentation and discussion of your statistical analysis_

4. Summary of your staffing recommendations. Make sure to justify your recommendations.

Question 4. Capstone Enterprises (CE), a multi-national company_ sells headphones as part of its core business. CE would like to determine a supplier for its headphone and investigate the management of its headphones inventory. The headphones are sold in cases. The initial level of headphone cases is 75. Customers of CE order with interdemand times distributed as exponential with mean 0.10 day (it's a round-the-clock operation) with the first demand occurring after one of these interdemand times (past time zero). Customers demand 2, 3, 4, or 5 headphone cases with respective probabilities 0.167, 0.333, 0.333, and 0,467. If a customer's demand can be met out of on-hand inventory_ the customer gets the full demand and goes away happy. If the on-hand inventory is less than the customer's demand, the customer gets whatever is on hand (which might be nothing), and the rest of the demand is backlogged, and the customer gets it later when inventory will have been sufficiently replenished. Customers with backlogged items are infinitely patient and never cancel their orders.

At the beginning of each day (including at time zero), CE 'takes inventory" to decide whether to place an order with its headphone supplier at that time. If CE's inventory position (be it positive or negative.) is (strictly) less than a constant minimum safety inventory level (denoted as 5), CE orders 'up to another constant inventory level (denoted as Sy What this means is that CE orders a quantity of headphone cases so that_ if they were to arrive instantly, the on-hand inventory level would go up to exactly S. This form of review/replenishment policy is called an (s, S) inventory policy.

Note: inventory position is defined as the sum of on-hand inventory and outstanding orders. So, it will be necessary to track both on-hand inventory and inventory position.

However, an order placed at the beginning of a day does not arrive instantly because a delivery lag exists (i.e. lead time). See Table 1 below for supplier lead time info. So when the order arrives, the on-hand inventory level will increase by an amount equal to the original order quantity but, if there were any demands since the order was placed. it will increase to something less than S when the order is finally delivered.

CE is interested in the average total operating cost per day of this system over 120 days. There are 5 components to the total operating cost. The cost components for each potential supplier and respective supplier distances to CE are given in Table 1.

Table 1. Supplier Information

Component	Supplier 1	Supplier 2	Supplier 3
Setup Cost (per order)	S60	S50	$40
Holding Cost (per case per day)	$30	S20	$15
Shortage Cost (per case per day)	$40	$30	$25
incremental Cost (per case ordered)	$50	$40	$30
Transportation Cost (per case per mile)	$4	$5	$6
Distance to CE (miles)	100	150	200
Lead Time (days)	expo(2)	expo(3)	expo(4)

Work To Do -

Develop a simulation model for this system with each replication running for 119.9999 days (exactly!!!!). Using Optquest and your simulation model, determine which supplier CE should select and the "best" inventory policy parameters (s and S) by evaluating the average total operating cost per day. You should develop a single optimization module that works with the simulation model to simultaneously determine the proper supplier and the inventory policy parameters. You should not evaluate each potential supplier separately.

Exercise Requirements -

Provide a short report (2-3 pages max) that contains:

1. Brief discussion of your Arena simulation model.

2. Details on the optimization component including the controls, responses, constraints, objective, run parameters, termination criteria, etc.

3. Discussion of the results from your simulation optimization run; include discussion of the effect of the inventory management parameters on the total cost and on the cost components.

4. Recommendation of the supplier to select and on the inventory policy parameters. Why?

Make sure to show all your work. Also, state any assumptions that you make.