A local car dealer wants to design its inventory system to minimize its total in
ID: 3382116 • Letter: A
Question
A local car dealer wants to design its inventory system to minimize its total inventory cost (TIC). TlC=ICC+CLS+CPO, where Inventory Carrying Cost (ICC): $95 per car per day. Cost of Lost Sales (CLS): $3,200 per car Cost of placing an order (CPO): $600 per order. Daily demand distribution is as follows: On any day, if the demand exceeds inventory on hand (IOH), only a portion of the demand is met and the rest is considered lost sales. For example, if the demand on a given day is for 25 cars, and the IOH (inventory on Hand) is 10 cars, then 15 cars are considered lost sales for that day. The dealer operates 7 days a week. IOH is examined at the end of each day period. If IOH is less than or equal to order level (OL) which is 40 cars, an order of 90 cars (OQ=90, Order Quantity) is placed. Orders arrive at the beginning of a day as follows: In other words, if an order is placed at the end of day 8, there is a 40% probability that it will arrive 3 days later, i.e. at the beginning of the 11^th day. With a 60% probability, it will arrive 5 days later, i.e. at the end of the 13^th day. Assume that IOH is 225 cars when the simulation starts. Design a simulation model to simulate the inventory system for 365 days to find and print TIC.Explanation / Answer
Assignment of Random numbers to daily demand per day:
Table 1
Demand per day
Probability
Cumulative
Probability
Interval of Random
Numbers
0 car
0.20
0.20
01 through 20
1 car
0.30
0.50
21 through 50
2 car
0.30
0.80
51 through 80
3 car
0.20
0.100
81 through 00
Assignment of Random numbers to days to receive an order:
Table 2
Days to receive an order
Probability
Cumulative
Probability
Interval of Random
Numbers
3 Days
0.40
0.40
01 through 40
5 Days
0.60
1.00
41 through 00
Day
Random Number
Demand per day
IOH
CLS
CPO
Random Number
Days to receive an order
1
03
0 car
225
0
0
2
80
2 car
223
1200
3
37
1 car
222
600
4
99
3 car
219
1800
5
19
0 car
6
11
0 car
7
68
2 car
217
1200
8
43
1 car
216
600
9
80
2 car
214
1200
10
22
1 car
213
600
11
13
1 car
212
600
12
19
1 car
211
600
Table 1
Demand per day
Probability
Cumulative
Probability
Interval of Random
Numbers
0 car
0.20
0.20
01 through 20
1 car
0.30
0.50
21 through 50
2 car
0.30
0.80
51 through 80
3 car
0.20
0.100
81 through 00
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