A local car dealer wants to design its inventory system to m

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.

Solution

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