Question

Problem 1(35 points): Consider the following inventory system. 8 items are currently in stock afnd there are 7 days until the end of sales and identically distibuted according to a known probability distribution. In addition, each custumer demand may be for multiple unit of items. Let B be the quantity demanded, then; season. The times between two demand points are indipendent P(B=1)-P(B-2)-5/12 0,417 and P(B=3) = 1/6 -0,167. Simulate the system till day 7. Assume that the system performance will be evaluated by the following output measures: the avarage inventory level and proportion of time that the inventory level is less than 5 items. Define two appropriate statistics to estimate these measures denoted by M1 and M2 Use the demand interarrival times (in days) at table 1 and use random digit at table 2 to generate realization (demand quantity) from B. Table 2: Random digit Table 1: Interarrival times 0.15 0.94 0.88 0.27 0.32 0.53 3.2 5.2 4.5 2.2 1.8 1.1

Answer 1

Solution

Assignment of Random numbers for B

B	P(B)	Cumulative Probability	Random #
1	0.417	0.417	0.01 - 0.42
2	0.417	0.834	0.43 - 0.83
3	0.167	1.001	0.84 - 0.00

Simulation Process

AT: Arrival time; AR: Number of arrivals

Day #	AT	AR	Random digit	B	Inventory
0				0	8
1				0	8
2	1.8	1	0.15	1	7
3				0	7
4				0	7
5	5	1	0.94	3	4
6				0	4
7	6.1	1	0.88	3	1

Total inventory over a 7-day period = 38

=> Average Inventory, M1 = 38/7 = 5.4 Answer 1

Number of days the inventory is less than 5 = 3 [last 3 days]

Proportion of days the inventory is less than 5, M2 = 3/7 = 0.43 Answer 2

DONE