Assignment:
Question. The dairy department of a Belizean supermarket is concerned about the supply of eggs to for its shelves. The deliveries were not steady and this situation resulted in stockouts, on occasion. The procurement division gathered information on the stocking and delivery of eggs, and they came up with the following -
The demand for eggs and the lead-time of orders, were given below (in thousands) -
|
Daily Demand (units)
|
Probability
|
|
Lead time (days)
|
Probability
|
|
2
|
0.09
|
|
1
|
0.10
|
|
3
|
0.10
|
|
2
|
0.45
|
|
4
|
0.14
|
|
3
|
0.29
|
|
5
|
0.16
|
|
4
|
0.16
|
|
6
|
0.13
|
|
|
|
|
7
|
0.17
|
|
|
|
8
|
0.09
|
|
|
|
9
|
0.08
|
|
|
|
10
|
0.04
|
|
|
Note : a lead-time of 2 days indicates an order placed at the end of the day that the stock falls below 20 units, will arrive after 2 full days. Each order quantity is 30 units and will cost $ 10.00 each. The cost of carrying the inventory is $ 1.50 per day, whereas, if there is no stock of eggs in the department, it will cost the supermarket $ 2.50 for each unit that is demanded during a stock out. The original stock of eggs is 40 units.
The random numbers for 20 days of the demand sequence are as follows -
|
Demand
|
39
|
95
|
26
|
7
|
46
|
60
|
23
|
79
|
33
|
88
|
35
|
15
|
55
|
5
|
17
|
11
|
40
|
83
|
30
|
65
|
|
Lead time
|
2
|
29
|
93
|
8
|
32
|
66
|
47
|
18
|
85
|
|
|
Use the following headings : Day; OI - open inventory; UR - units received ; AI - available inventory; RN - random number; D - demand; DF - demand filled; EI - ending inventory; SO - stock out; OR - order; RN - random number; LT - lead time; IC - inventory cost; SOC - stock out cost; OC - order cost; TC - total cost
1. Determine the probability distribution s for Demand and Lead times
2. Simulate the processing of the orders over twenty days, and
3. Calculate the average daily cost to the department.