Graduate (S) Business Administration 502

INFORMATION AND ANALYSIS
Spring 2017
 
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Decision Analysis Assignment

Consider a company that buys a perishable product from a supplier and resells it on the retail market. In the past, the company bought five units each period, which is the maximum that can be held in its storage facilities. The number of units that the firm sold in each of the last 50 time periods is given in the table below. The firm thinks it might be more profitable to order a smaller number of units each time period. If it orders a large number of units, such as five, the product will be available when customers want to buy it. However, a cost is incurred to purchase and process each unit, which is incurred whether or not the units are sold. Ordering a smaller number of units will reduce these costs, but will result in foregone revenue during periods when there is a large demand.

The following information is given:

  • The product sells for $100 per unit.
  • The cost of purchasing and processing each unit $50.
  • Units purchased in one period and not sold during that period will go bad. They cannot be saved to sell in future periods.
  • If the product is not there when customers want it, they might be upset.  The estimated monetary value of the loss of goodwill that results is $20 (treat as -$20).

Approach

1.  This is similar to the revenue management problem, but does not involve the binomial distribution.  Instead, use a discrete probability distribution to get the probability of each level of sales.

2. Create a probability distribution for the possible level of sales.

3. Use the relative frequency as the simple or marginal probability of each of the different levels of sales occurring (empirical classical probability).

4. Calculate the expected monetary value that results for each level of sales for each possible amount of product ordered.

5. Calculate the variance and standard deviation for each possible amount of product ordered.

Question

How much of the product should the firm order for a particular time period?  Base your decision on the order level that results in the highest expected monetary value.  Also compare the relative riskiness of each order level by comparing the variance and standard deviation for each order level.

Data

Period Sales   Last Name (X) (Y) (Z)
1 4 Anchustegui 4 1 0
2 1   Arcodia 4 1 1
3 4   Aspeytia 4 2 0
4 5   Battaile 4 2 1
5 3   Campagna 4 2 2
6 2   Clague 4 3 0
7 5   Deitrick 4 3 1
8 0   Duebler 4 3 2
9 4   Fella 4 4 0
10 5   Hallock 4 4 1
11 3   Khouri 4 4 2
12 5   Kretzer 4 4 3
13 2   Lang 5 3 1
14 2   Lui 5 3 2
15 4   Mendoza 5 3 3
16 1   Oshman 5 3 5
17 1   Peck 5 4 1
18 2   Pruzansky 5 4 2
19 2   Schoenberg 5 4 3
20 5   Seaman 5 4 4
21 4   Shaban 5 5 2
22 1   Shanks 5 5 3
23 4   Taro 5 5 4
24 5   Tugnait 5 5 5
25 2          
26 4          
27 5          
28 3          
29 4          
30 0          
31 5          
32 3          
33 5          
34 5          
35 5          
36 3          
37 2          
38 3          
39 5          
40 0          
41 4          
42 3          
43 5          
44 4          
45 1          
46 3          
47 3          
48 (X)          
49 (Y)          
50 (Z)          

Output

Submit your answers and any supporting material by Wednesday, February 15. If the output is a hard copy, it should be typed on 8 ½ x 11 or A4 paper. The output may also be submitted as an e-mail attachment.