Problem Set: Binary Programming
Problem 1: Moore Office Products (Revisited) Revisit the Moore Office Products example of this chapter, where there have been some revisions in the problem's data. The information is summarized below.
|
Family
|
Demand
|
Contribution
|
Fixed cost
|
|
F1
|
290,000
|
$1.20 |
$60,000 |
|
F2
|
200,000
|
1.80 |
200,000 |
|
F3
|
50,000
|
2.30 |
55,000 |
Each product requires work on three machines. The standard productivities and capacities are given below.
|
Hours per 1000 units
|
|
Machine
|
F1
|
F2
|
F3
|
Hours available
|
|
A
|
3.205
|
3.846
|
7.692
|
1900
|
|
B
|
2.747
|
4.808
|
6.410
|
1900
|
|
C
|
1.923
|
3.205
|
9.615
|
1900
|
a. Determine which products should be produced, and how much of each should be produced, in order to maximize profit contribution.
b. Suppose the demand potential for F3 is doubled. What is the maximum profit contribution? How much of each product should be produced?
Problem 2: Selecting R&D Projects The Northeast Communications Company (NCC) is contemplating a research and development program encompassing eight major projects. The company is constrained from embarking on all of the projects by the number of available scientists (40) and the budget available for project expenses ($300,000). The following table shows the resource requirements and the estimated profit for each project.
|
Project
|
Expense ($000)
|
Scientists required
|
Profit($000)
|
|
1
|
60
|
7
|
36
|
|
2
|
110
|
9
|
82
|
|
3
|
53
|
8
|
29
|
|
4
|
47
|
4
|
16
|
|
5
|
92
|
7
|
56
|
|
6
|
85
|
6
|
61
|
|
7
|
73
|
8
|
48
|
|
8
|
65
|
5
|
41
|
a. What is the maximum profit, and which projects should be selected?
b. Suppose that management determines that projects 2 and 5 are mutually exclusive. What is the revised project portfolio and the revised maximum profit?
c. Suppose that management also decides to undertake at least two of the projects involving consumer products. (These happen to be projects 5-8.) What is the revised project portfolio and the revised maximum profit?
Problem 3: Plant Location
The Spencer Shoe Company manufactures a line of inexpensive shoes in one plant in Pontiac and distributes to five main distribution centers (Milwaukee, Dayton, Cincinnati, Buffalo, and Atlanta) from which the shoes are shipped to retail shoe stores. Distribution costs include freight, handling, and warehousing costs. To meet increased demand, the company has decided to build at least one new plant with a capacity of 40,000 pairs per week. Surveys have narrowed the choice to three locations, Cincinnati, Dayton, and Atlanta. As expected, production costs would be low in the Atlanta plant, but distribution costs are relatively high compared to the other two locations. Other data are as follows.
|
Distribution costs per pair from
|
|
To distribution centers
|
Pontiac
|
Cincinnati
|
Dayton
|
Atlanta
|
Demand (pairs/wk)
|
|
Milwaukee
|
$0.42
|
$0.46
|
$0.44
|
$0.48
|
10,000
|
|
Dayton
|
0.36
|
0.37
|
0.30
|
0.45
|
15,000
|
|
Cincinnati
|
0.41
|
0.30
|
0.37
|
0.43
|
16,000
|
|
Buffalo
|
0.39
|
0.42
|
0.38
|
0.46
|
19,000
|
|
Atlanta
|
0.50
|
0.43
|
0.45
|
0.27
|
12,000
|
|
Capacity (pairs/wk)
|
32,000
|
40,000
|
40,000
|
40,000
|
|
|
Production cost/pair
|
$2.70
|
$2.64
|
$2.69
|
$2.62
|
|
|
Fixed cost/wk
|
$7000
|
$4000
|
$6000
|
$7000
|
|
a. Assume that Spencer Shoe Company will keep operating at Pontiac and build a plant at one of the three new alternatives. Which alternative will lead to the lowest total cost, including production, distribution, and fixed costs, and what is the minimum weekly cost?
b. Assume that Spencer Shoe Company could start from scratch and operate any combination of the four plants. Determine the plant locations that minimize total cost. Compared to the result in part (a), how much weekly cost could be saved with the optimal system design?
Attachment:- Problems.xlsx