AMS 341 (Fall, 2023) Operations Research I: Deterministic Models Homework Set # 7
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AMS 341 (Fall, 2023)
Operations Research I: Deterministic Models
Homework Set # 7
Due on BrightSpace by noon (12 pm), Friday, November 3, 2023.
Read Chapter 7 Sections 1,2,3
Submit the following two problems:
(1). A large baking company bakes cakes at 3 diferent bakeries. The cost of baking 1 cake at bakery 1 is $6, at bakery 2 $4, and at bakery 3 $5. Each bakery can bake up to 100 cakes. The company then sends these cakes to 3 stores. Store 1 demands least 125 cakes, store 2 at least 120 cakes and store 3 at least 80 cakes. The shipping costs per cake from bakeries to stores are given in the table below: (The “-” means that bakery 1 cannot ship to store 1.) In addition, the company can purchase cakes from an outside supplier at a cost of $13 per cake ($10 for the cake plus $3 for shipping to any store).
|
store 1 |
store 2 |
store 3 |
bakery 1 |
- |
1.5 |
3 |
bakery 2 |
2.5 |
4 |
5 |
bakery 3 |
1 |
2 |
3 |
The company’s goal is to minimize the total cost. Formulate the problem as a Balanced Transportation problem by giving the the transportation tableau (cost and requirement matrix).
(2). Consider the following (minimum) Balanced Transportation problem:
|
warehouse 1 |
warehouse 2 |
warehouse 3 |
warehouse 4 |
dummy |
supply |
A B C |
17 13 12 |
20 26 15 |
15 19 10 |
25 20 13 |
0 0 0 |
200 300 100 |
demand |
100 |
100 |
100 |
100 |
200 |
|
(a) Find an initial BFS for the problem using the northwest corner method.
(b) Find an initial BFS for the problem using the min cost method.
(c) Find an initial BFS for the problem using Vogel’s method.
2023-12-27