XYZ company produces metal shelves that are made of metal bars. There are three different sizes of
Question:
XYZ company produces metal shelves that are made of metal bars. There are three different sizes of metal bars that XYZ purchases from some suppliers (small-size bars, medium-size bars, large-size bar, extremely-large-size bar). In fact, XYZ buys "batches" of metal bars from 15 different suppliers. Table 1 provides information on the cost of a batch bought from different suppliers. This table also provides information on the number of bars with different sizes that a batch from each supplier includes. As an example, as Table 1 shows, one batch from Supplier 1 costs $4400 and includes 16 extremely large bars, 28 large bars, 45 medium bars, and 37 small bars. Similar information is available for other suppliers in Table 1. XYZ must buy at least 600 extremely large, 540 large, 650 medium, and 790 small bars each week. Because of some operational reasons, XYZ can buy at most 1000 bars per week from each supplier.
Supplier | Cost Per batch ($) | The number of extremely large bars in each batch | The number of large bars in each batch | The number of medium bar in each batch | The number of small bars in each batch |
1 | 4400 | 16 | 28 | 45 | 37 |
2 | 3700 | 34 | 35 | 21 | 40 |
3 | 4400 | 30 | 19 | 26 | 34 |
4 | 3500 | 43 | 36 | 36 | 17 |
5 | 5300 | 37 | 24 | 23 | 18 |
6 | 4700 | 36 | 32 | 21 | 18 |
7 | 5100 | 26 | 28 | 26 | 41 |
8 | 5200 | 44 | 20 | 44 | 32 |
9 | 4700 | 40 | 27 | 14 | 33 |
10 | 3100 | 23 | 14 | 10 | 24 |
11 | 5600 | 23 | 20 | 34 | 35 |
12 | 4000 | 42 | 13 | 28 | 39 |
13 | 3300 | 30 | 32 | 44 | 48 |
14 | 3200 | 34 | 27 | 44 | 20 |
15 | 4100 | 36 | 27 | 44 | 46 |
16 | 4400 | 44 | 39 | 33 | 11 |
17 | 3500 | 24 | 16 | 43 | 33 |
18 | 5600 | 30 | 38 | 24 | 23 |
19 | 4200 | 28 | 26 | 35 | 12 |
20 | 4000 | 28 | 10 | 32 | 50 |
Part a)Formulate a mathematical programming model to minimize the total cost.
Part b)How would you modify the model to ensure that at least 60 percent of purchased small bars are purchased from Suppliers 4 and 5.
International Marketing And Export Management
ISBN: 9781292016924
8th Edition
Authors: Gerald Albaum , Alexander Josiassen , Edwin Duerr