| Minimize the cost of operating 3 different types of machines while meeting product demand over a | ||||||
| week's time. Each machine has a different cost and capacity. There are a certain number of machines | ||||||
| available for each type. | ||||||
| Information on machines | ||||||
| Initial cost per day | Additional cost per product | Products per day (Max) | Number of machines | |||
| Alpha-1000 | $200 | $1.00 | 40 | 8 | ||
| Alpha-2000 | $275 | $1.80 | 60 | 5 | ||
| Alpha-3000 | $325 | $1.90 | 85 | 3 | ||
| Number of machines to use | ||||||
| Monday | Tuesday | Wednesday | Thursday | Friday | ||
| Alpha-1000 | 0 | 0 | 0 | 0 | 0 | |
| Alpha-2000 | 0 | 0 | 0 | 0 | 0 | |
| Alpha-3000 | 0 | 0 | 0 | 0 | 0 | |
| Number of products to make per day | ||||||
| Monday | Tuesday | Wednesday | Thursday | Friday | ||
| Alpha-1000 | 0 | 0 | 0 | 0 | 0 | |
| Alpha-2000 | 0 | 0 | 0 | 0 | 0 | |
| Alpha-3000 | 0 | 0 | 0 | 0 | 0 | |
| Made | 0 | 0 | 0 | 0 | 0 | |
| Carry-over | 0 | -600 | -1400 | -2400 | -3125 | |
| Total | 0 | -600 | -1400 | -2400 | -3125 | |
| Demand | 600 | 800 | 1000 | 725 | 750 | |
| Maximum number of products that can be made | ||||||
| Monday | Tuesday | Wednesday | Thursday | Friday | ||
| Alpha-1000 | 0 | 0 | 0 | 0 | 0 | |
| Alpha-2000 | 0 | 0 | 0 | 0 | 0 | |
| Alpha-3000 | 0 | 0 | 0 | 0 | 0 | |
| Total | ||||||
| Cost | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| Problem | ||||||
| A company has three different types of machines that all make the same product. Each machine has | ||||||
| a different capacity, start-up cost and cost per product. How should the company produce its | ||||||
| product with the available machines to meet the demand over a week's time? | ||||||
| Solution | ||||||
| The solution is very similar in structure to the one found on worksheet Alloc1. | ||||||
| 1) The variables are the number of machines to use and the number of products to make on each | ||||||
| machine. In worksheet Alloc2, these given the names Products_made and Machines_used. | ||||||
| 2) First, there are the logical constraints. These are | ||||||
| Products_made >= 0 via the Assume Non-Negative option | ||||||
| Machines_used >= 0 via the Assume Non-Negative option | ||||||
| Machines_used = integer. | ||||||
| Second, there are the demand and capacity constraints. These are: | ||||||
| Alpha1000s_used <= Alpha1000s_available | ||||||
| Alpha2000s_used <= Alpha2000s_available | ||||||
| Alpha3000s_used <= Alpha3000s_available | ||||||
| Products_made <= Maximum_products | ||||||
| Total_made >= Demand | ||||||
| 3) The objective is to minimize cost. This is defined on the worksheet as Total_cost.. | ||||||
| Remarks | ||||||
| Please see the comments on integer constraints in worksheet Alloc1. In this model we allow for | ||||||
| products made on one day to be carried over to the next. This makes it possible to meet a demand | ||||||
| for one day that exceeds the capacity of the machines on that particular day. | ||||||
