Question

During the next four quarters Dorian Auto must meet (on time) the following demands for cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3; 1000 in quarter 4. At the beginning of quarter 1, there are 300 cars in stock. The company has the capacity to produce at the most 3000 cars per quarter. At the beginning of each quarter, the company can increase (but not decrease) its production capacity. It costs $100 to increase production capacity by one unit. For example, it would cost $10,000 to increase production capacity from 3000 cars per quarter to 3100 cars per quarter. It also costs $40 per quarter to maintain each unit of production capacity (whether it is used or not). The variable cost of producing a car is $2000. A holding cost of $150 per car is assessed for each quarter’s ending inventory. It is required that at the end of quarter 4, plant capacity must be at least 4000 cars.

(1) Determine how to minimise the total cost incurred during the next four quarters. There is a concern that due to rising material and labor costs the variable cost in the fourth quarter may increase by 10%.

(2) Should you change your production plan if you believe this increase will occur?

(3) What would you do if you believed that there would be a 20% increase in variable costs in the fourth quarter?

(4) Describe and formulate another similar problem and solve the problem again.

Answer 1

1)

We need to decide how much capacity we should increase every month and how much of that capacity should be used in production. The best approach is to use LP model to solve this.

Use the model as shown below

The formulas are shown below

The solver parameters are shown below

Ther result is shown below

2)

If there is a 10% increase in the 4th quarter, we will assume that the increase in cost will take place in every cost. The solution is shown below

We can see that there is no change in the plan due to 10% additional increase in cost in last quarter.

3)

If the increase is 20% then the impact will be 200 per unit in the last quarter. By the given data we know that the holding cost is 150 per unit. This means that it will be cheaper to hold extra 1000 units in the previous quarter than to produce it in the last quarter. Our solution will change. The updated solution is shown below.