a. Establish a production schedule that minimizes production and inventory costs

Question

a. Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements. What inventories will be maintained, and what are the monthly labor requirements?

b. If the company changed the constraints so that monthly labor increases and decreases could not exceed 250 hours, what would happen to the production schedule? How much would the cost increase? What would you recommend?

EXHIBIT 13.18 Silver Star Bicycle Data Labor Required for Manufacturing (hours) Labor Required for Assembly (hours)Current Inventory Model Men's Women's Production Costs $40 $30 10 3 20 30

Explanation / Answer

Given: Please refer to table...

The linear programming model for the table is as shown below:

Let xij=number of model i (1 for men and 2 for women's) produced in month j, and

sij= inventory at end of month j.

Min 40X11 + 30X21 + 40x12 + 30x22 +0.8s11 + 0.6s21 +0.8s12 + 0.6s22

subject to -Material balance equations:

Ending inventory requirements:

Labor force smoothing:

All variables are nonnegative.

The optimal solution is x11= 130; x21 =181; x12=225; x22=89.

Total cost =$22,386.60

If there were changes in the right hand sides of the labor force smoothing constraints , a new solution will be obtained.

x11=130; x21=206; x12= 225, x22=64.

Now when you solve the LP equation you will get,

$22,401.60

Since the labor changes results in a very small increase in the cost, I would recommend the company to change over to the new labor smoothing as that would also smooth the production schedule as well.

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