Operations Research :Linear programming

Tasca Motors, Inc. (TMI) manufactures two different electrical motors for sale under contract to Drexel Corp., a well-known producer of small kitchen appliances. Its model TM3A is found in many Drexel food processors and its model TM3B is used in the assembly of blenders. Three times each year, the procurement officer at Drexel contacts TMI to place a monthly order for each of the coming four months. Drexel's demand for motors varies each month based on its own sales forecasts, production capacity, and financial position. TMI has just received the May-August order and must develop its own production plan. The demand for motors during this period is given below:

(see chart in attached file)

Production planning at Tasca Motors involves consideration of four factors. Although these factors often conflict, they form the basis for the production scheduling function.

? The desirability of producing the same quantity of each motor each month. This simplifies planning and the scheduling of workers and machines.
? Minimizing inventory carrying, or holding, costs. Therefore, producing in each month only what is needed in that month is desirable.

? Warehouse limitations cannot be exceeded without high additional storage costs.

? The company maintains a no-layoff policy which is effective in preventing unionization of the shop. This suggests that a minimum production capacity should be used each month.

Production costs are currently $10 per TM3A motor produced and $6 per TM3B unit produced. A labor agreement which takes effect on July 1, 2006 will increase these costs by 10%. Each TM3A motor held in inventory costs $0.18 per month while each TM3B motor has a carrying cost of $0.13 per month. TMI accountants allow monthly ending inventories as an acceptable approximation to the average inventory levels during the month.

TMI is beginning this four-month production period with a change in design specifications. No older version motors will be left in stock as of May 1 for use in this production plan. TMI wants to have on hand, however, an additional 450 TM3A motors and 300 TM3B motors at the end of August. Storage of motors is restricted to a maximum of 3,300 motors of either type at any one time.

TMI has a base employment level of 2,240 labor hours per month. Although the company does not consider layoffs in its planning, it can employ skilled part-time workers in busy periods to increase capacity up to 2,560 hours per month. Each TM3A motor produced requires 1.3 hours of labor while each TM3B motor requires a worker 0.9 hour for completion.

a. Formulate a linear programming model that can be used to determine the four month production schedule.

b. Determine the optimal production schedule, including the monthly production levels for each product, units held in inventory each month, labor hours used each month, and the total cost for the schedule.