The Silver Star Bicycle Company will manufacture both men’s and women’s models for its Easy-Pedal bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men’s and 125 women’s models to be shipped during the first month and 200 men’s and 150 women’s models to be shipped during the second month. Additional data are as follows:
Last month, the company used a total of 1,000 hours of labor. The company’s labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months. (Hint: Define variables for production and inventory held in each period for each product. Then use a constraint to define the relationship between these: inventory from end of previous period 1 produced this period 2 demand this period 5 inventory at end of this period.)
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 50 hours, what would happen to the production schedule? How much will the cost increase? What would you recommend?