Question 4 :In the planning of themonthly production for the next four months, in each month acompany must operate either a normal shift or an extended shift(but not both) if it produces. It may choose not to produce in amonth. A normal shift costs $100,000 per month and can produce upto 5,000 units per month. An extended shift costs $140,000 permonth and can produce up to 7,500 units per month.
The cost of holding inventory is estimated to be $2 per unit permonth (based on the average inventory held during each month) andthe initial inventory is 3,000 units (i.e., inventory at thebeginning of Month 1). The inventory at the end of month 4 shouldbe at least 2,000 units. The demand for the company's product ineach of the next four months is estimated to be as shown below:
Month | 1 | 2 | 3 | 4 |
Demand | 6000 | 6500 | 7500 | 7000 |
Production constraints are such that if the company producesanything in a particular month it must produce at least 2,000units. The company wants a production plan for the next four monthsto meet its demands. Formulate an integer programming model tosolve the problem at minimum cost.
Decision variables :
Objective function :
Constraints :
Additional constraint 1 :The company can operate anextended shift in Month 1 only if it operates a normal shift ineach of Month 2, Month 3 and Month 4.
Additional constraint 2 :The company must produce in eitherMonth 1 or Month 2 (or both) if it does not produce in Month 3.
Additional constraint 3 :For each of Month 2, 3 and 4,thecompany cannot operate an extended shift in a month if it operatesone in the previous month.
