Integer programming example

In the planning of the monthly production for the next six months a company must, in each month, operate either a normal shift or an extended shift (if it produces at all). A normal shift costs 200,000 per month and can produce up to 10,000 units per month. An extended shift costs 360,000 per month and can produce up to 14,500 units per month. Note here that, for either type of shift, the cost incurred is fixed by a union guarantee agreement and so is independent of the amount produced.

It is estimated that changing from a normal shift in one month to an extended shift in the next month costs an extra 30,000. No extra cost is incurred in changing from an extended shift in one month to a normal shift in the next month.

The cost of holding stock is estimated to be 4 per unit per month (based on the stock held at the end of each month) and the initial stock is 6,000 units (produced by a normal shift). The amount in stock at the end of month 6 should be at least 4,000 units. The demand for the company's product in each of the next six months is estimated to be as shown below:

Month 1 2 3 4 5 6

Demand 12,000 13,000 14,000 14,000 12,000 12,000

Production constraints are such that if the company produces anything in a particular month it must produce at least 4,000 units. If the company wants a production plan for the next six months that avoids stockouts, formulate their problem as an integer program.

Hint: first formulate the problem allowing non-linear constraints and then attempt to make all the constraints linear.

You are required to define a problem related to Operations Research, define the decision variables of the problem, its parameters, profit and costs if any, solve the problem in excel solver and interpret the results.