a) Formulate the model by defining decision variables, objective function and contraints. 

b) Put your model in an Excel spreadsheet and solve the problem using Excel solver.

You are requested to find optimum Aggregate Production plan for the next 12 months. Demand forecast, available working days per months are given in below Table. 

There are 4 holiday days in each month, which can be used as overtime. Overtime hours available for holidays is 8 hours. The regular working hours is 8 hours per day. Allowable overtime hour for each normal workday is 2 hours. There are 2 employee types: Permanent and temporary. The limits for minimum and maximum numbers of permanent workers are 660 and 1,120 respectively.

 The limit for maximum number of temporary workers is 400. Average productivity rates of permanent and temporary workers are 5 and 4.5 units per man-day, respectively. Amount of required safety stock in each period is zero. Subcontracting has no limitation. 

Average monthly wage per permanent employee is 6.000 TL. Average wage per day per temporary employee is 300 TL. Each temporary employee cannot be hired longer than four months, because of law. Average cost of hiring one temporary worker is 1.300 TL. Laying off cost of temporary worker is negligible. Average inventory holding cost per unit per month is 200 TL. 

Overtime costs per man-hour per permanent worker during normal workday is 40 TL and during holiday is 50 TL. Overtime costs per man-hour per temporary worker during normal workday is 35 TL and during holiday are 45 TL. Subcontracting cost is 350 TL per unit. Initial inventory is zero. 

The required amount of inventory at the end of the last period is the average demand forecast. There are currently 600 permanent workers and it is the company policy to keep the number at this level. The company hired 150, 150, and 100 temporary workers three periods ago, two periods ago, and one period ago. They were hired at the beginning of periods. 

Ma Au No De Months Jan Feb Mar Apr Jun Jul Sep Oct v Number of Workdays 23 20 25 21 22 23 15 16 22 21 20 18 Demand Forecast (1000) 135 140 144 150 150 145 90 40 50 80 100 120