(Aggregate planning case study) XYZ company is preparing its aggregate production plan for 2012. The monthly demand forecasts are given in Table 2.23. The company is expected to have 100 workers on the payroll and 150 units in inventory at the end of 2011. Each worker can produce 10 units per month on regular time and 2 units per month in overtime. Additional data:
1. Regular time production cost—$200 per unit
2. Overtime production cost—$300 per unit
TABLE 2.23 2012 Monthly Demand Forecasts (Exercise 2.16)
Month Demand
1 500
2 600
3 600
4 800
5 1300
6 2000
7 2500
8 3000
9 2400
10 1800
11 1500
12 1200
3. Hiring cost—$500 per worker
4. Firing cost—$3000 per worker
5. Desired final inventory (December 2012)—100 units
6. Desired final workforce (December 2012)—150 workers
7. Inventory holding cost is charged based on the average inventory at the beginning and end of the month at $50 per unit per month
8. No shortages are allowed
(a) Determine a production plan using the “chase” strategy.
(b) Determine a production plan using the “level” strategy.
(c) Formulate a linear programming (LP) model that will determine the optimal production plan for 2012. You must define your variables clearly, write out the constraints that must be satisfied explaining the significance of each, and write the objective function with explanation.
(d) Solve the LP model using any optimization software.
(e) Compare the three production plans (chase strategy, level strategy, and LP solution) with respect to the following: (i) Monthly inventory levels (ii) Hiring and firing (iii) Overtime use (iv) Total cost.