Aggregate Planning

Plan production for a four month period: June through to September. For June and July you should produce to exact demand forecast. For August and September you should use overtime and inventory with a stable workforce. Stable means the number of workers needed for July will be held constant through September. However the Ministry of Labour regulations put a maximum of 5000 hours of overtime labour per month in August and September (Zero overtime in June and July). If demand exceeds supply, then backorders will occur. There are 100 workers on May 1. You are given the following demand forecasts: June 80,000, July 64,000, August 99,200 and September 40,320. Productivity is four units per worker hour, 8 hours per day, and 20 days per month. Assume zero inventory on June 1. Costs are as follows:

Hiring                             K250,000 per new worker

Layoff                             K350,000 per worker laid off

Inventory holding                K5,000 per unit per month

Straight time labour           K50,000 per hour

Overtime                          K75,000 per hour

Back order                      K100,000 per unit

Find the total cost of this plan.