Yeasty Brewing Company produces a popular local beer known as Iron Stomach. Beer sales are somewhat seasonal, and Yeasty is planning its production and manpower levels on March 31 for the next six months. The demand forecasts are:

Additional Information:

• As of March 31, Yeasty had 50 workers on the payroll.
• Over a period of 20 working days, when there were 100 workers on the payroll, Yeasty produced 10,000 cases of beer.
• The cost to hire is $125/worker and the cost to fire is $300/worker.
• The company pays each worker $2000/month.
• Holding costs amount to $75/case/month.
• As of March 31, Yeasty expects to have 4,500 cases of beer in stock.
• Yeasty plans to start October with 3,000 cases on hand.

Perform the following tasks:

1. Formulate this problem as a linear programming (LP) to determine the optimal workforce plan and the cost of that plan. Clearly define your variables, and use the data given for this problem when you write the objective function and the constraints.
2. Solve the LP.
3. The simplest formulation does not allow backorders, meaning that while production in period t can be used to satisfy demand in period t+1, it is not possible to “hold” demand from period t and satisfy it in period t+1. Now allow backorders at a cost of $120/case-month, modify your LP formulation, and resolve.

BIG PICTURE: This is a traditional workforce planning exercise given at the end of a semester, and because of time constraints we were unable to develop the envisioned tool support for aggregate and workforce planning. The exercise is simple enough to be solved with the Excel solver, but what it lacks is that after development any plan should be simulated, is almost always discovered inadequate due to variability, has its parameters adjusted (the most interesting part - what control levers are available in the LP formulation?), is re-solved, re-simulated, etc.