You’ve recently joined a paper company and are now responsible for planning its production and workforce levels on January 1st, 2016, for the next 3 months. The company estimates the following demand for its paper products (in cases) over the next three months:
Month January February March
Demand Forecast 1000 800 1000
There are currently 10 workers working at the company and it is estimated that one worker can produce 2 cases per day, where it can be assumed that each month has 20 working days. The hiring cost is $1000 and the firing cost is $2000 per worker. Inventory cost is $10 per case per month. The company will have 200 cases of paper in inventory at the beginning of January, and would like to have at least 400 cases in inventory at the end of March. Assume that stockout or backorders are not allowed.
a) Determine the optimal workforce plan (hiring and/or firing in each month) using Linear Programming approach. You are only required to formulate the problem and you do not need to solve this problem.
Next, consider the same problem but suppose now that you have an option of subcontracting part of the workload. The contractor charges a fixed price of $1,000 for every month in which it produces paper products for your company (for instance, if you decide to use the contractor in Jan and March, the total fixed price is 2*1,000=$2,000). The contractor also charges $20 per case of paper product which it produces.
b) Formulate this problem using Linear Programming approach; you are not required to solve this problem.