The objective is to propose a production plan to the company C&C for the next six months. Since the production cycle is short, the sales for each month are totally produced during the same month. You should evaluate in a first step, three possible plans:

Plan #1: The plan consists of producing exactly the monthly sales by varying the number of workers.

Plan #2: The plan consists of producing at each month the average sales for six months by keeping a constant number of workers. The unsatisfied demand at any period can be backordered.

Plan #3: The plan consists of producing at each month the minimum sales (April) by keeping a constant number of workers and by sub-contracting the requirements that can not be satisfied by the internal production.

In order to simplify the problem, we assume that the company C&C can recruit or dismiss workers each month as much as it is necessary. Obviously, recruitment costs are incurred if additional workers are recruited. The costs are due to their training. Dismissal costs are incurred if workers are dismissed, i.e. lower number of workers is needed for the following month. This latter assumption is unrealistic, but it simplifies the problem.

The forecasts of the sales from January to June are given in the following table.

Month	January	February	March	April	May	June
Sales (units)	1800	1500	1100	900	1100	1700

We assume that sales that can not be satisfied in a particular month can be anticipated by using anticipating stocks. We also assume that there is no initial stock available at the beginning of January.

The company starts at the beginning of January with 42 workers. In the first part of this problem we assume that the policy of the company C&C is to not use any overtime working. Hence, the computations should be done by considering only one shift of 8 hours per day and 20 working days per month.

The following costs are considered by the company when it evaluates the different plans:

Material ............................................100 /unit

Inventory holding cost .....................10 /unit- month

Stock-out cost ..................................50 /unit-month

Sub-contracting cost.........................200 /unit

Recruitment cost...1 000 /recruitment

Dismissal cost...................................2 000 /dismissal

Necessary working time per unit......5 hours/unit

Working hour cost (regular time)....15 /hour

Working hour cost (overtime).........25 /hour

Questions

1. Evaluate the total cost for each production plan. Present the result graphically in tables by detailing the computations.

2. What is the best plan for the company?