Question: Workforce Training

A department store experiences significant increase in the number of customers during the end of each calendar year. To accommodate the customers, the store has to make sure enough sales people are available. Starting in July each year the store starts hiring new sales people who have to be trained by the sales people already working in the store. The training takes one month and one sales person can train up to 20 new trainees every month. (The trainers are exclusively committed to training during the month and are not part of the active sales force). Experience has shown that one in every ten trainees fails to complete the training. The monthly estimated demand for sales people in the second half of the year are as follows:

As of July, 150 sales people are available for sales or training, and personnel records indicate that three percent of workforce leave the store at the end of the month. Each trainee is paid $2000 per month and each sales person is paid $3000 per month with a $500 per month premium per month while assigned to training. It is the store's policy not to lay off sales people in the second half of the year.

Objective: Determine the training schedule for the months of July through December that meets the demand requirements at the least cost. What is the optimal hiring plan (allow for fractional decisions)? What is the optimal cost?

(hint: Optimal cost equals $3111)