A company wants to reorganize its labour force. It currently has 3 different kind of employees; untrained, moderately trained and highly trained. Over the next 3 years, the company expects a necessary shift to more trained employees. How should the company reorganize to minimize cost? Or minimize the number of employees that have to be laid off? Employee information Cost of lay-off Available to be hired per year Cost of hiring Retraining of employees Cost Highly Trained \$700 500 \$250 Untrained -> Moderately trained \$400 Moderately Trained \$500 800 \$150 Moderately trained-> Highly trained \$500 Untrained \$350 1200 \$100 Estimated number of employees that are required. Current Year 1 Year 2 Year 3 Highly Trained 800 1200 1500 2000 Moderately Trained 1500 1500 2000 2500 Untrained 2000 1600 1000 0 Number of employees that are trained, hired or laid off. Number of employees trained Year 1 Year 2 Year 3 Cost Untrained -> Moderately trained 0 0 0 \$0 Moderately trained-> Highly trained 0 0 0 \$0 Number of employees hired Year 1 Year 2 Year 3 Cost Highly Trained 0 0 0 \$0 Moderately Trained 0 0 0 \$0 Untrained 0 0 0 \$0 Number of employees laid off Year 1 Year 2 Year 3 Cost Highly Trained 0 0 0 \$0 Moderately Trained 0 0 0 \$0 Untrained 0 0 0 \$0 Total number of employees laid off 0 Number of employees working Year 1 Year 2 Year 3 Highly Trained 800 800 800 Moderately Trained 1500 1500 1500 Untrained 2000 2000 2000 Total cost of reorganizing \$0 Problem A company has three different kinds of employees. These are highly trained, moderately trained and untrained workers. The company expects a shift towards more highly trained employees necessary over the next few years. It is possible to train people at a certain cost Laying people off also costs a certain amount. How should the company reorganize to save costs and/or have as few lay-offs as possible? Solution 1) The variables are the number of people that are trained, hired and laid off. On worksheet HireFire these are given the names Trainees, Employees_hired, and Employees_laid_off. 2) The constraints can be divided into 2 parts. First, there are the logical constraints, all of which are defined via the Assume Non-Negative option: Trainees >= 0 Employees_hired >= 0 Employees_laid_off >= 0 Second, we have the training, laying off and hiring constraints. These do not use defined names, but are represented on the worksheet by the following cells: C22 <= B17 C23 <= B16 C26 : C28 <= C9 : C11 C31 : C33 <= B15 : B17 C40 : E42 = C15 : E17 D22 <= C41 D23 <= C42 D26 : D28 <= C9 : C11 D31 : D33 <= C40 : C42 E22 <= D41 E23 <= D42 E26 : E28 <= C9 : C11 E31 : E33 <= D40 : D42 In general, these constraints reflect the movement of employees from being hired untrained to becoming moderately trained or highly trained. 3) The main objective is to minimize cost. This is defined on the worksheet as Total_cost. Remarks The model as presented here will find the method of organization that has the lowest cost. It can involve large lay-offs. It is even possible that there are alternate solutions that require fewer lay-offs! To check this, you can add the constraint Total_cost = Solution, where Solution is the amount previously found by the solver. Then change the objective to minimize lay-offs. This way you are sure to find the solution that is least expensive and involves the fewest layoffs. If the number of lay-offs is still unacceptable, you could solve the original problem again and this time include a constraint like total_laid_off = 0, or * 1000. When this problem is solved you can use the sensitivity analysis report to see how much an extra lay off would cost.