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. | |||||||