Management Science Methods

Operations Management Application- Workforce Assignment

LP can be used in operations management to aid in decision-making about product mix, production

scheduling, staffing, inventory control, capacity planning, and other issues. An important application of LP

is multi-period planning such as production scheduling. Usually the objective is to establish an efficient,

low-cost production schedule for one or more products over several time periods. Typical constraints

include limitations on production capacity, labor capacity, storage space, and more.

Example:

National Wing Company (NWC) is gearing up for the new B-48 contract. NWC has agreed to produce 20

wings in April, 24 in May, and 30 in June. Currently, NWC has 100 fully qualified workers. A fully

qualified worker can either be placed in production or can train new recruits. A new recruit can be trained

to be an apprentice in one month. After another month, the apprentice becomes a qualified worker. Each

trainer can train two recruits.

The production rate and salary per employee type is listed below.

Type of Employee Production Rate (wings/month) Wage per month

Production 0.6 $3,000

Trainer 0.3 $3,300

Apprentice 0.4 $2,600

Recruit 0.05 $2,200

At the end of June, NWC wishes to have no recruits or apprentices, but have at least 140 full-time workers.

Considering the above limitations, write a linear programming model to help NWC determine the number

of employees in each type at each month (April, May, June) so as to minimize total wedge cost.

Hint 1: you need to define 9 decision variables;

- 3 decision variables for the number of producers in April, May, and June,

- 2 decision variables for the number of trainers in April and May (Why not June?)

- 2 decision variables for the number of apprentices in May and June (Why not April?)

- 2 decision variables for the number of recruits in April and May (Why not June?)

Hint 2: The objective function is:

Minimize total wage cost for producers, trainers, apprentices, and recruits for April, May, and June

Hint 3: Constraints:

- Total production in Month 1 (April) must equal or exceed contract for Month 1

- Total production in Months 1-2 (April, May) must equal or exceed total contracts for Months 1-2

- Total production in Months 1-3 (April, May, June) must equal or exceed total contracts for Months

1-3

- In April there are 100 employees that can be producers or trainers:

- At the end of June, there are to be at least 140 employees

- 2 constraints for each trainer can train at most two recruits in April and May

- 2 constraints for the number of producers and trainers in a month must equal the number of

producers, trainers, and apprentices in the previous month

- 2 constraints for the number of apprentices in a month must equal the number of recruits in the

previous month

Hint 4: Can you consider negative number of employees at each month?