Question

A local consulting firm currently has 5 jobs that have to be completed by its contract employees. After analyzing the time that it would take each specific employee to complete each specific job, and, the wages each specific employee is paid per hour, it determined how much it would cost if specific employees were assigned to specific jobs. These costs were calculated to be:

Cost ($)	Job
Employee	1	2	3	4	5
A	1,200	1,850	1,375	3,500	1,900
B	1,175	1,920	1,540	3,375	2,050
C	1,080	1,885	1,475	3,400	2,010
D	1,190	1,905	1,400	3,600	2,100
E	1,250	1,900	1,390	3,520	1,975
F	1,200	1,950	1,465	3,400	1,950
G	1,075	1,820	1,480	3,250	1,920

1. If each employee can only be assigned at most one job and each job requires only one employee, which employees should be assigned to which jobs? For remaining parts, the changes are separately made based on the base model in part a.
2. Because of some unprofessional conduct of employee C when he was previously assigned to job 1, he can no longer be assigned to job 1. Now which employees should be assigned to which jobs? Who benefits and who loses because of this unprofessional conduct?
3. Because employees B and E belonged to “designated” groups, these two employees must be assigned jobs. Now, which employees should be assigned to which jobs? Who benefits and who loses because of this designation?
4. Because the consulting firm has a policy that states that only one relative can be assigned a job, employees A and C cannot both be assigned jobs. Now which employees should be assigned to which jobs? Who benefits and who loses because of this company policy?
5. Employees F and G took the consulting firm to court as the firm would only allow them to work one job, therefore, the firm now is forced to allow F and G to work up to two jobs. Given this new fact, which employees should be assigned to which jobs?

Note:This question is not a standard Assignment problem of the network models. It should be regarded as an integer programming problem with binary decision variables. Binary constraints are needed in both model formulation and solver solutions.

Answer 1

a)

b)

c)