Question

1. Jamison Day Consultants has been entrusted with the task of evaluating a business plan that has been divided into four sections?marketing, finance, operations, and human resources. Chris, Steve, Juana, and Rebecca form the evaluation team. Each of them has expertise in a certain field and tends to finish that section faster. The estimated times taken by each team member for each section have been outlined in the table below. Further information states that each of these individuals is paid $60 per hour.

	MARKETING	FINANCE	OPERATIONS	HR
Chris	80	120	125	140
Steve	20	115	145	160
Juana	40	100	85	45
Rebecca	65	35	25	75

Table 1: Times Taken by Team Members for Different Sections (minutes)

1. Assign each member to a different section such that Jamison Consultants’s overall cost is minimized.
2. What is the total cost of these assignments?

Answer 1

	MARKETING	FINANCE	OPERATIONS	HR
Chris	80	120	125	140
Steve	20	115	145	160
Juana	40	100	85	45
Rebecca	65	35	25	75

Time taken in minutes

Each individual is paid at $60 per hour

	MARKETING	FINANCE	OPERATIONS	HR
Chris	1	0	0	0
Steve	0	1	0	0
Juana	0	0	1	0
Rebecca	0	0	0	1

Each member is to be assigned to a different section such that the overall cost is minimized

The assignment is done as above randomly where 1 implies the individual being assigned to that function and 0 implies not

These values are integers and can only be 0 or 1

Total cost = (total time taken for the four functions/60)X60 [converting minutes to hrs and multiplying by cost per hr]

=sumproduct of time matrix and assignment matrix (this needs to be minimized)

Subject to the conditions where sum of each row and each column in the assignment matrix above is 1 to ensure to a function is uniquely allotted to a unique individual

The problem is formulated in excel as shown below:

The formulation is done in solver as shown:

As can be seen, the objective is to minimize the overall cost which is 355 as the initial condition based on the assignment done above

Also, the assignment matrix values are constrained such that all are integers, either 0 or 1. Also sum of each row and each column is 1

The solution is obtained as shown below:

From above, Marketing is assigned to Steve, Finance to Chris, Operations to Rebecca and HR to Juana

The overall cost is minimized to $210