Question

Wildcat Gym, with its 3 branches located in Central New York, wants to assign three recently hired health consultants - Todd, Josh, and Nina - to its 3 branches in Cortland, Auburn, and Oneonta. It is clearly indicated from its Headquarters that none of these three consultants will be assigned to the same locations.

The relocate costs are shown here in the table.

Consultant/Location	Cortland	Auburn	Oneonta
Todd	$720	$680	$550
Josh	$700	$710	$588
Nina	$655	$635	$495

Part a) The Headquarters is trying to find the optimal assignment of personnel to these 3 branches with a minimal relocate cost. Use the network concept and create a network program for the above problem. Make sure you define the variables used and clearly list the objective function and constraints. You do not need to solve the program.

Part b) Later the Headquarters received an update that Todd has left Wildcat Gym and now works for a different company. How will you modify your above program to reflect this update?

Answer 1

Answer A)

A	Variables
	Location	Cortland	Auburn	Onetona
	Todd	X1	X2	X3
	Josh	X4	X5	X6
	NINA	X7	X8	X9

B	Constraints
	a)	X1+x2+x3	=	1
		X3+X4+X5	=	1
		X6+X7+X8	=	1
	b)	X1+X3+X6	=	1
		X2+X4+X7	=	1
		X3+X5+X8	=	1
	c)	X1 to X9	All to be Integer
	d)	X1 to X9	all to be binary

C	Objective function is		=	720 * X1	+	680 * X2	+	550 * X3
			+	700 * X4	+	710 * X5	+	588 * X6
			+	655 * X7	+	635 * X8	+	495 * X9

The objective fucntion has to be minimized

Solution is attached

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Answer b

A	Variables
	Location	Cortland	Auburn	Onetona
	Josh	X4	X5	X6
	NINA	X7	X8	X9

B	Constraints
	a)	X3+X4+X5	=	1
		X6+X7+X8	=	1
	b)	X4+X7	<=	1
		X5+X8	<=	1
		X6+X9	<=	1
	b)	X4+X7	>=	0
		X5+X8	>=	0
		X6+X9	>=	0
	d)	X3 to X9	All to be Integer
	e)	X3 to X9	all to be binary

C	Objective function is		=	700 * X4	+	710 * X5	+	588 * X6
			+	655 * X7	+	635 * X8	+	495 * X9

The objective fucntion has to be minimized

Solution is attached