Question

Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 4000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

Component	Manufacturing Cost	Purchase Cost
Frame	$32.00	$45.00
Support	$9.50	$13.00
Strap	$6.50	$7.50

Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows:

	Department
Component	Cutting	Milling	Shaping
Frame	2.9	1.9	2.5
Support	1.2	1.5	2
Strap	0.8	—	1.5
Capacity (hours)	330	390	640

Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased?

Let
	FM = number of frames manufactured
	FP = number of frames purchased
	SM = number of supports manufactured
	SP = number of supports purchased
	TM = number of straps manufactured
	TP = number of straps purchased

Min

FM

+

FP

+

SM

+

SP

+

TM

+

TP

s.t.

2.9FM

+

SM

+

TM

?

FM

+

1.5SM

?

FM

+

SM

+

1.5TM

?

FM

+

FP

?

SM

+

SP

?

TM

+

TP

?

FM, FP, SM, SP, TM, TP ? 0

If required, round your answers to the nearest whole number.

	Manufacture	Purchase
Frames
Supports
Straps

Answer 1

To produce 4000 Liftmasters, let the following be the required number of components, other than the motors

• FM = number of frames manufactured
• FP = number of frames purchased
• SM = number of supports manufactured
• SP = number of supports purchased
• TM = number of straps manufactured
• TP = number of straps purchased

These are the variables

The costs of manufacturing and purchasing 1 unit of each of these (frames, Supports and Statrps) are given below

Component	Manufacturing Cost	Purchase Cost
Frame	$32.00	$45.00
Support	$9.50	$13.00
Strap	$6.50	$7.50

The total cost of producing 4000 Liftmasters is

dollars

This is the objective function and Frandec company wants to minimize this cost by setting the quantites to be manufactured and/or purchased

Now the constraints

the number of components required to produce 1 lift master are

• one frame, that is FP+FM =1
• a motor - always purchased, hence not in the optimization
• two supports, that is SP+SM = 2
• a metal strap, that is TP+TM = 1

That means to produce 4000 Lift master,

• Number of frames required is
• Number of supports required is
• Number of metal straps required is

Next we look at the the available capacity (in hours) for the three departments.

The time (in minutes per unit) required to process each component in each department are

	Department
Component	Cutting	Milling	Shaping
Frame	2.9	1.9	2.5
Support	1.2	1.5	2
Strap	0.8	—	1.5

We also know the capacity available in each of these departments, we will convert the hours to minutes

	Department
Component	Cutting	Milling	Shaping
Capacity (hours)	330	390	640
capacity (minutes)	19800	23400	38400

We can not exceed these available capacity

• Total minutes required in cutting department to manufacture FM frames and SM supports and TM straps is (and this total has to be lesss than or equal to 330*60 = 19800 minutes)
  • ?
• Total minutes required in Milling department to manufacture FM frames and SM supports, straps do not require time in milling department (and this total has to be lesss than or equal to 390*60 = 23400 minutes)
  • 
• Total minutes required in Shaping department to manufacture FM frames and SM supports, TM straps is (and this total has to be lesss than or equal to 640*60 = 38400 minutes)
  • 

The linear programming model is

Minimize

s.t

• 
• 
• 
• 
• 
• 
• 

The following is the excel sheet with the formulation

The formula used to set this up are

Set up the solver as below using data--->solver

Get the following

the required quantities after rounding to whole numbers is

Component	Number manufactured	Number purchased
Frame	4,000	-
Support	6,833	1,167
Strap	-	4,000

Manufacture all the frames, and purchase all the straps, use a combination of manufacture and purchase for supports