Question
Course Number and Name: MNGT 520 – Advanced Production Management
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 5000 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 $38.00 $51.00
Support $11.50 $15.00
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 3.5 2.2 3.1
Support 1.3 1.7 2.6
Strap 0.8 — 1.7
Capacity (hours) 350 420 680
a. 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?
a. 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 38FM + 51FP + 11.5SM + 15SP + 6.5TM + 7.5TP
s.t.
3.5FM + 1.3SM + 0.8TM ? 21,000
2.2FM + 1.7SM ? 25,200
3.1FM + 2.6SM + 1.7TM ? 40,800
FM + FP ? 5,000
SM + SP ? 10,000
TM + TP ? 5,000
FM, FP, SM, SP, TM, TP ? 0.
Solution:
Manufacture Purchase
Frames 5000 0
Supports 2692 7308
Straps 0 5000