United Express Service (UES) uses large quantities of packaging materials at its
ID: 327042 • Letter: U
Question
United Express Service (UES) uses large quantities of packaging materials at its four distribution hubs. After screening potential suppliers, UES identified six vendors that can provide packaging materials that will satisfy its quality standards. UES asked each of the six vendors to submit bids to satisfy annual demand at each of its four distribution hubs over the next year. The following table lists the bids received (in thousands of dollars). UES wants to ensure that each of the distribution hubs is serviced by a different vendor. Which bids should UES accept, and which vendors should UES select to supply each distribution hub?
The value of the objective function is _______ thousands of dollars.
Distribution Hub Bidder 1 2 3 4 Martin Products 185 180 130 235 Schmidt Materials 150 240 145 215 Miller Containers 220 225 140 240 D&J Burns 165 185 185 275 Larbes Furnishings 210 180 145 240 Lawler Depot 235 195 140 255Explanation / Answer
This problem will be solved using binary decision variables.
The variables are defined in the table below. It means that if a11 = 1 then Martin Products will service 1st distribution hub. If it is 0 then it will not service the hub.
Objective function: 185a11+180a12+130a13+235a14+150b11+240b12+145b13+215b14+220c11+225c12+140c13+240c14+165d11+185d12+185d13+275d14+210e11+180e12+145e13+240e14+235f11+195f12+140f13+255f14
This has to be minimized.
Constraints:
1. a11+a12+a13+a14<=1
2. b11+b12+b13+b14<=1
3. c11+c12+c13+c14<=1
4. d11+d12+d13+d14<=1
5. e11+e12+e13+e14<=1
6. f11+f12+f13+f14<=1
7. a11+b11+c11+d11+e11+f11 = 1
8. a12+b12+c12+d12+e12+f12 = 1
9. a13+b13+c13+d13+e13+f13 = 1
10. a14+b14+c14+d14+e14+f14 = 1
11. all variables are binary.
The excel's solver function gives the following solution:
Required solution table:
The value of the objective function is 690 thousands of dollars.
1 2 3 4 Bidder Martin Products a11 a12 a13 a14 Schimdt Materials b11 b12 b13 b14 Miller Containers c11 c12 c13 c14 D&J Burns d11 d12 d13 d14 Larbes Furnishings e11 e12 e13 e14 Lawler Depot f11 f12 f13 f14Related Questions
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