Factory 1 is in McKinney, just north of Dallas, and drivers have been complainin
ID: 387444 • Letter: F
Question
Factory 1 is in McKinney, just north of Dallas, and drivers have been complaining about having to make deliveries from Factory 1 to the Oklahoma cities when there are other deliveries to be made in Dallas and Fort Worth. Because of current conditions in the transportation market, your manager is especially eager to make his drivers happy, as long as it doesn’t cost too much extra. Your manager asks you to determine how much more costly it would be to restrict Factory 1 to deliver only to Dallas and Fort Worth, while Factories 2 and 3 continue to be able to make deliveries to any of the four cities.
What additional constraints would you need to add to your model to answer your manager’s question? Answer algebraically in terms of the decision variables.
Sign in transportation_soda_data (B - Protected View - Excel AutoSaveO File Home Insert Page Layout Formulas Data Review View Help lell me what you want to do PROTECTED VIEW Be careful-files from the Internet can contain viruses. Unless you need to edit its safier to stay in Protected view. Enable Editing 83 Cost (S/Truckload) Factory 1 Factory 2 Factory 3 2 Dallas, TX 3 Fort Worth, TX 4 Oklahoma City, OK 5 Tulsa, OK 6 Annual Output 300 650 450 480 520 690 360 1130 390 315 280 250 660 780 420 Annual Demana 400 280 315 135 + 295% E- Data 49 9/19/2018 Type here to searchExplanation / Answer
This is an unbalanced Transportation problem (More output/supply and less demand) and dummy demand location is to be used. Since the IFS (Initial Feasible Solution) method is not specified, solving through North West Corner (NWC) method, with and without factory 1 delivery conditions there is no difference in cost. But to minimize cost, if we estimate transportation cost through Least Cost Method (LCM) then 75 truck loads demand remains unfulfilled in spite of availability. Now to ensure all demand is met LCM is applied to estimate transportation cost without factory 1 delivery restriction and NWC is applied with Factory 1 delivery restriction. While applying LCM and NWC in combination there is increase in transportation cost.
Total cost of transportation without delivery restriction through LCM is 419000 $.
Total cost of transportation with delivery restriction of Factory 1 through NWC is 669850 $.
Hence increase in cost of transportation after applying delivery restriction (No delivery to Oklahoma & Tulsa, Ok) from factory 1 is 250850 $.
Additional Constraints applied:
Numerical Illustration:
Estimating Total cost of transportation without delivery restriction throughLCM:
Fac1
Fac2
Fac3
AD
Dallas, Texas
300 (260)
690
280 (140)
400
Fort Worth, Texas
650
360
250(280)
280
Oklahoma City, OK
450 (260)
1130 (55)
660
315
Tulsa, OK
480
390 (135)
780
135
Dummy
0
0 (185)
0
185
O/P
520
375
420
1315
Table A
(A ) Cost of Transportation = 300x260 + 280x140 + 250x280 + 450x260 + 1130x55 + 390 x135 + 0x185 = 419000 $
Total cost of transportation with delivery restriction of Factory 1 through NWC (No delivery to Oklahoma & Tulsa, Ok )
Fac1
Fac2
Fac3
AD
Dallas, Texas
300 (400)
690
280
400
Fort Worth, Texas
650 (120)
360 (160)
250
280
Oklahoma City, OK
450
1130 (215)
660 (100)
315
Tulsa, OK
480
390
780 (135)
135
Dummy
0
0
0 (185)
185
O/P
520
375
420
1315
Table B; Note: Value in () in both tables is allocation in that cell while taking care of RIM conditions.
(B) Cost of Transportation = 400x300 + 650x120 + 360x160 + 1130x215 + 660x100 + 780x135 + 0x185
= 669850 $
Additional Cost = 669850 $ - 419000 $ = 250850 $
Hence, manager has to bear additional cost of 250850 $ cost while accepting the demands of Factory 1 drivers.
Important;
Please understand that this problem could also be solved through VAM (Vogel’s Approximation Method) and it could get better results after optimizing the IFS through MODI method.
Fac1
Fac2
Fac3
AD
Dallas, Texas
300 (260)
690
280 (140)
400
Fort Worth, Texas
650
360
250(280)
280
Oklahoma City, OK
450 (260)
1130 (55)
660
315
Tulsa, OK
480
390 (135)
780
135
Dummy
0
0 (185)
0
185
O/P
520
375
420
1315
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