A hurricane has been predicted to make landfall in Louisiana. The counties that lie within the path of the storm along with current population estimates are given in Table 1 below. There are several regional warehouses located in Texas, Alabama and Georgia that have capacity available to lease so that supplies can be prepositioned in advance of the storm. The lease capacity available at each of the warehouses is 100,000 units of MREs (meals ready-to-eat). The cost to lease each warehouse along with the capacity available is displayed in Table 2. The distance (in miles) to ship product to each of the counties from each possible warehouse location is summarized in Table 3. Assume travel cost is proportional to distance traveled. Formulate a mathematical model that will determine which of the warehouses to use to preposition MREs and the amount shipped from each warehouse to each of the counties to assist those who are in need after the storm. Assume that 25% of the population will be severely affected by the storm and require assistance (in terms of MREs)
A hurricane has been predicted to make landfall in Louisiana. The counties that lie within the path of the storm along with current population estimates are given in Table 1 below. There are several regional warehouses located in Texas, Alabama and Georgia that have capacity available to lease so that supplies can be prepositioned in advance of the storm. The lease capacity available at each of the warehouses is 100,000 units of MREs (meals ready-to-eat). The cost to lease each warehouse along with the capacity available is displayed in Table 2. The distance (in miles) to ship product to each of the counties from each possible warehouse location is summarized in Table 3. Assume travel cost is proportional to distance traveled. Formulate a mathematical model that will determine which of the warehouses to use to preposition MREs and the amount shipped from each warehouse to each of the counties to assist those who are in need after the storm. Assume that 25% of the population will be severely affected by the storm and require assistance (in terms of MREs).
Table 1. Population estimates for affected counties
|
County |
Population |
|
Assumption |
22874 |
|
Jefferson |
443342 |
|
Lafourche |
93682 |
|
Orleans |
354850 |
|
Plaquemines |
20942 |
|
St. Bernard |
40655 |
|
St. Charles |
51611 |
|
St. James |
21054 |
|
St. John The Baptist |
47086 |
|
St. Mary |
50815 |
|
St. Tammany |
231495 |
|
Terrebonne |
109291 |
Table 2. Warehouse Capacity and Cost Information
|
Warehouse location |
Warehouse Capacity |
Fixed Cost to lease capacity ($) |
|
Abilene ,TX |
100,000 |
125,000 |
|
Amarillo ,TX |
100,000 |
125,000 |
|
Austin ,TX |
100,000 |
125,000 |
|
Beaumont,TX |
100,000 |
125,000 |
|
Corpus Christi ,TX |
100,000 |
120,000 |
|
Dallas ,TX |
100,000 |
150,000 |
|
Ft. Worth ,TX |
100,000 |
125,000 |
|
Savannah ,GA |
100,000 |
100,000 |
|
Valdosta ,GA |
100,000 |
100,000 |
|
Chattanooga ,GA |
100,000 |
50,000 |
|
Birmingham ,AL |
100,000 |
120,000 |
|
Huntsville,AL |
100,000 |
110,000 |
|
Montgomery ,AL |
100,000 |
95,000 |
Table 3. Travel Distance in Miles **note, to fit the table on the page, the counties have been numbered d1 to d12 and the warehouses w1-w13.
|
d1 |
d2 |
d3 |
d4 |
d5 |
d6 |
d7 |
d8 |
d9 |
d10 |
d11 |
d12 |
|
|
w1 |
610.15 |
666.77 |
648.61 |
671.65 |
699.80 |
683.62 |
651.12 |
626.16 |
639.43 |
596.00 |
669.83 |
641.15 |
|
w2 |
810.25 |
861.22 |
849.93 |
865.03 |
897.08 |
876.75 |
846.92 |
822.97 |
834.25 |
800.72 |
856.11 |
844.57 |
|
w3 |
450.86 |
511.21 |
485.07 |
517.20 |
538.63 |
528.75 |
494.80 |
470.22 |
485.21 |
431.25 |
524.68 |
475.25 |
|
w4 |
202.80 |
263.23 |
237.28 |
269.28 |
290.74 |
280.76 |
246.80 |
222.35 |
237.47 |
183.38 |
278.51 |
227.81 |
|
w5 |
463.62 |
521.44 |
487.40 |
528.20 |
538.33 |
537.96 |
505.90 |
484.88 |
500.25 |
439.17 |
546.65 |
475.38 |
|
w6 |
440.78 |
493.51 |
480.35 |
497.71 |
528.64 |
509.58 |
478.71 |
454.36 |
466.29 |
430.54 |
491.68 |
474.62 |
|
w7 |
470.11 |
523.31 |
509.61 |
527.58 |
558.26 |
539.46 |
508.41 |
483.97 |
496.05 |
459.39 |
521.91 |
503.68 |
|
W8 |
683.67 |
625.59 |
660.24 |
618.81 |
611.28 |
609.24 |
641.09 |
662.46 |
647.01 |
707.88 |
601.45 |
672.48 |
|
W9 |
522.61 |
462.81 |
495.50 |
456.22 |
444.35 |
445.77 |
478.89 |
501.78 |
486.30 |
545.73 |
443.25 |
507.37 |
|
W10 |
547.21 |
507.98 |
544.47 |
501.92 |
516.38 |
498.34 |
517.68 |
528.36 |
516.10 |
571.86 |
470.68 |
556.16 |
|
W11 |
390.02 |
349.75 |
386.30 |
343.69 |
358.58 |
340.15 |
359.59 |
370.82 |
358.28 |
414.89 |
312.56 |
398.04 |
|
W12 |
469.62 |
435.18 |
470.64 |
429.51 |
447.74 |
427.28 |
443.40 |
451.75 |
440.48 |
493.67 |
396.93 |
481.83 |
|
W13 |
364.47 |
314.49 |
351.79 |
307.83 |
314.19 |
301.49 |
327.29 |
343.65 |
329.25 |
389.81 |
281.56 |
364.19 |
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