# [SOLVED] Annual fixed cost

## [SOLVED] Annual fixed cost

Annual fixed cost The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:

Proposed Plant Annual Fixed Cost Annual Capacity
Detroit \$175,000 10,000
Toledo \$300,000 20,000
Denver \$375,000 30,000
Kansas City \$500,000 40,000

The company’s long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:

Distribution Center Annual Demand
Boston 30,000
Atlanta 20,000
Houston 20,000

The shipping cost per unit from each plant to each distribution center is shown in table below.

A network representation of the potential Martin-Beck supply chain is shown in figure below.

Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. Annual fixed cost Annual fixed cost Annual fixed costAnnual fixed cost

1. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)
 Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3
 Min fill in the blank 1x11 + fill in the blank 2x12 + fill in the blank 3x13 + fill in the blank 4x21 + fill in the blank 5x22 + fill in the blank 6x23 + fill in the blank 7x31 + fill in the blank 8x32 + fill in the blank 9x33 + fill in the blank 10x41 + fill in the blank 11x42 + fill in the blank 12x43 + fill in the blank 13x51 + fill in the blank 14x52 + fill in the blank 15x53 + fill in the blank 16y1 + fill in the blank 17y2 + fill in the blank 18y3 + fill in the blank 19y4
 s.t. fill in the blank 20x11 + fill in the blank 21x12 + fill in the blank 22x13 + fill in the blank 23y1 =≥≤<> fill in the blank 25 Detriot capacity fill in the blank 26x21 + fill in the blank 27x22 + fill in the blank 28x23 + fill in the blank 29y2 =≥≤<> fill in the blank 31 Toledo capacity fill in the blank 32x31 + fill in the blank 33x32 + fill in the blank 34x33 + fill in the blank 35y3 =≥≤<> fill in the blank 37 Denver capacity fill in the blank 38x41 + fill in the blank 39x42 + fill in the blank 40x43 + fill in the blank 41y4 =≥≤<> fill in the blank 43 Kansas City capacity fill in the blank 44x51 + fill in the blank 45x52 + fill in the blank 46x53 =≥≤<> fill in the blank 48 St. Louis capacity fill in the blank 49x11 + fill in the blank 50x21 + fill in the blank 51x31 + fill in the blank 52x41 + fill in the blank 53x51 =≥≤<> fill in the blank 55 Boston demand fill in the blank 56x12 + fill in the blank 57x22 + fill in the blank 58x32 + fill in the blank 59x42 + fill in the blank 60x52 =≥≤<> fill in the blank 62 Atlanta demand fill in the blank 63x13 + fill in the blank 64x23 + fill in the blank 65x33 + fill in the blank 66x43 + fill in the blank 67x53 =≥≤<> fill in the blank 69 Houston demand xij ≥ for all i and j; y1 =≥≤<> 0,101 , y2 =≥≤<> 0,101 , y3 =≥≤<> 0,101 , y1 + y2 =≥≤<> 0,101
2. Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)
 Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3
 Min fill in the blank 78x11 + fill in the blank 79x12 + fill in the blank 80x13 + fill in the blank 81x21 + fill in the blank 82x22 + fill in the blank 83x23 + fill in the blank 84x31 + fill in the blank 85x32 + fill in the blank 86x33 + fill in the blank 87x41 + fill in the blank 88x42 + fill in the blank 89x43 + fill in the blank 90x51 + fill in the blank 91x52 + fill in the blank 92x53 + fill in the blank 93y1 + fill in the blank 94y2 + fill in the blank 95y3 + fill in the blank 96y4
 s.t. fill in the blank 97x11 + fill in the blank 98x12 + fill in the blank 99x13 + fill in the blank 100y1 =≥≤<> fill in the blank 102 Detriot capacity fill in the blank 103x21 + fill in the blank 104x22 + fill in the blank 105x23 + fill in the blank 106y2 =≥≤<> fill in the blank 108 Toledo capacity fill in the blank 109x31 + fill in the blank 110x32 + fill in the blank 111x33 + fill in the blank 112y3 =≥≤<> fill in the blank 114 Denver capacity fill in the blank 115x41 + fill in the blank 116x42 + fill in the blank 117x43 + fill in the blank 118y4 =≥≤<> fill in the blank 120 Kansas City capacity fill in the blank 121x51 + fill in the blank 122x52 + fill in the blank 123x53 =≥≤<> fill in the blank 125 St. Louis capacity fill in the blank 126x11 + fill in the blank 127x21 + fill in the blank 128x31 + fill in the blank 129x41 + fill in the blank 130x51 =≥≤<> fill in the blank 132 Boston demand fill in the blank 133x12 + fill in the blank 134x22 + fill in the blank 135x32 + fill in the blank 136x42 + fill in the blank 137x52 =≥≤<> fill in the blank 139 Atlanta demand fill in the blank 140x13 + fill in the blank 141x23 + fill in the blank 142x33 + fill in the blank 143x43 + fill in the blank 144x53 =≥≤<> fill in the blank 146 Houston demand xij ≥ for all i and j; y1 =≥≤<> 0,101 , y2 =≥≤<> 0,101 , y3 =≥≤<> 0,101 , y3 + y4 =≥≤<> 0,101

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