[SOLVED] The optimal production strategy

the optimal production strategy Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.

Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports ’N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports ’N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers.

 

Choose the correct network representation of this problem.

(i) (ii)
(iii) (iv)

 

Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. What is the optimal production strategy and shipping pattern for Sports of All Sorts? What is the minimum attainable transportation cost? If required, round your answers to two decimal places.

Let xij = units shipped from node i to node j.

Min fill in the blank 2
x1,4 + fill in the blank 3
x1,5 + fill in the blank 4
x1,6 + fill in the blank 5
x1,7 + fill in the blank 6
x2,4 + fill in the blank 7
x2,5 + fill in the blank 8
x2,6 + fill in the blank 9
x2,7 + fill in the blank 10
x3,4 + fill in the blank 11
x3,5
+ fill in the blank 12
x3,6 + fill in the blank 13
x3,7 + fill in the blank 14
x4,8 + fill in the blank 15
x4,9 + fill in the blank 16
x4,10 + fill in the blank 17
x5,8 + fill in the blank 18
x5,9 + fill in the blank 19
x5,10
+ fill in the blank 20
x6,8 + fill in the blank 21
x6,9 + fill in the blank 22
x6,10 + fill in the blank 23
x7,8 + fill in the blank 24
x7,9 + fill in the blank 25
x7,10

subject to
fill in the blank 26
x1,4 + fill in the blank 27
x1,5 + fill in the blank 28
x1,6 + fill in the blank 29
x1,7 ≤ fill in the blank 30
fill in the blank 31
x2,4 + fill in the blank 32
x2,5 + fill in the blank 33
x2,6 + fill in the blank 34
x2,7 ≤ fill in the blank 35
fill in the blank 36
x3,4 + fill in the blank 37
x3,5 + fill in the blank 38
x3,6 + fill in the blank 39
x3,7 ≤ fill in the blank 40
fill in the blank 41
x1,4 + fill in the blank 42
x2,4 + fill in the blank 43
x3,4 = fill in the blank 44
x4,8 + fill in the blank 45
x4,9 + fill in the blank 46
x4,10
fill in the blank 47
x1,5 + fill in the blank 48
x2,5 + fill in the blank 49
x3,5 = fill in the blank 50
x5,8 + fill in the blank 51
x5,9 + fill in the blank 52
x5,10
fill in the blank 53
x1,6 + fill in the blank 54
x2,6 + fill in the blank 55
x3,6 = fill in the blank 56
x6,8 + fill in the blank 57
x6,9 + fill in the blank 58
x6,10
fill in the blank 59
x1,7 + fill in the blank 60
x2,7 + fill in the blank 61
x3,7 = fill in the blank 62
x7,8 + fill in the blank 63
x7,9 + fill in the blank 64
x7,10
fill in the blank 65
x1,4 + fill in the blank 66
x2,4 + fill in the blank 67
x3,4 ≤ fill in the blank 68
fill in the blank 69
x1,5 + fill in the blank 70
x2,5 + fill in the blank 71
x3,5 ≤ fill in the blank 72
fill in the blank 73
x1,6 + fill in the blank 74
x2,6 + fill in the blank 75
x3,6 ≤ fill in the blank 76
fill in the blank 77
x1,7 + fill in the blank 78
x2,7 + fill in the blank 79
x3,7 ≤ fill in the blank 80
fill in the blank 81
x4,8 + fill in the blank 82
x5,8 + fill in the blank 83
x6,8 + fill in the blank 84
x7,8 ≥ fill in the blank 85
fill in the blank 86
x4,9 + fill in the blank 87
x5,9 + fill in the blank 88
x6,9 + fill in the blank 89
x7,9 ≥ fill in the blank 90
fill in the blank 91
x4,10 + fill in the blank 92
x5,10 + fill in the blank 93
x6,10 + fill in the blank 94
x7,10 ≥ fill in the blank 95
xij,yij ≥ 0

for all i and j.

Solving the formulation above, the optimal cost is $ fill in the blank 96
per week.

Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.)

 

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor. the optimal production strategy