Capacity Building for a Supply Chain in Process Industry

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An industrial company is considering the enlargement of its production capacity due to increases in demand in the last decade. To assist the company make the right decision about increasing its capacity, a mathematical decision model must be developed first. An Integer Programming Model is chosen for this case. Map.1. in the appendix shows the shipment routes for the supply chain.

The following VARIABLES represent the quantities that can be changed to produce the optimal value of the objective function:

Xthi: The amount of raw material shipped from supplier (h) to minor-plant (i) in year (t) Wtij: The amount of semi-product shipped from minor-plant (i) to main-production plant (j) in year (t) ZAtjk: The amount of product(1) shipped from main plant (j) to customer (k) in year (t) ZBtjk: The amount of product(2) shipped from main plant (j) to customer (k) in year (t)

Chi: The cost of shipping from (h) to (i) per unit
Cij: The cost of shipping from (i) to (j) per unit
Cjk: The cost of shipping from (j) to (k) per unit

Mh: the capacity of raw material (h) supplied.
Mi: the capaciy of semi-product (i) prduced.
Mtj: the capacity of products1-2 produced at plant j at year (t)

Where; h = 1,2,3,4,5,6. i = 1,2,3,4,5. j = 1,2,3,4,5,6,7,8,9. t =1,2,3 k = 1,2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14.

{ 1 if a minor plan is built in Adana
Y1 = { 0 otherwise

{ 1 if a minor plan is built in Bursa
Y2 = { 0 otherwise

{ 1 if a minor plan is built in Eskişehir
Y3 = { 0 otherwise

{ 1 if a new capacity of 37,500 units(2011) is built in Afyon Y4= { 0 otherwise

{ 1 if a new capacity of 37,500 units(2011) is built in GaziAntep Y5 = { 0 otherwise

{ 1 if a new capacity of 37,500 units(2011) is built in Samsun Y6 = { 0 otherwise

{ 1 if a new capacity of 50,000 units(2011) is built in Afyon Y7 = { 0 otherwise

{ 1 if a new capacity of 50,000...
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