Linear Programming Solution
The network diagram shown in Figure represents the transportation model of M/s GM Textiles units located at Chennai, Coimbatore and Madurai. GM Textiles produces ready-made garments at these locations with capacities 6000, 5000 and 4000 units per week at Chennai, Coimbatore and Madurai respectively. The textile unit distributes its ready-made garments through four of its wholesale distributors situated at four locations Bangalore, Hyderabad, Cochin and Goa. The weekly demand of the distributors are 5000, 4000, 2000 and 4000 units for Bangalore, Hyderabad, Cochin and Goa respectively.
The cost of transportation per unit varies between different supply points and destination points. The transportation costs are given in the network diagram.
The management of GM Textiles would like to determine the number of units to be shipped from each textile unit to satisfy the demand of each wholesale distributor. The supply, demand and transportation cost are as follows:
Transportation cost per unit
A linear programming model can be used to solve the transportation problem.
X11 be number of units shipped from source1 (Chennai) to destination 1 (B’lore).
X12 be number of units shipped from source1 (Chennai) to destination 2 (Hyderabad).
X13 number of units shipped from source 1 (Chennai) to destination 3 (Cochin).
X14 number of units shipped from source 1 (Chennai) to destination 4 (Goa) and so on.
Xij = number of units shipped from source i to destination j, where i = 1,2,……..m and, j = 1,2,………n.
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