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As we discussed just above, Transportation models deals with the transportation of a product manufactured at different plants or factories (supply origins) to a number of manufactured at different warehouses (demand destinations).

As we discussed just above, Transportation models deals with the transportation of a product manufactured at different plants or factories (supply origins) to a number of manufactured at different warehouses (demand destinations). The objective is to satisfy the destination requirements within the plant’s capacity constraints at the minimum transportation cost. Transportation models thus typically arise in situations involving physical movement of goods from plants to warehouses, warehouses to wholesalers, wholesalers to retailers and retailers to customers. Solution of the transportation models requires the determination of how many units should be transported from each supply origin to each demands destination in order to satisfy all the destination demands white minim sing the total associated cost of transportation

Consider a soft drink manufacturing firm, which has m plants located in

Let us consider the m-plant locations (origins) as O1, O2… Om and the n-retail markets (destination) as D1, D2… Dn respectively. Let ai ≥ 0, i= 1, 2 ….m, be the amount available at the ith plant-Oi. Let the

amount required at the jth market-Dj be bj ≥ 0, j= 1,2,….n.

Let the cost of transporting one unit of soft drink form ith origin to jth destination be Cij, i= 1, 2 ….m, j=1, 2….n. If Xij ≥ 0 be the amount of soft drink to be transported from ith origin to jth destination then the problem is to determine xij so as to Minimize the total cost of transportation, which is denoted as Z.

The above set of constraints represents ‘m+n’ equations in m X n non-negative variables. Each variable Xij appears in exactly two constraints, one is associated

with the origin and the other is associated with the destination. It allows us to put the above LPP in the matrix form, the elements of A are either 0 or 1.

A basic assumption is that the distribution costs of units from source i to destination j is directly proportional to the number of units distributed.

Moreover,

On the other hand,

For many applications, the supply and demand quantities in the model will have integer values and implementation will require that the distribution quantities also be integers. Fortunately, the unit coefficients of the unknown variables in the constraints guarantee an optimal solution with only integer values.

Tags : Operations Management - Transportation / Assignment & Inventory Management

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