The basic steps of the transportation method are: 1. To set up the transportation table. 2. Examine whether total supply equals total demand. If not, introduce a dummy row/column having all its cost elements as zero and Supply/Demand as the (+ive) difference of supply and demand. 3. To find an initial basic feasible solution. An initial BFS for a TP with m sources and n destinations must include m+n–1 basic variables. This initial solution may or may not be optimal. Thus, the initial solution in the transportation method serves the same purpose as the ...

Operations Research approach of problem solving Optimization is the act of obtaining the best result under any given circumstance. In various practical problems we may have to take many technical or managerial decisions at several stages. The ultimate goal of all such decisions is to either maximize the desired benefit or minimize the effort required. We make decisions in our every day life without even noticing them. Decision-making is one of the main activity of a manager or executive. In simple situations decisions are taken simply by common sense, sound judgment and expertise without ...

Transportation problem is a particular class of linear programming, which is associated with day-to-day activities in our real life and mainly deals with logistics. It helps in solving problems on distribution and transportation of resources from one place to another. The goods are transported from a set of sources (e.g., factory) to a set of destinations (e.g., warehouse) to meet the specific requirements. In other words, transportation problems deal with the transportation of a single product manufactured at different plants (supply origins) to a number of different warehouses (demand ...

We see that the primal and the dual of linear programming are related mathematically, we can now show that they are also related in economic sense. Consider the economic interpretation of the duality of linear programming — first for a maximisation problem and then for a minimisation problem. The maximisation problem: Consider the following linear programming problem. The optimal solution to this problem dives production of 18 units of Xi and 8 units of x2 per week. It yields the maximum prof of a Rs. 1000, Maximise Z = 40x1 + 35x2, Subject to 2x1 + 3X2 < or = 60, Raw materials ...

Corresponding to every linear programming problem, there is another linear programming problem. The given problem is called the primal and the other its dual. Although the idea of duality is essentially mathematical, it has important interpretations. This can help managers in answering questions about alternative courses of action and their effect on values of the objective function. When the primal problem is of the maximisation type the dual is of the minimisation type and vice versa. It is an interesting feature of the simplex method that we can use it to solve either the original problem ...

FORMULATION OF LINEAR PROGRAMMING PROBLEM (LPP): Formulation of a Linear Programming Problem involves constructing a mathematical model from the given data. This can be done only if the following requirements are met: There should be a clearly identifiable objective and it should be measurable in quantitative terms. E.g. In a manufacturing problem the objective can be maximisation of profit or minimisation of cost. The resources to be allocated in the problem should be identifiable and quantitatively measurable. E.g. The use of labour time, or raw material in the manufacturing ...