Abstract
In real world decision making problems, the decision maker has to often optimize more than one objective, which might be conflicting in nature. Also, it is not always possible to find the exact values of the input data and related parameters due to incomplete or unavailable information. This work aims at developing a model that solves a multi objective distribution programming problem involving imprecise available supply, forecast demand, budget and unit cost/ profit coefficients with triangular possibility distributions. This algorithm aims to simultaneously minimize cost and maximize profit with reference to available supply constraint at each source, forecast demand constraint at each destination and budget constraint. An example is given to demonstrate the functioning of this algorithm.
Highlights
The distribution planning decision (DPD) problem involves optimizing the distribution plan for transporting goods from a set of sources to a set of destinations in a supply chain
This work aims at developing a model that solves a multi objective distribution programming problem involving imprecise available supply, forecast demand, budget and unit cost/profit coefficients with triangular possibility distributions
With a variety of distributing routes, the aim of the DPD problem is to determine how many units should be shipped from one source to one destination so that the available supply at each source and the forecast demand at each destination are satisfied
Summary
The distribution planning decision (DPD) problem involves optimizing the distribution plan for transporting goods from a set of sources to a set of destinations in a supply chain. In practical DPD problems, input data and related parameters, such as available supply, forecast demand and related cost/time/profit coefficients, are often imprecise (fuzzy) because of incomplete or (and) unavailable information. Chanas et al [4] presented a fuzzy linear programming (FLP) method to solve DPD problems with crisp cost coefficients and fuzzy supply and demand. Tien-Fu Liang [10] integrated the available concepts to solve multi-objective DPD problems involveing imprecise available supply, forecast demand and unit cost/time coefficients with triangular possibility distributions. We aim to solve a multi objective distribution programming problem which simultaneously minimizes cost and maximizes profit with reference to available supply constraint at each source, forecast de-. We have assumed the available supply, forecast demand, budget and related cost and profit coefficients to be imprecise with triangular possibility distributions. The proposed methodology can be applied to various real world multi objective problems such as assignment problems, transportation problems and many more such problems in which the information is given in the form of triangular possibility distributions
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