Incorporating a Decision Maker’s Value Judgement in Linear Programing Formulation

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Author(s) H.G.Mu'azu | R.O. Afolabi
Pages 782-791
Volume 6
Issue 4
Date April, 2017
Keywords AHP, Decision Maker, Decision Variables, Linear Programming, Optimum Solutions, Priority, Value Judgment
Abstract

Conventional (tradition) linear programming (LP) formulation assumes that the decision variables have equal preferences. This assumption thus neglects the unequal preferences that a decision maker may consider in terms of attaching priorities to the decision variables. In this research, a modified form of LP model formulation was carried out. A furniture making company (producing six different furniture products)was used as a case study for the model formulation. The modified form incorporated the value judgment of a decision maker in terms of utility (priority) as a result of some criteria the decision maker uses in assessing the alternative decision variables. Analytic hierarchy process (AHP) was used to determine the priority rankings of the criteria and the decision variables derived from the subjective assessment made by the Proprietor of the company. Saaty’s 9-point scale was used to quantify the verbal assessment from which pairwise comparism matrices for both the criteria and the decision variables were developed. Ease of construction, Ease of delivery and sales patronage were identified as criteria the proprietor( owner) of the company uses in prioritizing the contribution of the decision variables to the optimum solution. Consequently, the overall weights and priorities ranking the six furniture products were determined as follows: 12 spring beds ( ) ranked first with weight of 0.3074, 10 spring beds ( ) ranked second with weight of 0.2893, wardrobes ( ) ranked third with weight of 0.1282, office chairs ( ) was ranked fourth with weight of 0.1188, office tables ( ) ranked fifth with weight of 0.0874 and upholstery chairs ( ) ranked sixth with weight of 0.0689. These weights were incorporated into both the objective function and the constraints simultaneously. The problem was formulated in two types: conventional LP formulation and the proposed LP-AHP formulation. Average monthly production schedules with associated average net profit were used as a bench mark for assessing the qualities of the optimum solutions obtained from the conventional LP formulation and the proposed LP-AHP. The optimum solutions obtained from the proposed formulation seem to provide more realistic solutions of the problem. Based on the outcome of the analyses of the results we therefore suggest that the value judgment of a decision maker should be incorporated into LP formulation.

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