Testing the Robustness of Linear Programming* Using a Diet Problem on a Multi-Shop System

Abstract

Time, raw materials and labour are some of the nite resources in the world. Due to this, Linear Programming* (LP) is adopted by key decision-markers as an innovative tool to wisely consume these resources. This paper test the strength of linear programming models and presents an optimal solution to a diet problem on a multi-shop system formulated as linear, integer linear and mixed-integer linear programming models. All three models gave different least optimal values, that is, in linear programming, the optimal cost was GHS15.26 with decision variables being continuous (R+) and discrete (Z+). The cost increased to GHS17.50 when the models were formulated as mixed-integer linear programming with decision variables also being continuous (R+) and discrete (Z+) and lastly GHS17.70 for integer linear programming with discrete (Z+) decision variables. The difference in optimal cost for the same problem under different search spaces sufficiently establish that, in programming, the search space undoubtedly affect the optimal value. Applications to most problems like the diet and scheduling problems periodically require both discrete and continuous decision variables. This makes integer and mixed-integer linear programming models also an effective way of solving most problems. Therefore, Linear Programming* is applicable to numerous problems due to its ability to provide different required solutions.