International Journal of Technical Research and Applications e-ISSN: 2320-8163, www.ijtra.com Volume 1, Issue 3 (july-aug 2013), PP. 95-102 95 | Page IMPROVEMENT OF SUPPLY CHAIN MANAGEMENT BY MATHEMATICAL PROGRAMMING APPROACH R.K.VERMA 1 , K.M.MOEED 2 , K.G.SINHA 3 , KAPIL CHOPRA 4 1 Research scholar, Integral University 2 Associate Professor, Integral University 3 Assistant Professor SR Institute of Management and Technology 4 Assistant Professor BNCET, Lucknow Department of Mechanical Engineering Abstract —this paper analyses the case of any production system by mathematical programming approach of a model for the existing or a new industry we can analyze the different aspects of manufacturing costs and then by using various techniques we can minimize the total cost from one end to another end so that the manufacturing cost decreases and profit increases. Index Terms—supply chain management, productivity, mathematical programming approach. (key words) I. INTRODUCTION Mathematical programming is one of the best tool available for quantitative decision making. The general purpose of mathematical programming is to find out an optimal solution for available allocation of limited resources to perform competing activities. The optimality may be defined with respect to important performance evaluation criteria, such as cost, time, and profit. Mathematical programming uses a compact mathematical model for describing the problem of concern. The solution is searched among all feasible alternatives for finding out optimal solution. The search is executed in an intelligent manner, allowing the evaluation of problems with a large number of feasible solutions for decision making. Mathematical programming finds many applications in supply chain management, at all decision-making levels. It is also widely used for supply chain configuration purposes. Out of several classes of mathematical programming models, mixed-integer programming models are used most frequently. Other types of models, such as stochastic and multi-objective programming models, are also emerging to handle more complex supply chain configuration problems. Although these models are often more appropriate, computational complexity remains an important issue in the application of mathematical programming models for supply chain configuration. This investigation is aimed to describe application of mathematical programming for supply chain configuration. It is followed by a description of generic supply chain configuration mixed integer programming model. Computational approaches for solving problems of large size are also discussed along with typical modifications of the generic model, especially, concerning global factors. II. FUNDAMENTALS Mathematical programming models are used to optimize decisions concerning execution of certain activities subject to resource constraints. Mathematical programming models have a well-defined structure. They consist of mathematical expressions representing objective function and constraints. The expressions involve parameters and decision variables. The parameters are input data, while the decision variables represent the optimization outcome. The objective function represents modelling objectives and makes some decisions more preferable than others. The constraints limit the values that decision variables can assume. The main advantages of mathematical programming models are that they provide a relatively simple and compact approximation of complex decision-making problems, an ability to efficiently find an optimal set of decisions among a large number of alternatives, and supporting analysis of decisions made. Specifically, in the supply chain configuration problem context, mathematical programming models are excellent for modelling its special aspects. There are also some important limitations. Mathematical programming models have a lower level of validity compared to some other types of models particularly, simulation. In the supply chain configuration context, mathematical programming models have difficulties representing the dynamic and stochastic