Application of Integer Linear Programing

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Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, January 9 – 10, 2010

Application of Integer Linear Programming Model for Vendor
Selection in a Two Stage Supply Chain
A. John Rajan
Department of Mechanical and Production Engineering
Sathyabama University, Chennai, India
K. Ganesh
Senior consultant, Global Business Services, IBM India Private Limited, Mumbai, India K.V. Narayanan
Controller of Examinations, Sathyabama University, Chennai, India Abstract
Contemporary organizations rely on outsourcing for success in today’s competitive marketplace, and selecting a vendor is an important process as developing new products. Vendor selection is one of the most important decisions of purchasing function. As organizations become more dependent on vendors, the direct and the indirect consequences of poor decision-making become more severe. Literature shows many vendor evaluation models. In this paper we have proposed a vendor selection model using Integer Linear Programming (ILP) Model for multiproduct, multi-vendor environment. The contribution of this research lies in the implementation of this model as a customized decision support system according to the expectation of any company. The model is validated with a case study by implementing the model for Agricultural equipments whole sale company.

Key words
Vendor selection, Integer Linear Programming (ILP) Model, Supply chain, Vendor Assignment.

1. Introduction:
ILP is a linear programming model in which there a particular function to be maximized is or minimized subject to several constraints. As the unknown variables are all required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. 0-1 integer programming or binary integer programming (BIP) is the special case of integer programming where variables are required to be 0 or 1 (rather than arbitrary integers). In ILP problem constraints forces the variables to take on binary values only. Much of the modeling flexibility provided by integer linear programming is due to the use of 0-1 variables. In vendor selection, 0-1 variables provide selections or choices with the value of the variable equal to 1 if a vendor is assigned to supply a product and equal to 0 if the vendor is not assigned. The decision variables defined in this model will determine the allocation of the products to the vendors. In this paper, the integer linear programming (ILP) problem is applied to develop a supplier selection model that can fulfill the requirements of the company. Supplier selection is widely considered to be one of the most important responsibilities of the purchasing function of management. An organization's suppliers directly affect the price, quality, delivery reliability, and availability of its products--all of which have a profound impact on customer satisfaction. Determining the most suitable suppliers is an important problem to deal with when managing supply chain of a company. The main objective of supplier selection process is to reduce purchase risk, maximize overall value to the purchaser, and develop closeness and long-term relationships between buyers and suppliers. It is vital in enhancing the competitiveness of the company and has a positive impact on expanding the life span of the company. There are several supplier selection applications available in the literature. Given an appropriate decision setting, Mathematical Programming (MP) allows the decision-maker to formulate the vendor selection problem in terms of a mathematical objective function that subsequently needs to be maximized (e.g., maximize profit) or minimized (e.g., minimize costs) by varying the values of the variables in the objective function (e.g., the amount ordered with vendor X).

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Some of the mathematical programming models (Chaudhry et al 1993; Rosenthal et al 1995; Sadrian and Yoon 1994; Ganeshan...
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