An integer programming model with special forms for the optimum provision of needed manufactures with an application example

  • Authors:

  • Said A. Hassan;Seraj Y. Abed

  • Affiliations:

  • Industrial Engineering Dept., King Abdulaziz University, Jeddah, Saudi Arabia;Industrial Engineering Dept., King Abdulaziz University, Jeddah, Saudi Arabia

  • Venue:
  • TELE-INFO'07 Proceedings of the 6th WSEAS Int. Conference on Telecommunications and Informatics
  • Year:
  • 2007

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Abstract

Many practical problems are concerned with the provision of manufactured components; the provision can be done using three different methods, production in normal and over times, importing/storing, and subcontracting. The decision maker can evaluate the market demand, and the total cost elements. The problem is to determine how many components should be provided using different methods in order to accomplish the required demand and to minimize the total provision cost. A mathematical model for such a problem is formulated. The decision variables represent the number of components to be provided using different methods. The objective function is to minimize the total fixed and variable costs. A special (If-Then) form for the objective function is generated due to the fixed costs associated with some of the provision methods. Another combined (If-Then/Or) form for the objective function is generated due to the fixed cost associated with the subcontracting method. A third special form for the objective function is generated due to the stepped unit prices associated with the subcontracting method. The problem contains many different constraints: the provision of the total demand, the maximum capacity constraints, the overtime conditions, the construction of more prevision lines, the subcontracting stepping prices conditions. The steps of the used algorithm are summarized, and a real example of application is presented, the mathematical model has 9 construction integer decision variables and 11 additional 0-1 variables. The model is solved using LINGO 9.0 software package, and the final solution is obtained. The obtained optimal solution comprises two combined different provision methods, and saves SR 580,000 or 27,750,000 compared to other solutions using only one method of provision.