Integrated mathematical and financial modeling with applications to product distribution, warehouse location and capacity problems



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Texas Tech University


The main objective of this study is to develop effective integrated models in product distribution system design. The integrated mixed Integer linear programming model developed in this paper concurrently assesses the optimal solution of interrelated problems. Conventional optimization models treat such problems separately. This research has combined the existing models of subproblems with minor modifications to achieve an overall objective. Existing models were drawn from the areas of production operations management, operations research, finance, and statistics. The research has produced general guidelines for:

  1. formulation of integrated decision models and their applications to product mix and distribution system design,
  2. warehouse location and capacity under diverse situations.

This thesis has contributed to production operations management and operations research decisions by developing integrated models with capabilities that serve to:

  1. provide a high degree of coordination, adaptability, and flexibility,
  2. provide cost-effective model usage,
  3. prevent suboptimality caused by treating the individual models separately.

The integrated decisions regarding which warehouses to operate and what quantity to ship from each warehouse have been the cornerstones of product distribution system design. The warehouse location problem has attracted much attention. Without warehouses, shipping direct from factory to customers may result in higher costs due to the inability to ship bulk and in long shipping time. Also, the warehouses act as collection points for several factories, thereby enabling a mix of products to be shipped to customers.

Existing warehouse location models do not integrate production decisions and are useful only to agencies or middlemen who are in the transportation or warehousing businesses, not producers themselves. The models that treat production problems individually may give suboptimal results and artificially-generated subjective supply figures; they suffer from the artificial restrictions Imposed by individual models such as subjectively predetermined supply figures, subjectively predetermined warehouse capacity ranges or meeting all the demand even when it is not profitable to do so. The integrated mixed Integer linear model developed in this research is more comprehensive. For this reason, there was a need for a more sophisticated and realistic integrated model capable of handling diverse problems without imposing the artificial restrictions mentioned above.

This research developed a unified and highly coordinated mixed integer programming model to address product mix, transportation, warehouse location, warehouse capacity and overcapacity Issues concurrently. This unified model allows insertion, deletion, and choice of individual models and it is very flexible. It has also been shown through test problems that profits were much higher using the integrated decision model developed in this paper than using conventional optimization techniques.

Finally, this study extended the warehouse location problem by analyzing various factors affecting warehouse location and distribution Analyzing techniques required experiments on the computer, followed by comprehensive mathematical proofs. The effects of an Increase or decrease in distances among possible warehouse sites on the degree of warehouse centralization were analyzed. In addition, the effects of changes in resource consumption of products were studied. The analysis ended with a study of relationship between warehouse location costs and warehouse distribution and appropriate conclusions were drawn.