Many different vendor selection models have been published in the purchasing literature. However there has been no systematic approach to compare the relative efficiency of the systems. In this paper we propose to use the concept of Total Cost of Ownership as a basis for comparing vendor selection models. We illustrate the comparison with the real life data set of the purchasing problem of ball bearings at Cockerill Sambre, a Belgian multinational company in the steel industry.Mathematical programming models outperform rating models and multiple item models generate better results than single item models from a Total Cost of Ownership perspective for this specific case study.
Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinational optimization problems.
The textbook Dantzig-Wolfe decomposition for the Capacitated Lot Sizing Problem (CLSP), as already proposed by Manne in 1958, has an important structural deficiency. Imposing integrality constraints on the variables in the full blown master will not necessarily give the optimal IP solution as only production plans which satisfy the Wagner-Whitin condition can be selected. It is well known that the optimal solution to a capacitated lot sizing problem will not necessarily have this Wagner-Whitin property. The columns of the traditional decomposition model include both the integer set up and continuous production quantity decisions. Choosing a specific set up schedule implies also taking the associated Wagner-Whitin production quantities. We propose the correct Dantzig-Wolfe decomposition reformulation separating the set up and production decisions. This formulation gives the same lower bound as Manne's reformulation and allows for branch-and-price. We use the Capacitated Lot Sizing Problem with Set Up Times to illustrate our approach. Computational experiments are presented on data sets available from the literature. Column generation is speeded up by a combination of simplex and subgradient optimization for finding the dual prices. The results show that branch-and-price is computationally tractable and competitive with other approaches. Finally, we briefly discuss how this new Dantzig-Wolfe reformulation can be generalized to other mixed integer programming problems, whereas in the literature, branch-and-price algorithms are almost exclusively developed for pure integer programming problems.
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