An efficient algorithm for the capacitated single item dynamic lot size problem

Kırca, Ö.
A dynamic programming based algorithm is developed for the single item lot size problem with concave costs and arbitrary capacities. By making use of the extreme point properties of the problem, first the set of all feasible cumulative production levels that may occur in an optimal solution is generated. In the second stage, a dynamic programming procedure is carried out over this set. The worst case computational effort is equal to that of the standard dynamic programming approach but extensive computational tests with the algorithm indicate that for T period problems the computational effort does not exceed O(T4). The performance of the algorithm is compared with the performance of the existing procedures in the literature for the general, the constant capacity, and the constant unit cost problems. The computational results demonstrate that our algorithm is at least three times faster than the other procedures for all problem types considered.
European Journal of Operational Research


KIRCA, O; KOKTEN, M (Elsevier BV, 1994-06-09)
In this paper a framework for a new heuristic approach for solving the single level multi-item capacitated dynamic lot sizing problem is presented. The approach uses an iterative item-by-item strategy for generating solutions to the problem. In each iteration a set of items are scheduled over the planning horizon and the procedure terminates when all items are scheduled. An algorithm that implements this approach is developed in which in each iteration a single item is selected and scheduled over the planni...
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In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical epsilon-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical epsilon-constraint method on the bi-objective integer programming problem for the sake of comple...
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Koksalan, M; Karasakal, Esra (Informa UK Limited, 2006-05-01)
We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an inte...
Citation Formats
Ö. Kırca, “An efficient algorithm for the capacitated single item dynamic lot size problem,” European Journal of Operational Research, pp. 15–24, 1990, Accessed: 00, 2020. [Online]. Available: