In this paper, we address the temporal knapsack problem (TKP), a generalization of the classical knapsack problem, where selected items enter and leave the knapsack at fixed dates. We model the TKP with a dynamic prog...
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In this paper, we address the temporal knapsack problem (TKP), a generalization of the classical knapsack problem, where selected items enter and leave the knapsack at fixed dates. We model the TKP with a dynamic program of exponential size, which is solved using a method called successivesublimationdynamicprogramming (SSDP). This method starts by relaxing a set of constraints from the initial problem, and iteratively reintroduces them when needed. We show that a direct application of SSDP to the temporal knapsack problem does not lead to an effective method, and that several improvements are needed to compete with the best results from the literature. (C) 2021 Elsevier B.V. All rights reserved.
This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the successivesublimation Dynami...
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This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the successivesublimationdynamicprogramming (SSDP) method. Its major drawback is heavy memory usage to store dynamicprogramming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems.
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