Abstract
This paper presents an algorithm to solve the multilevel location–allocation problem when sabotage risk is considered (MLLAP-SB). Sabotage risk is the risk that a deliberate act of sabotage will happen in a living area or during the transportation of a vehicle. This can change the way decisions are made about the transportation problem when it is considered. The mathematical model of the MLLAP-SB is first presented and solved to optimality by using Lingo v. 11 optimization software, but it can solve only small numbers of test instances. Second, two heuristics are presented to solve large numbers of test instances that Lingo cannot solve to optimality within a reasonable time. The original differential evolution (DE) algorithm and the extended version of DE—the modified differential evolution (MDE) algorithm—are presented to solve the MLLAP-SB. From the computational result, when solving small numbers of test instances in which Lingo is able to find the optimality, DE and MDE are able to find a 100% optimal solution while requiring much lower computational time. Lingo uses an average 96,156.67 s to solve the problem, while DE and MDE use only 104 and 90 s, respectively. Solving large numbers of test instances where Lingo cannot solve the problem, MDE outperformed DE, as it found a 100% better solution than DE. MDE has an average 0.404% lower cost than DE when using a computational time of 90 min. The difference in cost between MDE and DE changes from 0.08% when using 10 min to 0.54% when using 100 min computational time. The computational result also explicitly shows that when sabotage risk is integrated into the method of solving the problem, it can reduce the average total cost from 32,772,361 baht to 30,652,360 baht, corresponding to a 9.61% reduction.
Highlights
Managing logistics and operating costs is the most important issue for managers to think about.Operating a logistics system includes managing transportation and inventory
We present an modified DE (MDE) that is efficient at solving a multilevel location–allocation problem
We present an MDEthe that is efficient at optimal solvingsolution a multilevel location–allocation traditional
Summary
Managing logistics and operating costs is the most important issue for managers to think about. Shows that the most important problem for the industry is transporting oil palms in the three southern border provinces. Thongdee and Rapeepan (2015) successfully employed the original DE to solve the multilevel location–allocation problem (MLLAP) They used DE to find a good location to establish an ethanol plant using bagasse and tapioca waste as the raw material, and these two materials are delivered from the sugar factory and tapioca starch. Among the studies mentioned above, some add more intensification behavior to search more intensively in some interested areas (Sethanan and Rapeepan 2016a, 2016b), and some use more diversification with the original DE to enhance its capability to explore more searching space (Wang et al 2016; Yong et al 2018); both ways are successful. The paper is organized as follows: Section 2 presents the problem definition and mathematics in which the authors can see the whole body of the proposed problem; Section 3 presents the proposed heuristics in which the differential evolution (DE) algorithm is explained; and Sections 4 and 5 are the computational results and conclusion
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