We study the profit oriented partial disassembly line balancing problem, which simultaneously determines (i) the parts whose demand is to be fulfilled to generate revenue,(ii) the tasks that will release the selected parts under task and station costs, (iii) the number of stations that will be opened, (iv) the cycle time, and (v) the balance of the disassembly line, i.e. the feasible assignment of selected disassembly tasks to stations such that various types of precedence relations among the tasks are satisfied. We characterize the precedence relation types in disassembly and provide a mixed integer programming formulation of the problem. We propose a linear programming based lower and upper bounding scheme.Computational results show that our approach provides near optimal solutions for small problems and is capable of solving larger problems with up to 320 disassembly tasks in reasonable time.

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Abstract:In this study, we present a new formulation for the air defense problem of warships in a naval task group and propose a solution method. We define the missile allocation problem (MAP) as the optimal allocation of a set of surface-to-air missiles (SAMs) of a naval task group to a set of attacking air targets. MAP is a new treatment of an emerging problem fostered by the rapid increase in the capabilities of anti-ship missiles (ASMs), the different levels of air defense capabilities of the warships against the ASM threat, and new technology that enables a fully coordinated and collective defense. In addition to allocating SAMs to ASMs, MAP also schedules launching of SAM rounds according to shoot-look-shoot engagement policy or its variations, considering multiple SAM systems and ASM types. MAP can be used for air defense planning under a given scenario. As thorough scenario analysis would require repetitive use of MAP, we propose efficient heuristic procedures for solving the problem.