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Dynamic lot sizing is the problem of determining the quantity and timing of ordering items while satisfying the demand over a finite planning horizon. This paper considers the problem with two practical considerations: minimum order size and lost sales. The minimum order size is the minimum amount of items that should be purchased and lost sales involve situations in which sales are lost because items are not on hand or when it becomes more economical to lose the sale rather than making the sale. The objective is to minimize the costs of ordering, item , inventory holding and lost sale over the planning horizon. To solve the problem, we suggest a heuristic algorithm by considering trade-offs between cost factors. Computational experiments on randomly generated test instances show that the algorithm quickly obtains near-optimal solutions.

We consider the problem of assigning ship assembly blocks to storage locations at a ship yard while allowing one-way movement of the blocks. The objective is to minimize the number of blocks obstructing other blocks’ movements. We show that the integer program in a previous study contains errors in identifying obstructive blocks and therefore, suggest another integer program without the error. Also, we suggest construction heuristics and a tabu search algorithm using properties characterizing optimal solutions of subproblems. Computational experiment results indicate that our heuristics outperform the existing algorithm in terms of solution quality.