This article presents a new model and an efficient solution algorithm for a bi-objective one-dimensional cutting-stock problem. In the cutting-stock—or trim-loss—problem, customer orders of different smaller item sizes are satisfied by cutting a number of larger standard-size objects. After cutting larger objects to satisfy orders for smaller items, the remaining parts are considered as useless or wasted material, which is called “trim-loss.” The two objectives of the proposed model, in the order of priority, are to minimize the total trim loss, and the number of partially cut large objects. To produce near-optimum solutions, a two-stage least-loss algorithm (LLA) is used to determine the combinations of small item sizes that minimize the trim loss quantity. Solving a real-life industrial problem as well as several benchmark problems from the literature, the algorithm demonstrated considerable effectiveness in terms of both objectives, in addition to high computational efficiency.
The classical economic order quantity (EOQ) considers that the ordered items are of perfect quality. In this research, a model for the economic order quantity of imperfect quality items is developed, where the incoming lot has fractions of scrap and re-workable items. These fractions are considered to be random variables with known probability density functions. The demand is satisfied from perfect items and reworked items; whereas the scrap items are sold in a single batch at the end of the cycle with a salvage cost. A numerical analysis is provided to illustrate the sensitivity of the model to the fractions of scrap and reworked items.
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