International Journal of Industrial Engineering & Production Research

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One of the basic assumptions of classical production-inventory models is that all products are of perfect quality. However, in real manufacturing situations, the production of defective items is inevitable, and a fraction of the items produced may be naturally imperfect. In fact, items may be damaged due to production and/or transportation conditions in the manufacturing process. On the other hand, some reworkable items exist among imperfect items that can be made perfect by additional processing. In addition, the classical production-inventory models assume that there is only one product in the system and that there is an unlimited amount of resources. However, in many practical situations, several products are produced and there are some constraints related to various factors such as machine capacity, storage space, available budget, number of allowable setups, etc. Therefore, we propose new constrained production-inventory models for multiple products where the manufacturing process is defective and produces a fraction of imperfect items. A percentage of defective items can be reworked, and these products go through the rework process to become perfect and return to the consumption cycle. The goal is to determine economic production quantities to minimize the total cost of the system. The analytical solutions are each derived separately by Lagrangian relaxation method, and a numerical example is presented to illustrate and discuss the procedure. A sensitivity analysis is performed to investigate how the variation in the inputs of the models affects the total cost of the inventory system. Finally, some research directions for future works are discussed.

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This paper designs a Scenario analysis approach to determine the joint production policy for two products under possible substitution. The Scenario analysis is designed to improve decision making by considering possible outcomes and their implications. The traditional multi-products production models assume that there is no possible substitution between products. However, in real-world cases, there are many substitutable products where substitution may occur in the event of a product stock-out. The proposed model optimizes production quantities for two products under substitution with the aim of minimizing the total cost of inventory system, including setup and holding costs, subject to a resource constraint. To analyze the problem, four special Scenarios are derived and discussed in detail. Furthermore, the total cost functions are derived for each Scenario separately, and then a solution procedure is suggested based on the Scenarios developed. The numerical examples are implemented, and the results are discussed in detail.

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Integrated treatment planning for cancer patients has high importance in intensity modulated radiation therapy (IMRT). Direct aperture optimization (DAO) is one of the prominent approaches used in recent years to attain this goal. Considering a set of beam directions, DAO is an integrated approach to optimize the intensity and leaf position of apertures in each direction. In this paper, first, a mixed integer-nonlinear mathematical formulation for the DAO problem in IMRT treatment planning is presented. Regarding the complexity of the problem, two well-known metaheuristic algorithms, particle swarm optimization (PSO) and differential evolution (DE), are utilized to solve the model. The parameters of both algorithms are calibrated using the Taguchi method. The performance of two proposed algorithms is evaluated by 10 real patients with liver cancer disease. The statistical analysis of results using paired samples t-test demonstrates the outperformance of the PSO algorithm compared to differential evolution, in terms of both the treatment plan quality and the computational time. Finally, a sensitivity analysis is performed to provide more insights about the performance of algorithms and the results revealed that increasing the number of beam angles and allowable apertures improve the treatment quality with a computational cost.