مدل‌سازی مسئلۀ زمان‌بندی تک‌ماشین با تولید دسته‌ای و خرابی تصادفی و حل آن به‌وسیلۀ روش شاخه و کران

در این مقاله مسئلۀ زمان‌بندی تک‌ماشین با تولید دسته‌ای و خرابی تصادفی ماشین بررسی می‌شود. در این مسئله هر کار متعلق به یک خانوادۀ کار است و هر خانوادۀ کار زمان آماده‌سازی معلوم و مستقل از توالی دارد. همچنین فرض می‌شود یک خرابی ماشین در طول افق برنامه‌ریزی اتفاق می‌افتد و زمان شروع و طول تصادفی با توزیع احتمال دلخواه و از قبل مشخص دارد. تابع هدف مسئله حداقل‌سازی مجموع حداکثر زودکرد و حداکثر دیرکرد موردانتظار کارهاست. تاکنون در پژوهش‌های گذشته مطالعه‌ای بر این مسئله مشاهده نشده است. برای این مسئله یک مدل جدید برنامه‌ریزی عدد صحیح خطی مختلط توسعه داده شده است. با توجه به nphard بودن مسئله برای حل بهینۀ آن، یک الگوریتم شاخه و کران جدید با اصول غلبه و یک حد پایین کارا ارائه شده است که از یک الگوریتم ابتکاری جدید برای به دست آوردن حد بالا استفاده می‌کند. به‌منظور ارزیابی عملکرد الگوریتم‌های معرفی‌شده، تعداد 2520 عدد مسئلۀ نمونه طراحی و با الگوریتم‌های ارائه‌شده، حل شده است. نتایج محاسباتی نشان می‌دهد 98% مسائل نمونه در محدودۀ زمانی مشخص‌شده با الگوریتم شاخه و کران به‌صورت بهینه حل شده‌اند و میانگین درصد انحراف از جواب بهینه در الگوریتم ابتکاری ارا‌ئه‌شده کمتر از 30% است. این موارد کارایی الگوریتم‌های ارائه‌شده را تایید می‌کند.

modeling a single machine scheduling problem with batch production and the random breakdown and solving it by branch and bound method

purpose: scheduling of batch production and machine disruption are the two main challenges in manufacturing organizations. due to the complexity of production processes, many industries try to group jobs according to family criteria and use a common setup time to process every family. also, machine breakdown is an influential factor in the planning of production systems. in this paper, the problem of scheduling a single machine with family setup times and breakdowns is studied. it is assumed that there is a breakdown with an uncertain start time and duration based on the specified probability distribution functions during the planning horizon. the objective function of this problem is the sum of the expected maximum earliness and maximum tardiness.design/methodology/approach: for the problem under study, a new mixed integer linear programming model has been developed. due to the nphardness of the problem, a new branch and bound algorithm with the dominance rules and an efficient lower bound is presented for its optimal solving, which uses a new heuristic approach to achieve the upper bound.findings: to evaluate the performance of the introduced algorithms, 2520 instances were designed and solved with the presented algorithms. the computational results indicated that 98% of the instances were optimally solved in the specified time limitation by the branch and bound algorithm, and the average percentage of deviation from the optimal solution in the proposed heuristic approach was less than 30%. the results demonstrated the efficiency of the proposed algorithms.research limitations/implications: considering the newness of the problem investigated in this paper, the proposed instances and algorithms can be used as a basis for evaluating other solution methodologies in future research studies. also, considering other modes of machine failures such as scenariobased failures or rescheduling the jobs to minimize the deviations of the actual schedule from the planned program, situations with more than one machine such as parallel machines, flow shops, and job shops, other objective functions related to scheduling such as maximum completion time or total completion time, as well as the development of other exact, heuristic or metaheuristic algorithms are suggested as subjects for future study.practical implications: the problem studied in this paper can be attractive and practical for manufacturing organizations. industries such as automotive, ship and aircraft manufacturing, steel, telecommunication power supply manufacturing, electronic, computer processors, and all industries and systems that somehow deal with the batch production process and unexpected machine breakdowns, can benefit from the results of this research.social implications: because in this study, the starting and finishing times of machine breakdowns were predicted, by applying the results of this research, the production of defective products will be prevented when the machine breaks down, and this leads to the reduction of waste in the environment. also, according to the objective function defined in the problem investigated in this article, the implication of the results of this research in production environments leads to the reduction of earliness and tardiness costs, which in turn increases the work efficiency of human resources and as a result, increases the job satisfaction.originality/value: it seems no study has been conducted on the single machine scheduling problem with batch production, random breakdown, and the objective function of minimizing the sum of the expected maximum earliness and maximum tardiness of the jobs. particularly, innovations of this paper are threefold: i) a new mixed integer linear programming model was developed for the problem; ii) a novel heuristic approach was proposed to solve the problem, based on hill climbing (phc); and iii) a new branch and bound algorithm with the dominance rules and an efficient lower bound was presented to solve the problem optimally, which used the phc heuristic approach to achieve the upper bound.