الگوریتم دوبعدی ثابت‌سازی–بهینه‌سازی برای حل مسئلۀ تعیین اندازۀ انباشته در سیستم‌های تولیدی انعطاف‌پذیر با محصولات همبسته

امروزه بیشتر صنایع تولیدی، با موجودی‌های درخور توجهی از مواد خام، محصولات نیم‌ساخته و کالاهای نهایی و همچنین تجهیزات، ماشین‌آلات، قطعات یدکی و نیروی انسانی مواجه‌اند که به علت عدم تعادل بین تامین یک کالا در یک محل با فروش یا مصرف آن ایجاد شده است. در برخی صنایع، تولید یک محصول به‌دلایل فیزیکی یا شیمیایی به تولید محصولات دیگر نیز منجر می‌شود که باید این همبستگی، در مدیریت موجودی‌ها لحاظ شود. همچنین با توجه به ویژگی‌هایی همچون زمان تحویل کوتاه، فشار هزینه‌ها و تغییرات متناوب در تقاضاها، صنایع بیش از گذشته به انعطاف‌پذیری در تولید نیاز دارند. با رشد سیستم‌های اتوماسیون صنعتی در کارخانه‌های تولیدی با محصولات همبسته، همچون پالایشگاه‌های نفت، نیاز به مدل‌سازی و ارائۀ راه حل برای این‌گونه مسائل، بیش‌ازپیش احساس می‌شود. در این مقاله، مسئلۀ تعیین اندازۀ انباشته در سیستم‌های تولیدی انعطاف‌پذیر با محصولات همبسته، مدل‌سازی و سپس با استفاده از برخی روابط بین متغیرها، این مدل ساده‌سازی شده است. یکی از روش‌های رایج حل مسائل اندازۀ انباشته، الگوریتم ثابت‌سازی–‌بهینه‌سازی است که بیشتر به‌صورت تک‌بعدی به کار گرفته می‌شود. در این پژوهش، یک الگوریتم دوبعدی برای حل این مسئله، پیاده‌سازی و با دو الگوریتم رایج تک‌بعدی، به کمک 63 سری دادۀ شبیه‌سازی‌شده مقایسه شد؛ نتایج نشان می‌دهد زمان رسیدن به جواب‌های این الگوریتم، از سایر الگوریتم‌های رایج بهتر است.

A Twodimensional Fix and Optimize Algorithm to Solve the Flexible Manufacturing System Lotsizing with Coproduction Problem

Purpose: In this paper, the flexible manufacturing system lotsizing with the coproduction problem is modeled. It is also simplified using the relationships between variables. One of the common methods for solving such problems is the fix and optimize algorithm, which is generally used in a onedimensional approach. Also, a twodimensional fix and optimize algorithm is applied to solve the problem. This algorithm is compared with two common algorithms using simulated data series. Design/methodology/approach: In this paper, Flexible Manufacturing System Lotsizing with Coproduction problem is modeled using mixedinteger programming. The production of products in this flexible system varies with the change of production mode, and a different mixture of products is produced for each production mode. Also, the planning interval includes T periods, and the demand for each product in each given period is constant. In each period, a fixed setup cost is added to the production and maintenance variable costs, if production occurs. The objective function of the model minimizes the sum of fixed setup costs and production and maintenance variable costs of inventory in each period and each production mode. Problem constraints include setup forcing constraints, inventory balance constraints, initial inventory constraints, coproduction constraints, production mode constraints, nonnegative variables constraints, and binary variable constraints. Among the methods proposed to solve this group of problems, the fix and optimize method is one of the most effective and general methods. The basic idea of ​​this approach is that due to the difficulty of solving the main problem with a longtime interval, a problem with a shorter time interval called the time window is solved instead. Except for the variables in the time window, other integer variables are considered continuous variables, so the resulting problem is easier to solve. In the following steps, the time window variables in the current step are assumed constant, and this repetition will continue until the end of the desired periods. Time windows can be considered with or without overlap. In this paper, two innovative onedimensional fix and optimize algorithms based on time and production mode variables and a new twodimensional algorithm based on time and production mode variables are applied to solve the model using simulated data at three levels of small, medium, and large scales. MATLAB 2016 software is used to code the algorithms of this study, and numerical calculations are performed by a personal computer with Intel®Core™i37100@3.90GHz processor and 8 GB RAM. Findings: The research results indicated the significant superiority of the proposed twodimensional algorithm in terms of response time over the two onedimensional algorithms. It is important to note that in terms of the quality of the answer in the studied problems, no significant difference was observed. Research limitations/implications: In many real cases, due to the fact that the cost parameters in different production situations (e.g., the oil, gas, and petrochemical downstream industries) are close to each other and in practice, determining production conditions in accordance with other parameters such as demand is independent of production costs, the efficiency of the proposed algorithm will be more visible in this article. The most important limitation in this study was the lack of real data for a flexible production system with correlated products, which is why simulated data were used to validate the model and test the proposed algorithms. Practical implications: In the future, researchers can use realtime case studies based on the proposed model and algorithms in this paper. They can also add other features to the model, such as limited production capacity and allowable shortages. Manufacturing plants that have features similar to this study can benefit from the findings to optimize production costs. Social implications Applying the results of this research can increase the productivity of production units and the use of nonrenewable energy resources. Originality/value: In this paper, a mathematical model (MILP) was proposed for the Flexible Manufacturing System Lotsizing with Coproduction problem. In addition, an innovative twodimensional fix and optimize algorithm was developed.