چکیده:
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 تأمین 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 ۶۳ سری دادۀ شبیهسازیشده مقایسه شد؛ نتایج نشان میدهد زمان رسیدن به جوابهای این الگوریتم، از سایر الگوریتمهای رایج بهتر است.
Purpose: In this paper, the flexible manufacturing system lot-sizing with the co-production 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 one-dimensional approach. Also, a two-dimensional 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 Lot-sizing with Co-production problem is modeled using mixed-integer 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, co-production constraints, production mode constraints, non-negative 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 one-dimensional fix and optimize algorithms based on time and production mode variables and a new two-dimensional 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™i3-7100@3.90GHz processor and 8 GB RAM. Findings: The research results indicated the significant superiority of the proposed two-dimensional algorithm in terms of response time over the two one-dimensional 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 real-time 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 non-renewable energy resources. Originality/value: In this paper, a mathematical model (MILP) was proposed for the Flexible Manufacturing System Lot-sizing with Co-production problem. In addition, an innovative two-dimensional fix and optimize algorithm was developed.
خلاصه ماشینی:
An effective multi-objective particle swarm optimization for the multi-item capacitated lot-sizing problem with set-up times and backlogging.
Hybrid matheuristics to solve the integrated lot sizing and scheduling problem on parallel machines with sequence-dependent and non-triangular setup.
Effective matheuristics for the multi-item capacitated lot-sizing problem with remanufacturing.
A fix-and-optimize approach for the multi-level capacitated lot sizing problem.
A relax-and-fix heuristic approach for the capacitated dynamic lot sizing problem in integrated manufacturing/remanufacturing systems.
Model formulations for the capacitated lot-sizing problem with service-level constraints.
1 Muckstadt, , & Sapra 2 Co-production 3 Kalay, & Taşkın 4 Wiedemann 5 Flexible manufacturing system 6 Shivanand 7 Remanufacturing 8 Cunha 9 Taş 10 Tavaghof-Gigloo, & Minner, 11 van Pelt & Fransoo 12 Jauhari, & Laksono 13 Wu 14 de Armas, , & Laguna 15 Vincent 16 Carvalho, & Nascimento 17 Ben Ammar 18 Bayley 19 Gören, & Tunali 20 Carvalho, & Nascimento 21 Service-level constraints 22 Batch Ordering 23 Stadtler, & Meistering 24 Cardona-Valdés 25 Prasad & Jayswal 26 Eimaraghy 27 Groover 28 Co-products 29 Ağralı 30 Suzanne 31 Cunha 32 Devoto 33 Bo 34 Fix and Optimize Heuristic 35 Flexible Manufacturing System Uncapacitated Lot sizing Problem with Co-production 36 Large-time bucket 37 Small-time bucket 38 Capacitated Lot-sizing Problem 39 Kang 40 Discrete Lot-sizing and Scheduling Problem 41 Fleischmann 42 The General Lot-sizing and Scheduling Problem 43 Fleischmann and Meyr 44 Sel, & Bilgen 45 Special-purpose heuristics 46 Schulz 47 Time window 48 Overlapping 49 Non-overlapping 50 Federgruen 51 Helber and Sahling 52 Xiao 53 Relax&Fix 54 Goren 55 Toledo 56 Production status, Production Mode