neda manavizadeh
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Journal of Advances in Industrial Engineering, Volume:56 Issue: 2, Summer and Autumn 2022, PP 199 -214Governments use online platforms to keep track of transactions in the supply chain (SC) of subsidized foods to prevent fraud. Although regular checks of warehouses and documents were conducted, current platforms failed to resolve the issue. Blockchain technology (BT) provides governments with the ability to access transparent and real-time data to address these challenges. In this paper, we examine the key challenges influencing the implementation of a BT platform for managing subsidized food products in Iran. The barriers appear to be interconnected. We present a model that integrates the Best-Worst method (BWM) for obtaining independent weights and the Weighted Influence Non-Linear Gauge System (WINGS) using a rescaling scheme for considering the interrelatedness between the criteria. Expert opinions and literature reviews are used to identify critical factors. According to the findings, the costs of implementing and maintaining the system, as well as the regular restructuring of government rules regarding the data to be collected, are the two main challenges of implementing this new technology. Moreover, there are concerns about the cooperation with downstream entities of SC, cultural differences among partners, and their knowledge level, which may affect the complexity of downstream implementation. The results of sensitivity analysis show that WINGS gives greater weight to factors that have more impact on others. Conversely, the weight of factors that are interwoven with other factors and factors that aren't influenced by other factors is reduced as compared to the independent relative importance obtained from BWM.Keywords: subsidy, Block Chain Based Platforms, Supply Chain Management, Fraud detection, Best-Worst Method (BWM), Weighted Influence Non-Linear Gauge System (WINGS)
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Contrary to the past that inventory decisions and pricing are taken into consideration separately, due to the influence of these decisions on each other and thus profit, researchers have investigated these two issues simultaneously. Sometimes, wholesalers offer incentive financial policies to their customers in order to increase their sale. In this paper, a different combined model of inventory control and the way of its pricing for a deteriorating item with different incentive schemes including totally advance payment and partially advance, partially delayed payment are developed. We adopt a demand function jointly time and price-dependent and a backordering rate waiting time-dependent. Also shortage of allowable inventory considered. In each case, optimum price, replenishment cycle, the time with no shortage are obtained. Sensitivity analysis is performed and represented in several figures and tables. The results show that with increasing deterioration and backordering rates, the total annual profit is reduced.Keywords: Inventory control, pricing, advance payment, deterioration products, Delayed payment, variable demand function, partial backordering
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در واقعیت، گاهی خریداران تمام یا درصدی از قیمت محصول را قبل از دریافت آن می پردازند و گاهی عمده فروش به آن ها اجازه می دهد تا در بازه های زمانی مساوی پیش پرداخت را انجام دهند. مطالعه حاضر با در نظر گرفتن پیش پرداخت های متوالی، یک مدل ریاضی جدید برای محصولات با نرخ زوال غیر آنی ارایه می کند. در مدل موجودی پیشنهادی، کمبود بصورت ترکیبی از فروش از دست رفته و پس افت بطور همزمان می باشد. همچنین، مدل، پشتیبانی را کاملا وابسته به زمان انتظار برای چرخه بعدی می داند. علاوه بر این، شرایط مناسب برای دستیابی به راه حل های بهینه ایجاد و مثال های عددی برای تصدیق و ارزیابی نتایج و روش حل ارایه شده است. راهکارهای موثر برای کاهش هزینه کل سالانه بر اساس نتایج تحلیل حساسیت ارایه شده است.کلید واژگان: مقدار سفارش اقتصادی، پشتیبانی جزئی غیر خطی، زوال پذیری غیر آنی، پیش پرداخت، اقلام زوال پذیرIn real life conditions, the buyers sometimes pay all or a percentage of the product price before receiving it, and the wholesaler sometimes allows them to prepay it at equal intervals. The present study develops a new mathematical model for products with non-instantaneous deteriorating rates by considering consecutive advance payments. In the proposed inventory model, the shortage is consisting of lost sales along with backorders simultaneously. In addition, the model considers the backlogging as totally dependent on the waiting time for the further cycle. In addition, the appropriate conditions to achieve the optimal solutions have been developed, and numerical instances have been provided to verify and evaluate the results and solution method. The useful methods to effectively reduce the annual total cost are provided according to the results of the sensitivity analysis.Keywords: Economic order quantity, non-linear partial backordering, non-instantaneous deterioration, advance payments, Deteriorating items
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In this paper, a type II robotic mixed-model two-sided assembly line balancing problem is considered. This paper presents a new mixed-integer programming model for type II robotic mixed-model two-sided assembly line balancing to minimize the cycle time, energy consumption, and purchased cost of robots for a given number of workstations. We provided an effective framework for optimizing the multi-objective robotic mixed-model two-sided assembly line balancing problem considering energy consumption and smoothing workload in the make to order environment to help the decision makers make the right decisions under stochastic demand. An augmented epsilon constraint and Lp-metric methods applied to solve the problem, and then, with the help of defining two vertical and horizontal criteria, we attempt to help the decision maker to choose a more efficient solution to make the production line more smooth workload. We demonstrate the efficiency of the proposed method by designing the numerical experiments. ZZ ZZ ZZ ZZ ZZKeywords: Balancing, Energy consumption, Robotic Mixed-Model Assembly Line, Smoothing Workload, Two-Sided Assembly Line
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تبلیغات مشارکتی یک استراتژی بازاریابی است که در آن بخشی از سرمایه گذاری تبلیغاتی خرده فروش ها توسط تولیدکننده ها تامین می شود. در سال های اخیر، سرمایه گذاری میان گزینه های تبلیغاتی نیز به یک موضوع بازاریابی پیچیده ای تبدیل شده است. در این مقاله، مسئله تبلیغات مشارکتی با گزینه های تبلیغاتی در حالت دو دوره ای بررسی شده است که در آن سهم بازار در دوره دوم به تصمیمات دوره اول وابسته است. مسئله در دو حالت وجود و عدم وجود قرارداد تبلیغات مشارکتی حل شده و مقایسه شده است. تحلیل مدل با استفاده از مفاهیم تعادل نش، بازی استکلبرگ، بازی های تصادفی و برنامه ریزی پویا انجام شده است. نتایج محاسباتی حاصل از مثال های عددی نشان می دهد که در صورتی که قرارداد تبلیغات مشارکتی در ناحیه برنده-برنده پیشنهاد شود، سود بازیکنان بطور قابل توجهی افزایش پیدا می کند.
کلید واژگان: تبلیغات مشارکتی، تئوری بازی ها، بازی های تصادفی، گزینه های تبلیغاتیCooperative advertising is a cost-sharing mechanism in which a part of retailers' advertising investments are financed by the manufacturers. In recent years, investment among advertising options has become a difficult marketing issue. In this paper, the cooperative advertising problem with advertising options is investigated in a two-period horizon in which the market share in the second period depends on the decisions made in the first period. The problem is solved for two cases of the absence and presence of cooperative advertising contract, and the results are compared. The solution to the problem is presented using the concepts of the Nash equilibrium, Stackelberg game, stochastic games, and dynamic programming. The computational results using numerical examples show that if the cooperative advertising contract is offered in the win-win condition, the players’ profit will increase significantly.
Keywords: Cooperative advertising, Game theory, stochastic games, advertising options -
این پزوهش به طراحی شبکه ی جمع آوری زباله های خطرناک پرداخته و برای انجام این کار از مفاهیم مکانیابی، مسیریابی، موجودی و زنجیره ی لجستیک معکوس استفاده شده است. موارد مربوط به ریسک احداث مراکز و حمل مواد به عنوان پارامترهای اجتماعی در این پژوهش به عنوان یک تابع هدف جداگانه در کنار تابع هدف اقتصادی، در نظر گرفته شده است. مساله مورد نظر در قالب مدل برنامه ریزی خطی عدد صحیح مختلط با دو تابع هدف فرموله شده است. در نظر گرفتن سیاست موجودی با استفاده از تسهیلات موجود، و محدودیتهای زمانی ارسال و ظرفیت وسایل سیستم حمل نقل از جمله ویژگی های دیگر مدل میباشد. با توجه به پیچیدگی محاسباتی مدل ارایه شده، برای حل این مدل از دو الگوریتم فراابتکاری NSGA-II و MOPSO استفاده شده است و نتایج آنها با یکدیگر مقایسه شده اند. طبق نتایج، روش NSGA-II عملکرد بهتری را در هر چهار شاخص فاصله گذاری، فاصله از آرمان و بیشترین گسترش نشان میدهد. همچنین نتایج نشان میدهد که زمان حل این روش به طور متوسط 6% کمتر از روش حل رقیب میباشد. طبق نتایج حاصل از تحلیل حساسیت، هزینه های سیستم به ازای در نظر گرفتن ناوگان خارجی تغییرات بیشتری را نسبت به استفاده از ناوگان داخلی، از خود نشان میدهد.
کلید واژگان: لجستیک معکوس، مدیریت پسماند خطرناک، مکان یابی-مسیریابی-موجودی، بهینهسازی چند هدفه، روشهای فراابتکاریThis paper proposes a bi-objective model for the waste collection problem and considers the location, routing and inventory of the system simultaneously. Considering the reverse flow of the system is another feature of the current study. In the proposed model, the total costs of the system are minimized. In addition, the related risks of opening new centers and transportaion are included as the second objective function of the problem. Considering the delivery time and cpacity of vehicels constraints, are the other features of the model. Due to the NP-hardness of the model, two metaheuristic algorithms namely a non dominated sort ordering genetic algorithm (NSGA-II) and a multi objective particle swarm optimization algorithm (MOPSO) are applied to solve the problem. According to the results, NSGA-II is able to reach better answers in all the propsed metrics. According to sesitivity analysis, foreign transportation fleets make a great impact on the costs of the system.
Keywords: hazardous waste management, Reverse Logistic, location-routing-inventory, Multi-Objective Optimization, Metaheuristic Algorithms -
Journal of Optimization in Industrial Engineering, Volume:13 Issue: 28, Summer and Autumn 2020, PP 165 -183
This paper formulates a mathematical model for the Green Vehicle Routing Problem (GVRP), incorporating bi-fuel (natural gas and gasoline) pickup trucks in a mixed vehicle fleet. The objective is to minimize overall costs relating to service (earliness and tardiness), transportation (fixed, variable and fuel), and carbon emissions. To reflect a real-world situation, the study considers: (1) a comprehensive fuel consumption function with a soft time window, and (2) an en-route fuel refueling option to eliminate the constraint of driving range. A linear set of valid inequalities for computing fuel consumption were introduced. In order to validate the presented model, first, the model is solved for an illustrative example. Then each component of cost objective function is considered separately so as to investigate the effects of each part on the obtained solutions and the importance of vehicles speed on transportation strategies. Computational analysis shows that, despite the limitation of an appropriate service infrastructure, the proposed model demonstrated an average reduction of 44%, 6% and 5% in carbon emission costs, total distribution costs, and transportation costs respectively. Moreover, the study found paradoxical effects of average speed, suggesting the need to manage trade-offs: while higher speeds reduced service costs, they increased carbon emission costs. In the next stage, some experiments modified from the literature are solved. According to these experiments, in all instances greater objective function values for Gasoline vehicles are gained. The difference in the carbon emission objective is also significant, with an average of 44.23% increase. Finally, managerial and institutional implications are discussed.
Keywords: green vehicle routing, carbon emission, bi-fuel light truck, soft time window, green logistics -
این مقاله یک مدل جدید برای ساختار قرارداد مشارکتی تقسیم درآمد ارائه میکند. در ساختار مدل پیش رو، خرده فروش های موجود در سیستم تعیین کننده مقدار سفارشات مربوط به فروش میباشند. همچنین تولید کنندگان تعیین کننده قیمت محصول تحت شرایط عمده فروشی میباشند. پژوهش حاضر نتایج حاصل از استراتژی های مختلف را در ساختار زنجیره تامین مد نظر، مورد بررسی قرار میدهد. در ساختار قرارداد مشارکتی تقسیم درآمد حاضر، دو نوع بازی وابسته به خرده فروش و وابسته به تولید کننده در نظر گرفته شده است. به منظور بررسی عملکرد قرارداد حاضر، نتایج ان تحت سیاست عمده فروشی و قرارداد پایه مورد بررسی قرار گرفته است. به دلیل پیچیدگی مدل، برای حل آن از یک روش ترکیبی وابسته به الگوریتمهای ابتکاری استفاده شده است. همچنین بر روی پارامترهای اساسی مدل تحلیل حساسیت صورت گرفته است و طبق نتایج افزایش تقاضای وابسته به قیمت منجر به سفارش تعداد کمتری کالا از سوی خرده فروشان میشود.
کلید واژگان: زنجیره تامین، قرارداد مشارکتی، تقاضای وابسته به قیمتThis study proposes a novel option-revenue sharing coordination contract framework. In the proposed model, the retailer determines the number of order sales effort. The manufacturer sets the price of products for the wholesale strategy. The investigated supply chain problem analyzes the results of different strategies. In the proposed coordination contract problem, two types of games including retailer-based game and manufacturer-based Stackelberg game are considered. In both cases the retailer adopts the value of order and the sales effort and the manufacturer determines the wholesale price. To assess the performance of the proposed contract, a wholesale and a basic selection contract are considered in the model. To obtain the Nash equilibrium in the retailer-based state of the proposed option-revenue sharing coordination contract problem, a hybrid algorithm consisting of a heuristic and a genetic algorithm is proposed by considering the computational complexities of the proposed model. A numerical comparison between the proposed contract and other cases demonstrates that the option-revenue sharing contract significantly dominates the basic option and the wholesale price contract. Finally, we implemented some numerical experiments on the critical parameters of the contract. Based on the results, increasing the price-dependency of demand results in less number of products ordered by the retailer.
Keywords: Supply Chain Management, coordination, Option-Revenue Sharing Contract, Price-Sales Effort Dependent Demand -
This paper presents a novel multi-objective location arc-routing model in order to locate disposal facilities and to design optimal routes of residential waste taking into consideration many complicated real constraints such as a heterogeneous fleet of vehicles, time windows for customers, disposal facilities and the depot, capacities for vehicles and facilities. The first objective is the minimization of transportation costs, including service costs and fuel costs of vehicles. The second one minimizes total number of utilized vehicles. And finally, the third objective function is considered for minimizing total number of established disposal centers. Moreover, to come closer to reality the service time, amount of demands, capacities and cost parameters are considered as fuzzy ones. To solve the proposed model, a credibility-based fuzzy mathematical model and its interactive solution method with three recent approaches, are used and the results are compared with each other.
Keywords: Waste collection problem, multi-objective optimization, time windows, interactive fuzzy programming, chance constraint programming -
This study introduces a green location, routing and inventory problem with customer satisfaction, backup distribution centers and risk of routes in the form of a non-linear mixed integer programming model. In this regard, time window is considered to increase the customer satisfaction of the model and transportation risks is taken into account for the reliability of the system. In addition, different factors are detected as the major factors affecting the risk of routs and a fuzzy TOPSIS method is applied to rank the related risk factors. Next, due to the complexity of the investigated model, two algorithms including multi-objective gray wolf optimization algorithms (MOGWO) and Non-Dominated Sorting Genetic algorithm (NSGA-II) are applied to solve the large-sized instances. The results prove the superiority of MOGWO in dealing with large-sized instances. In the next step, some sensitivity analysis is implemented on the model based on a case study andthe related results of case study are reported as well.
Keywords: Location routing inventory, Green supply chain, backup strategy, Customer Satisfaction, Fuzzy TOPSIS, multi objective gray wolf optimization algorithm -
توازن ظرفیت ، به عنوان سطح میانی برنامه ریزی تولید سلسله مراتبی در سیستم های تولید ترکیبی MTS/MTO، تصمیمات مهم متعددی را شامل می شود. در این مقاله، دو مورد از این تصمیمات شامل یافتن بهترین استراتژی برای رد یا قبول سفارشات ورودی و تعیین موعد تحویل سفارشات، مورد بررسی قرار می گیرد. همچنین یک مدل شبیه سازی با هدف ارزیابی کارایی مدل عدد صحیح مختلط ارائه شده، تبیین می گردد. در نهایت، یک مطالعه موردی صنعتی در یک کارخانه فرآوری مواد غذایی مورد بررسی قرار می گیرد تا چارچوب ارائه شده مورد ارزیابی قرار گرفته و تحلیل حساسیت های مورد نیاز انجام گیرد.کلید واژگان: برنامه ریزی تولید، ساخت بر مبنای انبارش، ساخت بر مبنای سفارش، پذیرش سفارشات، شبیه سازی بهینه سازیCapacity coordination, as the tactical level of hierarchical production planning in hybrid MTS/MTO systems, includes numerous important decisions. In this paper, two of these decisions i.e. finding the best strategy for the acceptance/rejection of incoming orders and determining orders’ due dates – are investigated. Also a simulation model is proposed to evaluate the efficiency of the presented mixed integer model. Finally, an industrial case study is considered in a food processing plant to evaluate the proposed framework and conduct suitable sensitivity analysis.Keywords: Production planning, Make to stock, Make to order, Order Acceptance, Simulation Optimization
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Industrial hazardous materials (hazmat) are byproduct of industrial production and include hazardous goods, such as flammable, toxic and corrosive materials that pose a risk to the environment.Hazardous waste management includes collection, transportation, treatment, recycling and disposal of industrial hazardous material in an organized manner. With the increasing industrialization of countries, the issue of waste management is more important than before. Therefore, the main purpose of this research is to optimize locations of recycling centers and routing hazardous. The methods used to solve the mathematical model include the ε-constraint method and the NSGA II algorithm.First, we examine the validation of proposed model. Then, the optimal values of the parameters of multi-objective meta-heuristic algorithm are determined by Taguchi approach and the proposed algorithms are used to solve the given problem for 19 examples with different sizes. Finally, two algorithms are compared based on the fiveidentified criteria. In addition, the run time for both methods was calculated and large-scale results were presented based on the multi-objective genetic algorithm. The results show the efficiencyofmulti-objective genetic algorithm in solving given problem, and in particular for problems with larger sizes.Keywords: Multi-objective location-routing, hazardous waste management, multi-objective model
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Scientia Iranica, Volume:24 Issue: 5, 2017, PP 2550 -2566In this paper a dynamic cell formation problem is presented considering some new and special characteristics. The concept of machine requirement by lucky parts, the parts which are allowed to be produced in a specific period, is combined with the depreciable property of machines. Therefore, purchasing and selling of machines according to their book-value and generating income have been taken into account. This leads to a new vantage characteristic in cell formation where in each period we are only dealing with the types and number of machines required. The new mathematical model is presented and solved by exact and ant colony optimization methods for three problem sizes.Keywords: Dynamic cell formation, Dynamic production planning, Integrated mathematical model, Lot splitting, Ant colony optimization
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Mixed-model assembly line (MMAL) is a type of production line where a variety of products models similar to products characteristics is assembled in the same line. Many manufacturers tend to use mixed-model assembly line in their production lines, since this policy make possible to assemble various products with the Make to order (MTO) environment. In this research, the sequence of U-type mixed model assembly line is achieved through considering downstream help and kits storage as effective help policies for reducing total line stoppages and tardiness of products delivering time to customers. Since this problem, is NP-hard, hybrid GA-Beam search algorithm is developed to solve the problem. Numerical experiments are used to evaluate the performance and effectiveness of the proposed algorithm. To the best of our knowledge, this is the first study that considers getting help from downstream worker or using kits storage, which has ready to assemble parts in the conditions that workers cannot complete the remained task in the work horizon.Keywords: MMAL, MTO, Kit's storage, downstream help, Hybrid GA, Beam search
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Due to strict competition in the global market for Tourism services and Hotels in the tourism industry and also the importance of satisfying tourists, awareness about the efficiency of hotel for hotel owners and hotel managers is very important. The purpose of this paper is measuring performance of hotels in Crete by using Robust Data Envelopment analysis (RDEA) technique considering uncertain data. The proposed method of this paper develops a RDEA method with the consideration of uncertainty on output parameters. In order to use robust optimization methods in this article, after the introduction of input and output, we calculate the efficiency of 50 luxury hotel in Crete by means of GAMS software. The method is based on the adaption of robust optimization approaches proposed in the literature. Finally, we compare the performance achieved with previous research on these hotels and our results. It is found that the efficiency decreases, but the level of confidence increases.
Keywords: Data Envelopment Analysis, Uncertainty, robust, hotel efficiency -
در این مقاله، مساله ی طراحی شبکه زنجیره تامین به صورت برنامه ریزی ریاضی عدد صحیح مختلط فازی چندهدفه مدلسازی شده است که اهداف آن را بیشینه سازی ارزش خالص فعلی درآمد، کمینه سازی تاخیر دریافت محصول توسط مشتری و همچنین بیشینه سازی قابلیت اطمینان تامین کننده ها با در نظر گرفتن ریسک تقاضا، عرضه و اختلال تشکیل میدهند که از رویکرد برنامه ریزی امکانی تعاملی برای حل مدل ریاضی چندهدفه استفاده شده است. جهت اطمینان یافتن از سطح بالای عملکرد زنجیره تامین در صورت رخداد اختلال، شاخص استواری با استفاده از رویکرد مدلسازی مبتنی بر سناریوها، بکار گرفته شده است. همچنین به دلیل کمبود اطلاعات، در مدل ارائه شده برخی از پارامترهای اقتصادی همچون نرخ مالیات و نرخ تورم به صورت فازی در نظر گرفته شده اند. به دلیل پیچیدگی مدل ارائه شده، از الگوریتم ژنتیک برای حل مسائل با ابعاد بزرگ استفاده شده است. در پایان، عملکرد و کارایی مدل و روش پیشنهادی در قالب مثالهای عددی مورد بررسی قرار میگیرند.کلید واژگان: طراحی زنجیره تامین، برنامه ریزی عددصحیح مختلط چندهدفه، برنامه ریزی امکانی، جریان نقدی، روش TH، الگوریتم ژنتیکIn this paper, supply chain network design problem is modeled as a fuzzy multi objective mixed integer programming which seeks to locate the plants, DCs, and warehouses by considering disruption, supply and demand risk. Maximizing net present value of supply chain cash flow, minimizing delivery tardiness and maximizing reliability of suppliers are considered as objective functions in the proposed mathematic model. In order to have a more reliable model in case of disruption, the robustness measure is used in the model. Moreover, because of the lack of information, the economic factors such as tax rate, interest rate, and inflation are considered as uncertain factors in the model. An interactive possibilistic programming approach is applied for solving the multi-objective model. To solve larger size instances, genetic algorithm is proposed. Finally numerical examples are presented to show how the model works in practice.Keywords: Supply Chain Design, Multi Objective Programming, Possibilistic Programming, Business Cash Flow, TH Method, Genetic Algorithm
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In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods, both based on particle swarm optimization, were provided and ran for small and large class problems and their efficiency were demonstrated. Also, efficiency of binary PSO to general PSO was tested and BPSO was shown to outperform the general method. This approach can be used in railway transportation.Keywords: periodic vehicle routing, particle swarm optimization, binary particle swarm optimization, railway
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در این مقاله یک مسئله برنامه ریزی تولید چند دوره ای، چند محصولی، چند تسهیلاتی در نظر گرفته شده است که مقدار تقاضا و هزینه های نیروی انسانی در شرایط نبود قطعیت هستند. در مدل ریاضی جدید ارائه شده، سیستم تولیدی، با توجه به خرابی در محصولات دوباره کاری شده و خرابی ناگهانی ماشین ها در نظر گرفته شده است. همچنین تخصیص بهینه نیروی انسانی و هزینه های مربوط به آن در شرایط نبود قطعیت، به واسطه وجود بالانس بین سود شرکت و مزایای کارکنان بررسی می شوند. در این مقاله، الگوریتمی بر مبنای الگوریتم بهینه سازی استوار ارائه شده است که توانایی در نظر گرفتن نبود قطعیت را دارد. برای نشان دادن کاربردی بودن الگوریتم ارائه شده، یک مورد مطالعاتی واقعی در صنعت در نظر گرفته شده است. در ادامه، مهم ترین پارامترهای مدل استوار ارائه شده تحلیل شدند تا بهترین سطح نبود قطعیت که کمترین مقدار نقض در محدودیت را دارد، تعیین شوند. نتایج نشان می دهند که مدل ارائه شده موثر و کارا است و می تواند یک برنامه ریزی تولید بهینه را در شرایط نبود قطعیت ارائه دهد.
کلید واژگان: دوباره کاری، خرابی ناگهانی ماشین ها، نبود قطعیت، بهینه سازی استوار، الگوریتم بهینه سازی توده ذراتIn this paper، we consider a multi-site production planning problem subject to uncertainty in demand and workforce expenses. In our new mathematical model، we presented a production planning system considering failure in rework and breakdown. We also survey human workforce allocation and its expenses which are considered uncertain due to some tradeoff between company’s benefits and workforce union’s advantages. We presented a new robust particle swarm optimization to propose a model with the ability of handling uncertainties. Firstly، we apply the presented robust optimization to handle demand uncertainty separately، and then we extended our model to regard both uncertainties simultaneously. To show the practicability of the proposed algorithm، we solved a real problem in an industrial case study. We also analyzed the most important parameters in the presented robust model to find out which level of uncertainty has less constraint violation and determine the maximum budget of uncertainties that could be considered in the proposed model to expect acceptable optimal objective. The results showed that the proposed model can prepare a promising approach to fulfill an efficient production planning in a multi-site production planning.Keywords: Backlogging, Robust optimization, Uncertainty in labor cost, Production planning, Failure, Rework, Particle swarm optimization, Uncertainty in demand
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