Multi-objective Linear Programming Model Research Articles

Modelling and simulation of energy consumption of ceramic production chains with mixed flows using hybrid Petri nets

Ceramic production chain consisting of discrete flow and continuous flow energy-intensive processes consumes substantial amounts of energy. This study aims to evaluate energy consumption performance and energy-saving potentials of the ceramic production chain. According to the energy consumption characteristics of manufacturing processes and process interaction constraints in a ceramic production chain, an approach integrating the first-order hybrid Petri net (FOHPN) model, an objective linear programming model and a sensitivity analysis is proposed. The FOHPN model will simulate the energy consumption patterns of the ceramic production chain. Meanwhile, multi-objective linear programming model and sensitivity analysis will suggest the optimal specific energy consumption (SEC) of the production chain and identify the influences of input parameters (i.e. production rate of a process) on the SEC in the optimal production scheme. Finally, a real case study from bathroom ceramic plant validates the approach. It provides a tool for modelling and simulation of energy consumption of ceramic production chains with mixed flows and helps operators to perform energy-saving actions in the ceramic enterprise.

A fuzzy multi-objective linear programming model for solving remanufacturing planning problems with multiple products and joint components

Remanufacturing planning issues involve extremely complex strategic decisions within the supply chain system, especially considering the multiple products and joint components that are involved. It is very important to know how to determine the appropriate amounts of procurement quantity and lot size. In actual lot-sizing production-to-order problems for recoverable remanufacturing systems, input data or parameters are often imprecise or fuzzy. This work develops a fuzzy multi-objective linear programming (FMOLP) model that simultaneously minimizes total costs, lead time and CO2 emissions with reference to multiple products and joint components. The proposed model evaluates cost-effectiveness, lead time and CO2 emissions, while integrating multi-products, multi-suppliers, multi-components, joint components and multi-machines into one remanufacturing production system. The analytical results presented in this work are able to assist decision-making managers to better understand systematic analyses, and the potential for cost-effectiveness, lead time and CO2 emissions in recoverable remanufacturing planning.

OPTIMAL LOT-SIZING DECISIONS WITH INTEGRATED PURCHASING, MANUFACTURING AND ASSEMBLING FOR REMANUFACTURING SYSTEMS

This work applies fuzzy sets to the integration of purchasing, manufacturing and assembling of production planning decisions with multiple suppliers, multiple components and multiple machines in remanufacturing systems. The developed fuzzy multi-objective linear programming model (FMOLP) simultaneously minimizes total costs, total $text{CO}_2$ emissions and total lead time with reference to customer demand, due date, supplier/manufacturer capacity, lot-size release and machine yield. The proposed FMOLP model provides a recoverable remanufacturing framework that facilitates fuzzy decision-making, enabling the decision maker (DM) to adjust interactively the membership function or parameters during the solution procedure to obtain a preferred and satisfactory solution. To test the model, it was implemented in various scenarios with a remanufacturing production system. The analytical results in this work can help planner by enabling systematic analysis of the cost-effectiveness of remanufacturing systems and their potential for improving $text{CO}_2$ emissions and lead time in terms of remanufacturing planning. Future investigations may apply the related patterns of non-linear membership functions to develop an actual remanufacturing planning decision.

Optimizing land use pattern to reduce soil erosion

Soil erosion hazard is one of the main problems can affect ecological balance in watersheds. This study aimed to determine the optimal use of land to reduce erosion and increase the resident's income of Qushchi watershed in West Azerbaijan province, Iran. Income and expenses for the current land uses were calculated with field studies. Damages resulting from the soil erosion were estimated by soil depth equal to the specified land uses. For three different options including the current status of land uses without and with land management, and the standard status of land uses, multi-objective linear programming model was established by LINGO software. Then the optimization problem of the land use was solved by simplex method. Finally, the best option of land use was determined by comparing erosion rate and its cost in each scenario. Then the circumstances and the recommended conditions were compared. The results indicated that the current surface area of current land uses is not suitable to reduce erosion and increase income of residents and should change in the optimum conditions. At the optimum level, there should change horticulture area of 408 to 507 (ha), irrigated land area of 169 to 136 (ha) and dry farming of 636 to 570 (ha), while conversion of rangeland area not indispensable. In addition, the results showed that in case of the optimization of land use, soil erosion and the profitability of the whole area will decrease 0.75% and increase 3.68%, respectively. In case of land management practices, soil erosion will decrease 42.27% and the profitability increase 21.39% while in the standard conditions, soil erosion will decrease 60.95% and profitability will increase 24.20%. The results of the sensitivity analysis showed that the changes in the horticulture and range land areas have the greatest impact on the increasing profitability and reducing soil erosion of Qushchi watershed. So, it is recommended using Education and Extension to promote the importance of land management to understand how proper use of the land.

An integrated approach with SEM, fuzzy-QFD and MLP for supply chain management strategy development

This study proposes an integrated approach to determine the most suitable strategies, based on structural equation modelling (SEM), fuzzy-QFD, and multi-objective linear programming model (MLP). The relationships between supply chain capabilities, competitive advantages, and business performance are identified using SEM. An integrated SEM and fuzzy-QFD approach is proposed to transform the significant factors into SCM strategies. Then, MLP model is applied to identify suitable strategic actions according to multiple conflicting objectives under a budget constraint. A case study from the Vietnamese food industry is given to illustrate the proposed methodology. The outcome of the study reveals that companies should pay more attention to supply chain capabilities for SCM strategy development, which can help to gain improvement of their competitiveness and business performance. The proposed methodology also provides a comprehensive picture for companies by transforming such relationships into specific SCM strategic actions to obtain the optimal solution according to their preference.

Multi-product dynamic advertisement planning in a segmented market

In this paper, a dynamic multi-objective linear integer programming model is proposed to optimally distribute a firm?s advertising budget among multiple products and media in a segmented market. To make the media plan responsive to the changes in the market, the distribution is carried out dynamically by dividing the planning horizon into smaller periods. The model incorporates the effect of the previous period advertising reach on the current period (taken through retention factor), and it also considers cross-product effect of simultaneously advertising different products. An application of the model is presented for an insurance firm that markets five different products, using goal programming approach.

Planning decisions for recycling products containing hazardous and explosive substances: A fuzzy multi-objective model

The rapid development of modern technology leads to the rapid consumption of natural resources, which in turn causes an increasing accumulation of waste materials. Manufacturers must now assume the responsibility for reclamation, recycling and disposal of their products that have reached the end of their life cycles. During the product recycling process, the detection and disposal of explosive substances must be performed with the utmost caution. This study proposes a fuzzy multi-objective linear programming model for use in planning of recycling processes for products that contain hazardous and explosive substances. Application of the proposed model has been carried out in a middle-sized factory, where various products that have completed their life cycles or has become inoperative are delivered to the factory at uncertain times from various warehouses. Results from the proposed model have been obtained using the system data to solve problems on various scales. A hybrid Monte Carlo simulation has been used to obtain Pareto-optimal solutions to solve the model. The planning model is shown to differ from the recycling production planning model in terms of its consideration of the explosion risk and the limitations and goals related to this risk; this model provides considerable flexibility for both the recycling process and the planning decisions taken for this process.

Fuzzy multi-objective decision model for calibration supplier selection problem

Quality products and competitively priced services are crucial in today’s global markets. To provide quality at an acceptable price, companies seek out not only raw material and product suppliers but also calibration services suppliers. The calibration of measurement devices is one of the ISO9001 standard requirements for quality. Although companies select and manage their calibration processes as economically as possible, cost is not their only selection criterion. Technical capability, documentation competence, performance history, warranties, and communications are also considered when selecting calibration suppliers. There are numerous criteria and methods in the current literature on supplier selection, but few studies have specifically examined the selection of calibration suppliers.This paper is the first study that specifically examines the selection process for calibration suppliers by utilizing selection criteria that were researched and presented prior to this study. Due to the varied linguistic expressions of criteria and the uncertain model parameters, this paper presents a fuzzy approach for selecting a calibration supplier. The model contains relevant calibration service quality parameters such as the weight of criteria, cost, calibration time, demand, technical capability, and number of experts. This study proposes a fuzzy multi-objective linear programming model that assigns the calibration supplier to the measurement device using two objectives: maximizing the fuzzy weight of the criteria and minimizing the fuzzy calibration cost through fuzzy calibration time, the number of certified experts, the technical capability of the company, and the measurement device demand. A two-phase approach is used to solve the fuzzy multi-objective decision model. Weight, cost, and calibration time are handled as fuzzy numbers for modelling the imprecise data. In an actual application, calibration suppliers are selected for 20 measurement device types and 161 measurement devices with the fuzzy multi-objective linear programming model.

A Resource-Constrained Project Scheduling Problem with Fuzzy Activity Times

This paper is about the Resource-Constrained Project Scheduling Problem) RCPSP) which is one of the most important problems in last three decades and many researchers have paid attention to it and have reached useful results. In this paper, to cope with uncertainty issue, the RCPSP is studied under fuzzy environment where activity times are assumed to be fuzzy numbers. For this problem with fuzzy numbers as activity times, a linear mathematical programming model is presented. The objective function of the model is minimizing the completion time of project. Since the activity times are fuzzy numbers, finish time is also a fuzzy number. Hence, the model is transformed to a crisp multi-objective linear programming model. To illustrate the solution method, a numerical example is solved under both fuzzy and crisp environment and the results are compared. To prove the efficiency of the proposed method the results of the proposed solution method, some benchmark problems obtained from PSPLIB are utilized.

Fuzzy Multi-Objective Linear Programming for Project Management Decision under Uncertain Environment with AHP Based Weighted Average Method

Smooth implementation and controlling conflicting goals of a project with the usage of all related resources through organization is inherently a complex task to management. At the same time deterministic models are never efficient in practical project management (PM) decision problems because the related parameters are frequently fuzzy in nature. The project execution time is a major concern of the involved stakeholders (client, contractors and consultants). For optimization of total project cost through time control, here crashing cost is considered as a critical factor in project management. The proposed approach aims to formulate a multi objective linear programming model to simultaneously minimize total project cost, completion time and crashing cost with reference to direct, indirect cost in the framework of the satisfaction level of decision maker with fuzzy goal and fuzzy cost coefficients.. To make such problems realistic, triangular fuzzy numbers and the concept of minimum accepted level method are employed to formulate the problem. The proposed model leads decision makers to choose the desired compromise solution under different risk levels and the project optimization problems have been solved under multiple uncertainty conditions. The Analytical Hierarchy Process is used to rank multiple objectives to make the problem realistic for the respective case. Here minimum operator and AHP based weighted average operator method is used to solved the model and the solution is obtained by using LINGO software

Economic-energy-environment analysis of prospective sugarcane bioethanol production in Brazil

Bioethanol from sugarcane can be produced using first-generation (1G) or second-generation (2G) technologies. 2G technologies can increase the capacity of production per sugarcane mass input and are expected to have a key role in future reductions of environmental impacts of sugarcane bioethanol. A hybrid Input-Output (IO) framework is developed for Brazil coupling the System of National Accounts and the National Energy Balance, which is extended to assess Greenhouse Gas (GHG) emissions. Life-cycle based estimates for two sugarcane cultivation systems, two 1G and eight 2G bioethanol production scenarios, are coupled in the IO framework. A multi-objective linear programming (MOLP) model is formulated based on this framework for energy-economic-environmental analysis of the Brazilian economic system and domestic bioethanol supply in prospective scenarios. Twenty-four solutions are computed: four “extreme” solutions resulting from the individual optimization of each objective function (GDP, employment level, total energy consumption and total GHG emissions - 1G scenario), ten compromise solutions minimizing the distance of the feasible region to the ideal solution (1G, 1G-optimized and prospective 1G+2G scenarios), and ten solutions maximizing the total bioethanol production (1G, 1G-optimized and prospective 1G+2G scenarios). Higher diesel oil and lubricants consumption in the mechanical harvesting process has counterbalanced the positive effects of more efficient trucks leading to higher energy consumption and GHG emissions. Lower overall employment level in the 1G+2G scenarios is achieved such that policies linked to reabsorption of sugarcane cutters in alternative activities are positive. Indirect effects from maximizing the bioethanol production increase the total energy consumption and the GHG emissions thus requiring efficiency measures and fossil energy substitution by cleaner sources. The integrated- or country-based analysis of the whole economic system has complemented the process design and process-based analysis, contributing to identify direct and indirect effects that can offset the benefits. Direct and indirect effects on the whole economic system have to be considered in policies and technological choices for prospective bioethanol production, since positive direct effects of 1G+2G plants can be counterbalanced by indirect impacts on other sectors, mainly from chemicals in the process.

Applying uncertain programming model to improve regional farming economic benefits and water productivity

The development of optimum crop area planning is valuable for agricultural water management in the arid and semiarid regions. However, the uncertain information existing in the crop area planning system is inevitable, and it cannot be tackled through the traditional multi-objective linear programming model (MOLP). In this study, an inexact multi-objective fuzzy programming model (IMOFP) was developed, considering the multi-objective characteristics, the vagueness associated with the objective functions and constraints, and the interval uncertainty in the parameters. Three objectives were considered including maximizing benefits, minimizing evapotranspiration (ET) and maximizing water productivity (WP). The IMOFP model was applied to solve the problem of crop area planning in Wuwei city of Gansu province in China, and the optimal results under different scenarios of water-saving levels and satisfactory degrees of the decision maker (DM) for available resources were obtained. Different scenarios were also considered to make in-depth analysis of interaction among weight coefficients, economic benefit and water conservation requirement. Moreover, violation variables were introduced to analyze the relationship among system satisfaction, risk level and benefit. Results indicate that using the IMOFP model made the economic benefit, water productivity and water production efficiency of planting in the region increased by 7.05–16.65%, 25.68–33.15% and 39.22–47.59% respectively, and the ET reduced by 20.96–23.10%. Compared to MOLP model, the proposed IMOFP model has advantages in effectively reflecting uncertainties expressed as discrete intervals and fuzzy sets, and can provide reasonable solutions and more stable decision alternatives.

Superstructure-based synthesis and optimisation of an oil palm eco-industrial town: a case study in Iskandar Malaysia

Malaysia is one of the world’s top edible oil producers, having more than 5.23 million hectares of palm oil plantations and more than 400 palm oil mills. The oil palm industry produces millions of tonnes of biomass waste during harvesting and mill processing. This paper presents an oil palm eco-industrial town (EIT) that integrates a palm oil mill with nine downstream oil palm-based industries, as well as a community. The downstream industries produce various types of products such as crude palm oil, bio-fertiliser, bio-gas, bio-diesel, bio-pellet, medium-density fibreboard (MDF), and are also involved in the paper industry, and livestock production. Through the concept of industry symbiosis, the oil palm EIT promotes energy and material sharing among the industries and the community to reduce energy consumption, virgin material consumption, and waste generation. Therefore, this concept could provide economic and environmental benefits to upstream industries (utilisation of biomass), downstream industries (conversion of biomass to valuable products), and the community (job creation). In this work, a multi-objective linear programming model is formulated to maximise economic performance, while minimising waste generation in the oil palm EIT. The applicability of the model is demonstrated using a case study in Iskandar Malaysia (IM). The optimised model suggests that the most efficient way to utilise abundant oil palm biomass is via the production of crude palm oil, MDF, bio-paper, paper, bio-gas, and bio-diesel. The model could assist decision makers to identify the sub-industries in the EIT that would promote sustainability in the oil palm industry.

A Fuzzy Multi-objective Linear Programming Model Based on Interval-valued Intuitionistic Fuzzy Sets for Supplier Selection

Nowadays, companies are paying more attention to supply chain management in order to achieve success in the competitions and keep the customers satisfied. Therefore, supplier selection is of prime importance in a supply chain which has a key role in determining the success or failure of a business. In this paper, fuzzy multi-objective linear programming model with group decision making is presented. Firstly, linguistic variables in the form of interval-valued intuitionistic fuzzy numbers and group decisions are defined. By using TOPSIS method, the weight of each criterion (objective) and weight of each constraint are determined. Then, with defining membership functions of the objectives and membership functions of suppliers’ constraints and using the achieved weights from the previous phase, the supplier selection problem will be converted to fuzzy multi-objective linear programming model which determines the appropriate ordering quantities for each supplier. Finally, two numerical examples for supplier selection are used to demonstrate the practicality and effectiveness of the proposed approach.

Development of hybrid optimization of train schedules model for N-track rail corridors

From a capacity perspective, efficient utilization of a railway corridor has two main objectives; avoidance of schedule conflicts, and finding a proper balance between capacity utilization and level of service (LOS). There are several timetable tools and commercial rail simulation packages available to assist in reaching these objectives, but few of them offer both automatic train conflict resolution and automatic timetable management features for the different types of corridor configurations. This research presents a new rescheduling model to address some of the current limitations. The multi-objective linear programming (LP) model is called “Hybrid Optimization of Train Schedules” (HOTS), and it works together with commercial rail simulation tools to improve capacity utilization or LOS metrics. The HOTS model uses both conflict resolution and timetable compression techniques and is applicable to single-, double-, and multiple-track corridors (N-track networks), using both directional and bi-directional operations. This paper presents the approach, formulation and data requirements for the HOTS model. Single and multi-track case studies test and demonstrate the model’s train conflict resolution and timetable compression capabilities, and the model’s results are validated by using RailSys simulation package. The HOTS model performs well in each tested scenario, providing comparable results (either improved or similar) to the commercial packages.

Bioeconomic optimization of conservation agriculture production systems (CAPS) for smallholder tribal farmers in the hill region of Nepal

This research was conducted to determine the potential for the use of Conservation Agriculture Production Systems (CAPS) in the hill region of Nepal, an area highly prone to food insecurity and soil losses. Conservation agriculture (CA) includes the practices of tillage reduction, soil cover maintenance, and optimal crop rotation. Farming in Nepal consists of two main cropping seasons: rainy and postrainy. Therefore, the annual production system includes different CA practices suitable for each cropping season. Due to conflicting criteria for maximizing farm profits while minimizing soil losses from CA, this study used a dynamic multiobjective linear programming model with a 20-year horizon to predict the optimal solution. Seven systems combining varying tillage practices (full versus strip tillage), cropping patterns (sole versus intercropping), and four crops were used for analysis. The results showed the optimal CAPS as strip tillage of maize (Zea mays L.) followed by intercropping millet (Eleusine coracana) and legumes; however, there are some variations in net present value (NPV) of profits due to the length of the planning horizon and discount rates. For long planning horizons of 20 years, farmers9 objectives would be optimized when all land is allocated to strip tillage systems by year 2. The results show that the economic gains from practicing strip tillage–based CA varies among villages, ranging from 29% to 110% using discount rates of 10% and 48% to 274% under lower/social discount rate of 3%. In addition to profit, adoption of a CA system reduces the amount of soil loss by 83% to 88% over 20 years. Despite long-term benefits from CA, the short-term differences in the economic returns from CAPS are not enough for farmers to abandon their traditional practices. Therefore, from a societal welfare standpoint, it is recommended that the government provide short-term financial support to pay for the environmental services provided by the CAPS, and that CAPS education and training be made available to farmers. Additionally, long-term research to develop locally adapted CA practices may be necessary to fully realize the benefits for smallholder farmers.

A fuzzy AHP and fuzzy multi-objective linear programming model for order allocation in a sustainable supply chain: A case study

Supplier selection is a critical process in sustainable supply chain management. Increased pressure from stakeholders has forced companies to search for methodologies that help in arriving at intelligent supplier selection decisions. This is a unique study as it illustrates how to optimise orders among various suppliers while taking into consideration all three dimensions of sustainability – economic, social, and environmental. Previous studies have mostly relied on simple ranking of suppliers on the basis of past performance for selection. Those studies that did emphasise on optimisation of orders among suppliers, did not consider all three dimensions of sustainability. To establish an improved sustainable supply chain, this study uses integrated fuzzy AHP and fuzzy multi-objective linear programming approach for order allocation among suppliers. fuzzy AHP has been used for weighing various factors such as quality, lead time, cost, energy use, waste minimisation, emission, and social contribution, and weights of the factors have been considered for developing linear programming. Demand has been taken as a fuzzy variable in this model. The case of an Indian automobile company has been taken as illustration.

Multi-objective Optimization of a Transportation Network of a HMSC

In this paper, we investigated a transportation network of a tri-layer Halal meat supply chain (HMSC) in which Halal meat transportation process was monitored by a Radio Frequency Identification (RFID) communication system to ensure safety and integrity of Halal meats. This monitoring system is subject to an extra cost in investment that needs to be taken into account. Thus, a multi-objective linear programming model (MOLPM) was developed aiming to minimize the total cost in transportation and number of transportation vehicles and maximize the service level in product quantity as requested by abattoirs and retailers. The facility location-allocation problem in farms, abattoirs and retailers needs also to be addressed in relevance to the quantity flow of products from farms to abattoirs and from abattoirs to retailers. The utility function method was employed to obtain Pareto-optimal solutions and the global criterion method was used for searching the most suitable Pareto solution by minimizing the distance to its ideal objective value. The research work shows that the developed model can be useful for supply chains design through a case study based on numerical results.

Fuzzy multi-objective supply chain master planning in a wood and paper industry: A case study

Providing an efficient production plan that integrates the procurement and distribution plans into a unified framework is significant to achieving competitive advantage. In this paper, we consider a supply chain master planning model consisting of multiple suppliers, one manufacturer and multiple distribution centers. We propose a new multi-objective linear programming model in a wood and paper industry for integrating procurement, production and distribution planning, considering various objectives simultaneously as well as the imprecise nature of some critical parameters such as market demands, cost coefficients and capacity levels. Then, we use a fuzzy ranking method to solve this fuzzy multi-objective supply chain master planning model. Afterwards we compare the results of this approach with the results of the deterministic one.

Enhanced Simulated Annealing for Solving Aggregate Production Planning

Simulated annealing (SA) has been an effective means that can address difficulties related to optimisation problems.SAis now a common discipline for research with several productive applications such as production planning. Due to the fact that aggregate production planning (APP) is one of the most considerable problems in production planning, in this paper, we present multiobjective linear programming model for APP and optimised bySA. During the course of optimising for the APP problem, it uncovered that the capability ofSAwas inadequate and its performance was substandard, particularly for a sizable controlledAPPproblem with many decision variables and plenty of constraints. Since this algorithm works sequentially then the current state will generate only one in next state that will make the search slower and the drawback is that the search may fall in local minimum which represents the best solution in only part of the solution space. In order to enhance its performance and alleviate the deficiencies in the problem solving, a modifiedSA(MSA) is proposed. We attempt to augment the search space by starting withN+1solutions, instead of one solution. To analyse and investigate the operations of the MSA with the standardSAand harmony search (HS), the real performance of an industrial company and simulation are made for evaluation. The results show that, compared toSAandHS,MSAoffers better quality solutions with regard to convergence and accuracy.