Multi-objective Mixed-integer Programming Model Research Articles

Multi-objective optimization for a closed-loop network design problem using an improved genetic algorithm

This paper develops a multi-objective Mixed Integer Programming model for a closed-loop network design problem. In addition to the overall costs, the model optimizes overall carbon emissions and the responsiveness of the network. An improved genetic algorithm based on the framework of NSGA II is developed to solve the problem and obtain Pareto-optimal solutions. An example with 95 cities in China is presented to illustrate the approach. Through randomly generated examples with different sizes; the computational performance of the proposed algorithm is also compared with former genetic algorithms in the literature employing the weight-sum technique as a fitness evaluation strategy. Computational results indicate that the proposed algorithm can obtain superior Pareto-optimal solutions.

Multi-objective mixed integer programming model for pairing scheduling of intelligent and autonomous vehicle

Multi-objective mixed integer programming model for pairing scheduling of intelligent and autonomous vehicle

An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production

This paper aims to provide a solution method for a real-world scheduling case from a welding process, which is one of the important processes in modern industry. The unique characteristic of the welding scheduling problem (WSP) is that multiple machines can process one operation at a time. Thus, WSP is a new scheduling problem. We first formulate a new multi-objective mixed integer programming model for this WSP based on a comprehensive investigation. This model involves some realistic constraints, controllable processing times (CPT), sequence dependent setup times (SDST) and job dependent transportation times (JDTT). Then we propose a multi-objective discrete grey wolf optimizer (MODGWO) considering not only production efficiency but also machine load on this real-world scheduling case. The solution is encoded as a two-part representation including a permutation vector and a machine assignment matrix. A reduction machine load strategy is used to adjust the number of machines aiming to minimize the machine load. To evaluate the effectiveness of the proposed MODGWO, we compare it with other well-known multi-objective evolutionary algorithms including NSGA-II and SPEA2 on a set of instances. Experimental results demonstrate that the proposed MODGWO is superior to the compared algorithms in terms of convergence, spread and coverage on most instances. Finally, MODGWO is successfully applied to this real-world WSP. This implies that the proposed model is feasible and the proposed algorithm can solve this real-world scheduling problem very well.

Optimizing capital investments under technological change and deterioration: A case study on MRI machine replacement

ABSTRACTWe study the multiple style and type parallel asset replacement problem (MST-PRES), which determines an optimal policy for keeping or replacing a group of assets that operate in parallel under a limited budget. Operating assets generally suffer from deterioration, which results in high operation and maintenance (O&M) cost and decreased salvage value, and technological improvements make it possible for new assets to operate more efficiently at a lower cost. In order to address these issues, we formulate a multi-objective mixed-integer programming (MIP) model that minimizes fixed and variable costs of purchasing new assets, O&M cost, inventory cost, and penalty cost for unmet demand minus salvage values, while considering technological advances and deterioration as a gain and loss in capacity, respectively. We apply our model to a case study involving two different styles of assets: a full-body magnetic resonance imaging (MRI) machine and a smaller extremity magnetic resonance imaging (eMRI) machine. Each has two types: high-field and low-field. We perform computational experiments and analyses using key model parameters and illustrate optimal replacement strategies considering the impact of technological advances and deterioration. Results show that the proposed MIP model provides valuable insights and strategies for companies, decision makers, and government entities on the capital asset management.

A NOVEL STRATEGY FOR STOWAGE PLANNING OF 40 FEET CONTAINERS IN CONTAINER TERMINALS

Owing that the container terminals increasingly secure a crucial position in today’s container transportation, the stowage planning, which is one of the important process during container-loading operations, gradually attracts the attention of terminal operators. In this paper, we discuss the vessel stowage planning problem for 40 feet outbound containers, in which a strategy named ‘ROIR’ is analyzed. By carefully studying the operational flow of vessel stowage, a multi-objective mixed integer programming model is put forward with regard to general principles. Then a specified genetic algorithm is proposed to solve the IP model. An integer encoding technique is employed in the algorithm, together with a self-crossover operator and a mutation operator. Furthermore, numerical tests are carried out and their results show the effectiveness and feasibility of the model. The application of the proposed theory provides a practical significance to improve loading efficiency and stowage quality.

Bi-objective optimization of integrating configuration generation and scheduling for reconfigurable flow lines using NSGA-II

Reconfigurable manufacturing system (RMS) is a new manufacturing system paradigm suited to the era of mass customization. A RMS is able to change its configuration by physical reconfiguration and/or logical reconfiguration, to provide exact functionality and capacity needed for every demand period. For the reconfigurable flow line (RFL) in which multiple parts within the same part family can be produced simultaneously, optimal design of physical configuration (called configuration generation) and proper scheduling of multiple products are crucial to operate RFL in a cost-effective manner. Considering the close coupling between configuration generation and scheduling of multiple products for RFL, a new multi-objective mixed integer programming model is established for the integrated optimization of configuration generation and scheduling. The two conflicting objectives are to minimize total cost including capital cost and reconfiguration cost and to minimize total tardiness. The validity of the model is verified through case analysis implemented by LINGO software. Subsequently, the nondominated sorting genetic algorithm II (NSGA-II) is adopted to obtain a set of nondominated solutions. In the NSGA-II, a hybrid encoding method ensuring any chromosome a feasible solution is devised. Case study is utilized to illustrate the effectiveness of the NSGA-II for solving the problem. The case study also reveals that only if performing configuration generation and scheduling concurrently can a set of solutions balancing cost and tardiness be identified effectively for the RFL.

Impact of Closed–Loop Supply Chains on Reducing Carbon Emission and Gaining Competitive Advantage: NSGA-II and MOPSO Solutions

The purpose of this paper is presenting a mathematical model of the closed-loop supply chain network design dynamic positioning facility, through a strategic review of Multi-period planning horizon in order to minimize the environmental impact and the gain the competitive advantage based on of Porter’s view. A new multi-objective mixed integer programming model for locating facilities and simultaneous designing of forward and reverse network is developed in order to determine the strategic long-term comprehensive solutions that maximize the Net Present Value (NPV) of cash flow for the entire supply chain and to minimize emissions of greenhouse gases products suppliers. The proposed algorithm parameters Multiple Objective Particle Swarm Optimization (MOPSO) and non-dominated sorting genetic algorithm version 2 (NSGA-II) are adjusted using the Taguchi method. Numerical results show that the new model with the above-mentioned meta-heuristic algorithms can be used obtain quantitative aspects of strategic planning in terms of closed-loop supply chain.

A particle swarm approach for optimizing a multi-stage closed loop supply chain for the solar cell industry

In order to implement sustainable strategies in a supply chain, enterprises should provide highly favorable and effective solutions for reducing carbon dioxide emissions, which brings out the issues of designing and managing a closed-loop supply chain (CLSC). This paper studies an integrated CLSC network design problem with cost and environmental concerns in the solar energy industry from sustainability perspectives. A multi-objective closed-loop supply chain design (MCSCD) model has been proposed, in consideration of many practical characteristics including flow conservation at each production/recycling unit of forward/reverse logistics (FL/RL), capacity expansion, and recycled components. A deterministic multi-objective mixed integer linear programming (MILP) model capturing the tradeoffs between the total cost and total CO2 emissions was developed to address the multistage CSLC design problem. Subsequently, a multi-objective PSO (MOPSO) algorithm with crowding distance-based nondominated sorting approach is developed to search the near-optimal solution of the MCSCD model. The computational study shows that the proposed MOPSO algorithm is suitable and effective for solving large-scale complicated CLSC structure than the conventional branch-and-bound optimization approach. Analysis results show that an enterprise needs to apply an adequate recycling strategy or energy saving technology to achieve a better economic effectiveness if the carbon emission regulation is applied. Consequently, the Pareto optimal solution obtained from MOPSO algorithm may give the superior suggestions of CLSC design, such as factory location options, capacity expansion, technology selection, purchasing, and order fulfillment decisions in practice. An integrated CLSC problem by using PSO algorithm in the solar energy industry has been studied.A deterministic multi-objective mixed integer programming model has been established.The results Pareto CLSC solutions between CPLEX and MOPSO have been compared.MOPSO provides a rapid algorithm to search Pareto solution compare to CPLEX in large scale issues.

Optimization of integrated scheduling of handling and storage operations at automated container terminals

Abstract Increasing demand for containerization compels container terminals to improve their performance. Uncoordinated scheduling of operations is one of the main factors accounting for poor performance at automated container terminals (ACTs). To increase land utilization efficiency and lower operational times, a new storage system called the split-platform automated storage/retrieval system (SP-AS/RS) has been introduced for temporary storage of containers. This paper describes a multi-objective mixed-integer programming (MIP) model that is based on a combination of multiple interacting sub-tasks. It is aimed at optimizing the integrated scheduling of handling and storage operations in ACTs. The MIP model objective function is to minimize delays in the loading/unloading tasks of the cranes and the travel time of vehicles and platforms in the SP-AS/RS. At the same time, a simulated annealing algorithm (SAA) that provides near-optimal solutions for the problem in a reasonable computation time is appraised. The results of this study show that the objective function of the MIP model is, on average, 58 % lower than that of the non-integrated scheduling method. On the other hand, the best objective function values obtained by the SAA indicate only a 3.7 % disadvantage in comparison with optimal values determined by the MIP model, demonstrating that the SAA is able to provide near-optimal solutions for the integrated scheduling of handling and storage operations.

Balanceable assembly lines with dynamic tool sharing and best matching decisions—a collaborative assembly framework

A Collaborative Assembly Framework (CAF), inspired by the design principles of the Collaborative Control Theory, is developed in this article to enhance the extent of balancing of assembly lines. The notion of the CAF lies in the dynamic utilization of idle resources to eliminate bottlenecks. The CAF is composed of two modules: the first one, the Tool Sharing Protocol (TShP), makes dynamic tool-sharing decisions among fully loaded (i.e., bottleneck) and partially loaded Work Stations (WSs), and the second one, the Best Matching Protocol (BMP), dynamically matches tasks and WSs (BMP-1) and partially and fully loaded WSs for tool sharing (BMP-2). A Multi-Objective Mixed-Integer Programming model is developed for mathematical representation and a Fuzzy Goal Programming approach is applied for optimization purposes. The objectives are to minimize (i) the number of WSs, (ii) cycle time, and (iii) the total collaboration cost. The developed CAF is proven to guarantee the relative extent of balancing of assembly lines, depending on pairwise tool compatibility and tool-sharing performance. Numerical experiments on a set of small-sized case studies repeated and expanded from previous research show the superiority of the CAF over the existing non-collaborative approaches in terms of line efficiency, utilization, and balancing.

Using Augmented ɛ-constraint Method for Solving a Multi-objective Operating Theater Scheduling

Operating Theaters are among the most critical parts in hospitals. Generally, an Operating Theater consists of three stages: Public Health Unit (PHU), Operating Rooms, and Post-Anesthesia Care Unit (PACU). Operating Theater significantly affects annual costs and revenues of a hospital due to requiring skillful staff and expensive equipment to operate surgeries beside high service fees. In this paper, proposing an operating theater daily schedule to serve surgical demands is considered as a three-stage flow-shop scheduling problem. The problem is formulated as a multi-objective mixed integer programming model aiming to balance workload of operating rooms and surgeons, minimize waiting times and maximize human (surgeons) reliability. Weighted-sum method and an augmented ɛ-constraint method are applied to solve two test problems. Analysis of obtained solutions verifies that both solution approaches are capable of providing appropriate schedules in a reasonable time.

Application of Two-Phase Fuzzy Optimization Approach to Multiproduct Multistage Integrated Production Planning with Linguistic Preference under Uncertainty

This paper tackles the challenges for a production planning problem with linguistic preference on the objectives in an uncertain multiproduct multistage manufacturing environment. The uncertain sources are modelled by fuzzy sets and involve those induced by both the epistemic factors of process and external factors from customers and suppliers. A fuzzy multiobjective mixed integer programming model with different objective priorities is proposed to address the problem which attempts to simultaneously minimize the relevant operations cost and maximize the average safety stock holding level and the average service level. The epistemic and external uncertainty is simultaneously considered and formulated as flexible constraints. By defining the priority levels, a two-phase fuzzy optimization approach is used to manage the preference extent and convert the original model into an auxiliary crisp one. Then a novel interactive solution approach is proposed to solve this problem. An industrial case originating from a steel rolling plant is applied to implement the proposed approach. The numerical results demonstrate the efficiency and feasibility to handle the linguistic preference and provide a compromised solution in an uncertain environment.

Integrated Optimization of Finished Product Logistics in Iron and Steel Industry Using a Multi-objective Variable Neighborhood Search

This paper is concerned with the integrated optimization of finished product logistics that consists of two sub-problems: consolidation planning and transportation scheduling. In this problem, three kinds of decisions should be made simultaneously, namely the selection of candidate finished products in each warehouse (i.e., consolidation planning) and the vehicle allocation and transportation sequence of selected finished products in each warehouse (i.e., transportation scheduling). Since the loading times of products to vehicles are sequence-dependent, a tradeoff should be made between two conflicting objectives: maximization of loadage of ships and maximization of efficiency of the whole logistics. In practical industry the schedulers usually handle the two sub-problems separately, which often cause much lower efficiency of the whole logistics and higher transportation cost. Therefore, in this paper the two sub-problems are integrated and formulated as a multi-objective mixed-integer programming model, and then a two-layer multi-objective variable neighborhood search (TLMOVNS) algorithm is developed to solve it. Computational results on simulated instances show that the proposed TLMOVNS is very efficient for this problem and much superior to the current scheduling method generally used in practice.

An integrated sustainable partner selection approach with closed-loop supply chain network configuration

Reverse logistics network design is a crucial issue in which it is important to take into account the selection of the most appropriate partner with sustainability concerns. This partner can be a supplier or a third-party reverse logistics provider (3PRLP). However, research works that consider reverse logistics (RL) network design, partner selection, and sustainability issues simultaneously are rather limited till now. This paper proposes an integrated sustainable approach for partner selection and closed-loop supply chain (CLSC) network configuration, particularly in the case of outsourcing reverse logistics process to third- party provider. We propose a trade-off between sustainability criteria for both supplier and 3PRL provider selection. A multi-objective mixed-integer programming (MILP) model is also proposed to configure CLSC network and to select the best partners. The model minimizes the total cost of sourcing, and the total greenhouse gas emissions, while it maximizes the total value of reverse logistics, and the number of new job opportunities. A numerical example is also presented to illustrate the proposed approach.

A Site Selection Model for a Straw-Based Power Generation Plant with CO2 Emissions

The decision on the location of a straw-based power generation plant has a great influence on the plant’s operation and performance. This study explores traditional theories for site selection. Using integer programming, the study optimizes the economic and carbon emission outcomes of straw-based power generation as two objectives, with the supply and demand of straw as constraints. It provides a multi-objective mixed-integer programming model to solve the site selection problem for a straw-based power generation plant. It then provides a case study to demonstrate the application of the model in the decision on the site selection for a straw-based power generation plant with a Chinese region. Finally, the paper discusses the result of the model in the context of the wider aspect of straw-based power generation.

A mixed-integer optimization model for the economic and environmental analysis of biomass production

Biofuel production from second-generation feedstock has become critical due to environmental concerns and the need for sustainable energy supply. This paper provides a unique optimization approach of quantifying and formulating the economic and environmental benefits of switchgrass production at the farm level. In particular, we propose a multi-objective mixed-integer programming model, which maximizes the revenue from harvested switchgrass biomass and the economic value obtained from the positive environmental impacts of switchgrass yield during a ten-year planning horizon. Environmental impacts include soil erosion prevention, sustainability of bird populations, carbon sequestration, and carbon emissions, while economic impacts are analyzed under various budget, yield, and sustainability scenarios. The proposed model is then applied to a case study in the state of Kansas. Results show that given the current market prices, switchgrass cultivation on grassland and cropland is highly profitable. The model results also suggest that if utilized by the government, conservation reserve program (CRP) incentives could make marginal land more favorable over cropland. We perform sensitivity analysis to address the uncertainty in budget, yield, and utilization of cropland, and present insights into the economic and environmental impacts of switchgrass production. This model can also be extended to biomass production from any other types of energy crops to identify the most efficient production planning strategies under various management scenarios.

Berth and quay-crane allocation problem considering fuel consumption and emissions from vessels

Resolving the berth and quay-crane allocation problem improves the efficiency of seaside operations by optimally allocating berthing spaces and quay cranes to vessels, typically by considering a vessel’s sailing speed and arrival time at a port as constant parameters, while ignoring the impact of arrival times on fuel consumption and emissions when sailing. This work applied a novel nonlinear multi-objective mixed-integer programming model that considered a vessel’s fuel consumption and emissions, and then transformed this model into a second-order mixed-integer cone programming model to solve the problem’s computational intractability. Furthermore, the impact of number of allocated quay cranes on port operational cost, and a vessel’s fuel consumption and emissions was analyzed. Additionally, a vessel’s emissions while moored are also calculated based on wait time. Experimental results demonstrate that the new berth and quay-crane allocation strategy with a vessel’s arrival time as a decision variable can significantly improve vessels’ fuel consumption and emissions, the air quality around ports and utilization of berths and quay cranes without reducing service quality.

Model and Method for Multiobjective Time-Dependent Hazardous Material Transportation

In most of the hazardous material transportation problems, risk factors are assumed to be constant, which ignores the fact that they can vary with time throughout the day. In this paper, we deal with a novel time-dependent hazardous material transportation problem via lane reservation, in which the dynamic nature of transportation risk in the real-life traffic environment is taken into account. We first develop a multiobjective mixed integer programming (MIP) model with two conflicting objectives: minimizing the impact on the normal traffic resulting from lane reservation and minimizing the total transportation risk. We then present a cut-and-solve basedε-constraint method to solve this model. Computational results indicate that our method outperforms theε-constraint method based on optimization software package CPLEX.

Study on Multi-Objective Optimizing Model of Cigarette Production Line

Based on the distinct characteristic of the cigarette production process, the production planning and scheduling of the packing line is described as the multi-objective mixed-integer programming model to decide the sequence and quantity of all the products, whose objective is not only to meet delivery date, but also to minimize all theprocessing costs and the transforming time in the process. The effectiveness of this model can be well verified in the scheduling decision support system for the production of the packing of real company.

A multi-objective mixed-integer programming model for a multi-floor facility layout

We consider a multi-floor facility layout problem in which the overall length and width of the facility, the size and location of each department, the number and the location of elevators and the number of floors in the facility are all modelled as decision variables. We adapt a linear approximation scheme to represent the area of each department. We consider two objective functions in our model, namely minimising material handling and facility building costs, and propose a lexicographic ordering technique to handle multiple objectives. The numerical experiments show that the slack used in the lexicographic ordering approach has a significant impact on the optimal solution. The experiments also show that the material handling cost can be significantly reduced in a multi-floor facility compared with a single-floor facility.