Multi-objective Mixed-integer Programming Model Research Articles

Group-to-group reviewer assignment problem

The Reviewer Assignment Problem is a critical management problem faced by academic journals, conferences, and research funding agencies. Previous relevant literature focuses on performing an optimized assignment of manuscripts (or proposals) to reviewers. In this paper, we study a group-to-group reviewer assignment problem, where manuscripts and reviewers are divided into groups, with groups of reviewers are assigned to groups of manuscripts. We formulate this problem as a multi-objective mixed integer programming model, which is proven NP-hard. An effective two-phase stochastic-biased greedy algorithm is then proposed to solve the problem. Results of comprehensive experiments demonstrate the effectiveness of the algorithm. The approach is applied to a real application, for which the result receive positive and encouraging feedback from users.

An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach

Reverse logistics consists of all operations related to the reuse of products. External suppliers are one of the important members of reverse logistics and closed loop supply chain (CLSC) networks. However in CLSC network configuration models, suppliers are assessed based on purchasing cost and other factors such as on-time delivery are ignored. In this research, a general closed loop supply chain network is examined that includes manufacturer, disassembly, refurbishing, and disposal sites. Meanwhile, it is managed by the manufacturer. We propose an integrated model which has two phases. In the first phase, a framework for supplier selection criteria in RL is proposed. Besides, a fuzzy method is designed to evaluate suppliers based on qualitative criteria. The output of this stage is the weight of each supplier according to each part. In the second phase, we propose a multi objective mixed-integer linear programming model to determine which suppliers and refurbishing sites should be selected (strategic decisions), and find out the optimal number of parts and products in CLSC network (tactical decisions). The objective functions maximize profit and weights of suppliers, and one of them minimizes defect rates. To our knowledge, this model is the first effort to consider supplier selection, order allocation, and CLSC network configuration, simultaneously. The mathematical programming model is validated through numerical analysis.

Portfolio construction on the Athens Stock Exchange: a multiobjective optimization approach

In this research article, our purpose is to propose a single-period multiobjective mixed-integer programming model for equity portfolio construction, in order to generate the Pareto optimal portfolios, using a variant of the well-known ε-constraint method. The decision maker's investment policy, i.e. constraints regarding the portfolio structure, is strongly taken into account. An illustrative application in the Athens Stock Exchange market is also presented.

A multi-objective optimization approach to balancing cost and traceability in bulk grain handling

This paper proposes a multi-objective optimization model that provides an effective method for minimizing traceability effort by minimizing the food safety risk caused by lot aggregation at a grain elevator. A mathematical multi-objective mixed-integer programming (MIP) model is proposed with two objective functions that allow in calculating the minimum levels of lot aggregation and minimum total cost of blending grain. Constraints on the system include customer contract specifications, availability of grain at the elevators and the blending requirements. The solutions include quantities of grain from different storage bins to be used for blending for a shipment while using the minimum number of storage bins and minimum total cost. The numerical results are presented for a corn shipment scenario to demonstrate the application of this model. Pareto optimal front is computed for the problem for simultaneous optimization of lot aggregation and cost of blending. Sensitivity analysis is conducted to analyze the application of the model under different operating conditions.

A supplier selection and order allocation model with multiple transportation alternatives

Numerous analytical methods ranging from simple weighted scoring to complex mathematical programming approaches have been proposed to solve supplier selection and order allocation problems. However, the traditional methods too often fail to consider: (1) situations in which goods are transported from a supplier to a receiver using different transportation alternatives (TAs) and (2) a finite planning horizon consisting of multiple discrete time periods. We present a structured framework with two separate but dependent phases. In the selection phase, we use a data envelopment analysis model to determine the relative efficiency of the suppliers and the TAs. In the allocation phase, we use a multi-objective mixed integer programming model with two objectives for minimizing the total costs and maximizing the overall efficiencies. The contribution of this paper is threefold: (1) It provides a comprehensive and systematic framework that embraces both quantitative and qualitative criteria; (2) it addresses the need in the supplier evaluation literature for methods that considers different TAs in the supplier selection and order allocation decisions encompassing multiple discrete time periods; and (3) it uses a real-world case study to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.

Facility location and distribution decisions in supply chains with fleet sizing considering both tangible and intangible criteria

This paper addresses location and distribution decisions in supply chains where decisions for locating distribution centers (DCs) and determining the best strategy for shipping products from plants to customers through DCs are taken into consideration. The goal is to select locations of DCs to be opened and to design the network flow of products so that all customers’ demands are satisfied at minimum total cost of the distribution network, while total value of locating DCs and shipping products is maximized. Unlike most of the past research that ignores availability of different transporters with different capacities and costs at each node of the supply chain network, our study takes into account different transportation modes that are available at each potential DC location as well as at each plant, and determines the fleet size on each arc of the network. Furthermore, in addition to opening and operating costs of each potential DC, the decision maker (DM) also takes into account the value of each potential DC location which is calculated through a multiple criteria decision making (MCDM) method. We develop a two-phase approach to deal with this problem. In the first phase, the decision maker scores and ranks all potential DC locations with regard to a set of criteria, and in the second phase through a multi-objective mixed integer programming (MOMIP) model final location and distribution decisions, which incorporates selection of transportation modes and their associated loads, are made.

Equity portfolio construction and selection using multiobjective mathematical programming

A multi-objective mixed integer programming model for equity portfolio construction and selection is developed in this study, in order to generate the Pareto optimal portfolios, using a novel version of the well known e-constraint method. Subsequently, an interactive filtering process is also proposed to assist the decision maker in making his/her final choice among the Pareto solutions. The proposed methodology is tested through an application in the Athens Stock Exchange.

A multi-objective optimisation approach for order management: incorporating activity-based costing in supply chains

Most of the supply chain order management decision making models proposed in the literature are based mainly on the material flow and capacity constraints without any consideration to the profitability factor. In this paper, we develop a multi-objective mixed-integer programming (MIP) model which considers profitability in order to effectively manage order acceptance decisions in supply chains, subject to capacity constraints by using activity-based costing (ABC). While there are a numbers of decision-making models in literature integrating ABC in supply chains, this study expands the previous models with a more customer-oriented approach. The proposed model fulfils a desirable amount of orders completely and accepts selective number of orders partially with an objective of minimising the amount of residual capacity and increasing the profitability.

A series—parallel redundant reliability system for cellular manufacturing design

This paper presents a novel, multi-objective mixed-integer programming model for designing a cellular manufacturing system (CMS) that minimizes the total cost and maximizes the overall system reliability. In general, it is impossible to avoid production interruptions while handling machine breakdowns. In this situation, changing the process route dynamically can provide a quick response to meet production requirements. By assuming alternative process plans for operation—part requirements, the concept of the ‘reliable route’ proposed in the literature is extended. In a redundant reliability system with a series—parallel configuration, each reliable route is associated with an operation of a part (i.e. an operation—part) as a parallel subsystem. This route consists of a number of units or alternative machines allocated to cells in such a way that parts are processed with the maximum reliability for a given period of time. When an alternative machine breaks down, unprocessed parts are transferred to the next predetermined machine on the reliable route in order to complete their processes. While the reliable route approach increases the overall system reliability, the operational costs of the system also increase. To assess the present proposed model as a useful decision tool for the manager, various numerical examples are solved and analysed. Finally, the related computational results are reported.

Multi-objective Maintenance Workforce Scheduling in a Steel Company

Abstract In this paper, a real maintenance workforce scheduling problem is formulated as a multi-objective mixed-integer programming model with the aim of simultaneous minimizing the workforce cost and maximizing the equipment availability. The workforce is provided by the internal and external resources using the regular time, overtime and contracting. The equipment availability is measured using the downtime due to the preventive maintenance (scheduled) and failure repair (unscheduled) jobs. The priority of the imminent or potential failures can be different because of the severity effect of the failures on the system. Hence, the total weighted flow time is used as a scheduling criterion to measure the equipment availability. The proposed model is verified using a comprehensive numerical example and the obtained results are discussed.

A comparative study of exponential distribution vs Weibull distribution in machine reliability analysis in a CMS design

The paper addresses machine reliability consideration by Weibull and exponential distribution approach in designing a cellular manufacturing system (CMS). A multi-objective mixed integer programming (MIP) model that considers machine system reliability and system cost simultaneously is presented to implement the approach. When a part has the option to be processed in alternative routes, the route with the highest system reliability can be selected by considering individual machine reliabilities along each route. A CMS design approach which selects processing routes for the part types with maximum system reliability, considering the machines along routes while optimizing system cost, will improve the overall performance of the system. The rerouting provision of the part types, integrated with the approach, will also help the user/designer to solve machine breakdown problems during processing of a part. This study offers the capability to model different failure characteristics, such as, an increasing, decreasing or constant machine failure rate. An example problem is solved to illustrate applicability of the model.

Reliability consideration in the design and analysis of cellular manufacturing systems

A multi-objective mixed integer programming model of cellular manufacturing system (CMS) design is presented which minimizes the total system costs and maximizes the machine reliabilities along the selected processing routes. A part may be processed under different process plans, each prescribing a sequence of operations to be performed at various machines in a serial configuration. Thus, each process route is associated with a level of reliability corresponding to the machines in the selected process plan. The CMS design problem consists of assigning the machines to cells, and selecting, for each part type, the process route with the highest overall system reliability while minimizing the total costs of manufacturing operations, machine under-utilization, and inter-cell material handling. The proposed approach provides a flexible routing which ensures high overall performance of the CMS by minimizing the impact of machine failure through the provision of alternative process routes in case of any machine failure. The paper also proposes a performance evaluation criterion in terms of system availability for the parts and process plan assignments. Numerical examples are provided to demonstrate the applicability of the model.

Advanced planning for minimizing makespan with load balancing in multi-plant chain

This paper deals with the advanced planning problem for minimizing makespan with workload balancing considering capacity constraints, precedence relations, and alternative resources with different operation times in a multi-plant chain. The problem is formulated as a multi-objective mixed integer programming (mo-MIP) model which determines the operations sequences with resource selection and schedules. In this model, a single unique solution does not exist since the objectives may be conflicting, which have to be globally minimized with respect to the two objectives. For effectively solving the alternative solutions of the advanced planning model, we develop an adaptive genetic algorithm (aGA) approach with the adaptive recombination functions and the revised adaptive weighted method. The experimental results are presented for the advanced planning problems of various sizes to describe the performance of the proposed aGA approach. The performance of the aGA approach is also compared with that of the Moon, Li and Gen (MLG) method.

A multiobjective model for non-point source pollution control for an off-stream reservoir catchment

Phosphorus loads from agricultural non-point source pollution (NPSP) significantly degrade reservoir water quality, making adequate control of agricultural NPSP necessary for improving the water quality. Controlling NPSP is generally accomplished using various Best Management Practices (BMPs). The present study applies the Agricultural Non-Point Source Pollution (AGNPS) model to simulate NPSP loading and BMP efficiencies and establishes an enhanced multiobjective mixed-integer programming model for NPSP control strategy analyses based on these results. Cost, phosphorus load, sediment load and equity are the four major objectives considered. A case study for the Posan reservoir is presented. Four commonly proposed and applicable BMPs are chosen. Non-inferior solutions obtained using the constraint method and trade-off relationships among different control objectives are described and discussed. Compared with a previously proposed fertilizer control model, results show that the model established herein is more cost-effective and achieves better phosphorus and sediment loading reduction and equity goals. Furthermore, the current model is expected to facilitate decision-making analysis for development of an appropriate cost-sharing program to encourage adoption of appropriate BMPs by farmers.

A fuzzy interval multiobjective mixed integer programming approach for the optimal planning of solid waste management systems

Various deterministic mathematical programming models were developed to evaluate single objective or multiple objectives planning alternatives for municipal solid waste management. The common objective of minimizing the present value of overall management cost/benefit was extended to deal explicitly with environmental considerations, such as air pollution, traffic flow limitation, and leachate and noise impacts. But uncertainty plays an important role in the search for sustainable solid waste management strategies. This paper proposes a new approach a fuzzy interval multiobjective mixed integer programming (FIMOMIP) model m for the evaluation of management strategies for solid waste management in a metropolitan region. In particular, it demonstrates how uncertain messages can be quantified by specific membership functions and combined through the use of interval numbers in a multiobjective analytical framework.

A new approach for long term planning of solid waste management systems using fuzzy global criterion

Recent studies regarding solid waste management system planning frequently emphasize that both socioeconomic and environmental impacts have to be considered simultaneously. While the total elimination of environmental risks is impossible, the analytical concern actually rests upon the concept of the minimization of both environmental risks and costs in an efficient management system. But uncertainty plays an important role in decision making. The related impreciseness/fuzziness of environmental risks were rarely taken into account in previous models. This paper illustrates a new approach, using fuzzy global criterion technique, to show how the concept of fuzzy environmental resources can be incorporated into an optimization process and create a set of more flexible optimal planning alternatives. A fuzzy multiobjective mixed integer programming model for long term planning of metropolitan solid waste management systems is applied as a method for generating such alternatives. The practical implementation of this approach is assessed by a case study in the City of Kaohsiung in Taiwan.

A multiobjective model for the dynamic location of landfills

Abstract The passage of the Resource Conservation and Recovery Act of 1976 and its subsequent renewals triggered controversies over where potentially hazardous garbage should be deposited. Such controversies originated from decade-long conflicts between the government agency seeking cost savings and the general public seeking safe environments. The controversies will go on without a settlement, unless more systematic and realistic decision-aid tools for locating landfills are developed which consider a multitude of dynamic factors affecting the location decision and then make trade-offs among them. These factors may include garbage collection services for regional communities, the explicit and hidden costs of developing landfills, transporting and disposing garbage, long-term health and safety hazards for neighboring residents and ecosystems, negative impacts on the regional economy, equity concerns and so forth. As an effective decision-aid tool that can incorporate these conflicting factors, we develop a dynamic (multiperiod), multiobjective mixed integer programming model. The model is tested in a hypothetical case resembling a real world scenario and the results are interpreted to provide insights into the multiobjective and dynamic nature of the model. Efficient alternatives are generated, using the weighting method, and reduced using a filtering method.