Multi-objective Mixed Integer Linear Programming Research Articles

Bi-objective optimisation over a set of convex sub-problems

During the last decades, research in multi-objective optimisation has seen considerable growth. However, this activity has been focused on linear, non-linear, and combinatorial optimisation with multiple objectives. Multi-objective mixed integer (linear or non-linear) programming has received considerably less attention. In this paper we propose an algorithm to compute a finite set of non-dominated points/efficient solutions of a bi-objective mixed binary optimisation problems for which the sub-problems obtained when fixing the binary variables are convex, and there is a finite set of feasible binary variable vectors. Our method uses bound sets and exploits the convexity property of the sub-problems to find a set of efficient solutions for the main problem. Our algorithm creates and iteratively updates bounds for each vector in the set of feasible binary variable vectors, and uses these bounds to guarantee that a set of exact non-dominated points is generated. For instances where the set of feasible binary variable vectors is too large to generate such provably optimal solutions within a reasonable time, our approach can be used as a matheuristic by heuristically selecting a promising subset of binary variable vectors to explore. This investigation is motivated by the problem of beam angle optimisation arising in radiation therapy planning, which we solve heuristically to provide numerical results.

Design of a sustainable integrated crude oil manufacturing network with risk cover and uncertainty considerations: a case study

The oil industry is one of the largest and most influential manufacturing systems in the world. In addition to being the world’s leading source of energy, oil plays an important role in determining the national power and international reputation of various countries. This industry has certain characteristics that distinguish it from other manufacturing systems. Some of these characteristics include the strategic importance of products, variable prices, and political pressure. This industry is one of the most sophisticated manufacturing systems in the world, incorporating integrated activities from vendor to customer. In this paper, we presented a multi-objective integrated mathematical model including all three upstream, midstream, and downstream sectors of the crude oil supply chain. Our proposed multi-product, multi-period, and multi-objective mixed-integer linear programming model address an optimal solution. We have a scenario-based approach which deals with two sources of uncertainty. Conditional value at risk approach was applied to minimize the risk. Also, the social and environmental aspects of the supply chain are considered simultaneously to propose a sustainable model. Finally, the performance of the model is illustrated and analyzed using the real data of a national refining and distribution company. According to the results, the risk coverage by conditional value at risk has a positive impact on the model.

Multi-objective route planning problem for cycle-tourists

ABSTRACT Cycle-tourism which is a type of niche and sustainable tourism is increasingly promoted by transport and tourism agencies in recent years, but there are still few researches on the cycle-tourist route planning. This paper aims to formulate the cycle-tourist route-planning problem, in order to maximize cycle-tourists’ utility of visiting points of interest (POIs), minimize the total travel time, maximize the Bicycle Level of Service (BLOS) and minimize the number of intersections on the cycle route taken, subject to monetary and time budget, etc. A multi-objective mixed integer linear programming model is formulated to optimize the cycle-tourist route plan. The problem is solved by augmented -constraint method (AUGMECON) whereby a set of nondominated solutions are generated to address the trade-offs among multiple objectives. The proposed model can help local government and agencies promote cycle-tourism and help cycle-tourists better plan the route to satisfy their personal requirements in a sustainable transportation system.

Fuzzy Interactive Approach for a Multi-objective Supplier Selection Problem under Robust Uncertainty

In this paper, the authors proposed a multi-objective Mixed Integer Linear Programming (MILP) model for supplier selection problems. The main aim of the system under the investigation is to plan the companies to supply goods to achieve financial benefit by minimizing the total costs and satisfying the customers with on-time delivery and minimizing rejected items. In this case, some restrictions such as multi-product and multi-period conditions, shortage inventory constraints, and discount circumstances simultaneously are considered. Despite these efforts, due to the uncertainty nature of the problem, some parameters are considering as uncertainty data. For this aim, applying robust counterparts for uncertain parameters plays an essential role in real-world applications of this case. It is concluded that the feasibility and optimality properties of the usual solutions of real-world LPs can be severely affected by small changes of the data and that the robust optimization (RO) methodology can be successfully used to overcome this phenomenon.

The water-energy-food-land nexus at the sugarcane-to-bioenergy supply chain: A sustainable network design model

In this paper, efforts have been devoted in tune with the voices for rights of nature and the pursuit of replacing traditional fossil energy with renewable energy for a safer global environment. A two phase-approach to design a sustainable sugarcane-to-bioenergy supply chain network is developed. In the first phase, a hybrid Best-Worst (BWM) and Combinative Distance-Based Assessment (CODAS) method is utilized for finding the most suitable regions for sugarcane cultivation according to climatic, ecological and social criteria. In the second phase, a novel multi-objective mixed-integer linear programming (MOMILP) model is formulated considering the Water-Energy-Food-Land (WEFL) nexus. A hybrid solution method of augmented ɛ-constraint (AUGMECON) and CODAS method is finally developed to solve the model. This method is utilized for obtaining Pareto solutions of three-objective functions; profit, Co2-equivalent emissions (Co2eq emissions), and water consumption. To evaluate the efficiency of the developed methodology, a real case study in Iraq is applied. The results show that the sugarcane can be cultivated on the available arable land area by 98.9%.

Dual-Channel Global Closed-Loop Supply Chain Network Optimization Based on Random Demand and Recovery Rate.

In the process of globalization, customer demand is usually difficult to predict, and product recycling is generally difficult to achieve accurately. It is also urgent to deal with increased inventory while avoiding shortages, with the purpose of reducing supply chain risks. This study analyzes the integrated supply chain decision-making problem in the random product demand and return environment. It proposes a multi-objective optimization model, which is an effective tool to solve the design and planning problems of the global closed-loop supply chain. It consists of a multi-period, single-product and multi-objective mixed integer linear programming model, which can solve some strategic decision problems, including the network structure, entity capacities, flow of products and components, and collection levels, as well as the inventory levels. From the perspective of economic, environmental and social benefits, three objective functions are defined, including maximizing the net present value (NPV) of the system, minimizing the total emissions of supply chain activities, and maximizing social sustainability indicators. Finally, a numerical example is provided to verify the advantages of this model, and sensitivity analysis results are provided. The results show that changes in product demand and return rate will have a great impact on economic and social performance.

A novel fuzzy multi-objective circular supplier selection and order allocation model for sustainable closed-loop supply chains

Maximizing the value of resources and producing less waste are strategic decisions affecting sustainability and competitive advantage. Sustainable closed-loop supply chains (CLSCs) are designed to minimize waste by circling back (repairing, reselling, or dismantling for parts) previously discarded products into the value chain. This study presents a novel two-stage fuzzy supplier selection and order allocation model in a CLSC. In Stage 1, we use the fuzzy best-worst method (BWM) to select the most suitable suppliers according to economic, environmental, social, and circular criteria. In Stage 2, we use a multi-objective mixed-integer linear programming (MOMILP) model to design a multi-product, multi-period, CLSC network, and inventory-location-routing, vehicle scheduling, and quantity discounts considerations. In the proposed MOMILP, the total network costs, the undesired environmental effects, and the lost sales are minimized while job opportunities and sustainable supplier purchases are maximized. A fuzzy goal programming approach is proposed to transform the MOMILP into a single objective model. We present a case study to demonstrate the applicability of the proposed method in the garment manufacturing and distribution industry.

Optimal sizing of grid-connected hybrid renewable energy systems without storage: a generalized optimization model

ABSTRACT In this study, a weighted multi-objective mixed-integer linear programming (WMO-MILP) model considering both economic and environmental factors is proposed for the optimal sizing of the grid-connected hybrid renewable energy systems without storage (HRES-WS). The proposed model is capable of designing the system including several different types of renewable energy generation units to meet the demands of various consumption points. One of the significant values of the model is that it holistically combines the operational, technical, physical and/or capacity constraints which are rarely considered in an integrated way in the literature. Another contribution of the model is its ability to evaluate the tradeoff between the cost-related and CO2 related conflicting objectives by allocating them various weights resembling the decision-maker’s cost-based, environmental-based, or partially cost- and environmental-based priorities. A case study is utilized to demonstrate the value of the model. In order to take into consideration the stochastic nature of the modeling environment, the Monte Carlo simulation is used to predict weather data and load demand based on the historical data. The findings indicate that the combined effect of environmental and cost-related objectives influences the demand to be met by RES at acceptable cost and CO2 emission level. For example, focusing only on the environmental objective, the annual amount of CO2 emission decreases by 14% and the total installed capacity increases by 41%, and therefore the system cost increases by 205% as compared to the base case in which the weight of each objective function is assumed to be equal. The proposed model has the potential to significantly support decision-making process when evaluating a grid-connected HRES-WS both economically and environmentally.

A Multi-objective Sustainable Medicine Supply Chain Network Design Using a Novel Hybrid Multi-objective Metaheuristic Algorithm

End-of-life products have a severe impact on the ecological system. Potential production policies and distribution strategies for the newly manufactured product have attracted significant attention to sustainable development. Sustainability in supply chain management has much importance to achieve eco-friendly goals. In this study, we have developed sustainable objectives in the supply chain optimization framework with different constraints. The trade-off between economic, environmental and social effects objectives have identified by ensuring the optimal allocation of different products among various levels. In this regard, a new sustainability multi-objective mixed-integer linear programming mathematical model in the medicine supply chain network is developed. Although the proposed model is an NP-hard problem, we develop a novel hybrid Particle Swarm Optimization and Genetic Algorithm to achieve Pareto solutions. Then, to adjust the important parameters of the algorithms and chose the optimum levels of the significant factors for more efficiency is employed the Taguchi method. The results show that the economic and environmental effects tend to be decreased and the social impacts tend to be increased in the medicine supply chain network which can exhibit the best sustainability performance. The various outcomes of numerical experiments indicate that the proposed solution algorithm is more reliable than other algorithms. The solution methods are complemented with several sensitivity analyses on the input parameters of the model.

Work continuity constraints in repetitive project scheduling considering soft logic

PurposeRepetitive projects play an important role in the construction industry. A crucial point in scheduling this type of project lies in enabling timely movement of crews from unit to unit so as to minimize the adverse effect of work interruptions on both time and cost. This paper aims to examine a repetitive scheduling problem with work continuity constraints, involving a tradeoff among project duration, work interruptions and total project cost (TPC). To enhance flexibility and practicability, multi-crew execution is considered and the logic relation between units is allowed to be changed arbitrarily. That is, soft logic is considered.Design/methodology/approachThis paper proposes a multi-objective mixed-integer linear programming model with the capability of yielding the optimal tradeoff among three conflicting objectives. An efficient version of the e-constraint algorithm is customized to solve the model. This model is validated based on two case studies involving a small-scale and a practical-scale project, and the influence of using soft logic on project duration and total cost is analyzed via computational experiments.FindingsUsing soft logic provides more flexibility in minimizing project duration, work interruptions and TPC, especial for non-typical projects with a high percentage of non-typical activities.Research limitations/implicationsThe main limitation of the proposed model fails to consider the learning-forgetting phenomenon, which provides space for future research.Practical implicationsThis study assists practitioners in determining the “most preferred” schedule once additional information is provided.Originality/valueThis paper presents a new soft logic-based mathematical programming model to schedule repetitive projects with the goal of optimizing three conflicting objectives simultaneously.

A Green Demand-Responsive Airport Shuttle Service Problem with Time-Varying Speeds

This study proposes a multiobjective mixed integer linear programming (MOMILP) model for a demand-responsive airport shuttle service. The approach aims to assign a set of alternative fuel vehicles (AFVs) located at different depots to visit each demand point within the specified time and transport all of them to the airport. The proposed model effectively captures the interactions between path selection and environmental protection. Moreover, users with flexible pick-up time windows, the time-varying speed of vehicles on the road network, and the limited fuel for the route duration are also fully considered in this model. The work aims at simultaneously minimizing the operating cost, vehicle fuel consumption, and CO2 emissions. Since this task is an NP-hard problem, a heuristic-based nondominated sorting genetic algorithm (NSGA-II) is also presented to find Pareto optimal solutions in a reasonable amount of time. Finally, a real-world example is provided to illustrate the proposed methodology. The results demonstrate that the model not only selects an optimal depot for each AFV but also determines its route and timetable plan. A sensitivity analysis is also given to assess the effect of early/late arrival penalty weights and the number of AFVs on the model performance, and the difference in quality between the proposed and traditional models is compared.

Integrating energy and water optimization in buildings using multi-objective mixed-integer linear programming

Energy and water are humans’ most significant needs, and many countries confront numerous problems in supplying water and energy resources. Some approaches to rendering these resources increase the emission of greenhouse gases. Concerning the high water and energy consumption in buildings and high energy and water loss and CO2 emission in the concentrated energy generation and water treatment, a presentation of an unconcentrated combined system considering water and energy use optimization and emission reduction in greenhouse gases is needed. While previous studies employed renewable technologies to optimize water and energy consumption separately, this study integratively used the renewable energy generation, energy storage, building smartening, zero energy building standards, and ground source heat pump technologies to decrease energy consumption and CO2 emission. It also exploited the rainwater harvesting and greywater recycling composition to decrease water consumption. Using MILP, we presented a mathematical model to examine the economic conditions besides reductions in energy and water use and CO2 emission, and we solved it by the epsilon constraint method and GAMS software. The results in 4 scenarios revealed that energy use, water use, and CO2 emission decreased by 47–94.7 %, 20–100 %, and 52–96 %. Besides, the model economically experienced reduced costs and yielded monetization possibility.

A New 2-Phase Optimization-Based Guaranteed Connected Target Coverage for Wireless Sensor Networks

Relying on a limited power source, WSNs present one of their most challenging concerns as energy consumption. In addition, coverage and connectivity are important quality of service metrics in the networks. In this paper, the problem of connected target coverage (CTC) with an optimistic view of energy usage is investigated. A new 2-phase optimization method is proposed that provides full target coverage and connectivity with the user throughout network lifetime. In the first phase of the algorithm, sensors are organized into maximum achievable disjoint cover sets (CSs) using a new multi-objective integer linear programming (ILP) model. Set of remaining nodes that could not be formed into an independent CS, are allocated to the existing CSs as a subset of potential cluster heads (CHs) i.e., for every active CS, CHs are chosen from its potential CH subset. In the second phase, the algorithm activates CSs one after another to gather information from targets and forward them to the user in a hierarchical manner via a modified multi-objective mixed integer linear programming (MILP) model. Both of the ILP and MILP models are solved using branch-and-bound method. The solutions of the optimization models are solved to optimality. The superiority of the proposed method is proven through numerous experiments in different scenarios compared with two of the most related works.

A dynamic multi-objective location-allocation model for search and rescue assets

This paper presents a dynamic multi-objective mixed integer linear programming model to optimize the location and allocation of search and rescue (SAR) boats and helicopters to enhance the performance of maritime SAR missions. Our model incorporates simulated incident scenarios to account for demand uncertainty and allows relocation of vessels seasonally. We define three objectives as responding to incidents within a critical time, generating a balanced workload distribution among vessels of various types, and minimizing costs associated with operations and vessel relocations. Implementing a goal programming approach, we solve the problem for various objective function term weights and compare the performance of each solution with respect to 10 different metrics. Using historical incident datasets for the Aegean Sea, we show that the proposed model and solution approach can significantly improve the SAR performance and provide decision support for planners in developing effective and efficient resource location-allocation schemes.

Multi-objective fuzzy programming model to design a sustainable supply chain network considering disruption

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mixed-integer linear programming (MILP) model for use in the design of a sustainable closed loop supply chain network under uncertain conditions. The proposed model aims to minimize total cost, optimize environmental impacts of establishment of facilities, processing and transportation between each level as well as social impacts including customer satisfaction. Due to changes in business environment the uncertainty existed in the research problem, in this paper the chance constrained fuzzy programming approach applied to cope with uncertainties in parameter of the proposed model. Then the proposed multi-objective model solves as single-objective model using LP-metric method.

A multi-objective mixed-integer linear model for sustainable fruit closed-loop supply chain network

PurposeThis paper aims to present a closed-loop supply chain (CLSC) optimization problem for a perishable agricultural product to achieve three pillars of sustainability, including minimizing total network costs and carbon dioxide emissions from different network activities and maximizing responsiveness to demands simultaneously.Design/methodology/approachThe research problem is formulated as a multi-objective mixed-integer linear programming model, and classical approaches, including the LP-Metric and weighted Tchebycheff method, have been applied to solve the optimization model. A set of test problems has been proposed to validate the model, and the results are presented.FindingsComputational time to find Pareto optimal solutions by using the weighted Tchebycheff method was twice as much as that of the LP-Metric method. Also, the result of the study is a mathematical model that can be applied to other products that are close to the fruit, such as vegetables.Research limitations/implicationsThe present study is limited to fruits supply chains and the inventory is considered at the distribution centers only. The study also considers only one type of transport.Practical implicationsThe paper can assist supply chain managers to define strategies to achieve a sustainable CLSC network configuration for the fruits.Originality/valueThis study is one of the early studies to consider environmental indicators in fruits supply chain design along with two other indicators of sustainability, namely, economic and social indicators. Therefore, this can help supply chain managers to achieve sustainability by optimizing location decisions, inventory quantities and flow between facilities.

Multi-objective optimization for the deployment of carbon capture utilization and storage supply chain considering economic and environmental performance

Carbon capture utilization and storage (CCUS) is widely recognized as a promising mitigation technology that would significantly reduce carbon dioxide (CO2) emission. This study develops an optimization-based framework for the deployment of CCUS supply chain with economic and environmental concerns. The overall supply chain is optimized based on superstructure method over a 20 years’ time horizon to provide the location and scale of capture and sequestration sites as well as the most efficient CO2 transport routes capable of meeting the reduction target. The resulting problem is a multi-objective mixed integer linear programming (MILP) problem, whose objectives include minimizing total annual cost and environmental impact. The environmental impact is measured by Global Warming Potential (GWP) imposed by the supply chain operation and quantified according to the principles of Life cycle assessment (LCA). ε-Constraint method is implemented to solve the resultant multi-objective model. A realistic case study that addresses the optimal design of the CCUS supply chain needed to meet the reduction target in Northeast China is studied to demonstrate the application of the proposed model. Results obtained provides valuable insights into the addressed problem and guides the decision-maker to adopt more sustainable alternatives in the deployment of CCUS.

Multi-objective optimization of sustainable biomass supply chain network design

This paper addresses the optimal design and planning of the biomass supply chain network that encompasses flow from poultry farms to biogas facilities. A novel multi-stage solution methodology is developed to solve the sustainable biomass supply chain network design problem. Geographical Information Systems, and Analytic Hierarchy Process Techniques are used to determine the candidate location of biogas facilities. The proposed multi-objective mixed integer linear programming model is capable of making strategic decisions (optimal biogas facility locations with capacities) along with the tactical decisions (transportation network flows). The model incorporates the two objective function of maximization of the profit, and minimization of total distance between poultry farms and biogas facilities. The aim is to determine the optimal number, location, and size of the biogas facilities, as well as the network flow, and electricity generated. The applicability of the model and solution methodology is demonstrated through a case study for a poultry supply chain network in Turkey. Additionally, sensitivity analysis is conducted to account for the impact of different parameters on the model. Sensitivity analysis show that both maximum distance parameter, and purchasing prices have major impact on decisions, and financial yield.

AN OPTIMAL C&D WASTE LOGISTICS NETWORK DESIGN FROM CONTRACTORS’ PERSPECTIVE

ABSTRACT The construction industry is one of the major producers of municipal solid waste. Although there are many studies in municipal solid waste management, the research on the recovery of recyclable building material from construction sites remains limited. This paper addresses the optimal design issue of the construction and demolition (C&D) waste logistics network based on the features of the construction industry from the contractors’ perspective. The purpose of this paper is to provide an optimal C&D waste recycling network decision (RND) model considering the change of construction sites location over time. A multi-period and multi-objective mixed-integer linear programming model was developed to minimize the cost of C&D waste disposal for contractors, and to minimize the carbon emissions from C&D waste transportation. An application study was conducted to assess the performance of the RND model. Through some sensitivity analysis experiments based on an immune genetic algorithm, the influences of environmental policies and carbon tax policy on improving the recycling rate of C&D waste and reduce the carbon emission were explored. The findings of this research suggest that: (1) a RND model with the feature of the construction industry developed in this paper can effectively optimize the C&D waste logistics network; (2) government policies and laws are valid political instruments to improve the recycling rate of C&D waste; (3) the carbon-tax analyses demonstrate that a carbon tax policy can effectively reduce carbon emissions.

Scalable Application- and User-aware Resource Allocation in Enterprise Networks Using End-Host Pacing

Providing scalable user- and application-aware resource allocation for heterogeneous applications sharing an enterprise network is still an unresolved problem. The main challenges are as follows: (i) How do we define user- and application-aware shares of resources? (ii) How do we determine an allocation of shares of network resources to applications? (iii) How do we allocate the shares per application in heterogeneous networks at scale? In this article, we propose solutions to the three challenges and introduce a system design for enterprise deployment. Defining the necessary resource shares per application is hard, as the intended use case, the user’s environment, e.g., big or small display, and the user’s preferences influence the resource demand. We tackle the challenge by associating application flows with utility functions from subjective user experience models, selected Key Performance Indicators, and measurements. The specific utility functions then enable a mapping of network resources in terms of throughput and latency budget to a common user-level utility scale. A sensible distribution of the resources is determined by formulating a multi-objective mixed integer linear program to solve the throughput- and delay-aware embedding of each utility function in the network for a max-min fairness criteria. The allocation of resources in traditional networks with policing and scheduling cannot distinguish large numbers of classes and interacts badly with congestion control algorithms. We propose a resource allocation system design for enterprise networks based on Software-Defined Networking principles to achieve delay-constrained routing in the network and application pacing at the end-hosts. The system design is evaluated against best effort networks in a proof-of-concept set-up for scenarios with increasing number of parallel applications competing for the throughput of a constrained link. The competing applications belong to the five application classes web browsing, file download, remote terminal work, video streaming, and Voice-over-IP. The results show that the proposed methodology improves the minimum and total utility, minimizes packet loss and queuing delay at bottlenecks, establishes fairness in terms of utility between applications, and achieves predictable application performance at high link utilization.