Multi-objective Mixed Integer Linear Programming Research Articles

A multi-objective optimisation model for production and transportation planning in a marine shrimp farming supply chain network

The traditional operation of marine shrimp farming is widely practiced in Southeast Asia. Giant freshwater prawn farming is one of the main types of marine shrimp farming that also still operates traditionally. Many of these farms operate without advanced techniques for production planning, inventory control, and transportation strategic decisions throughout the supply chain network which are among the most important managerial activities in commercial farming. Maintaining product freshness is of vital importance for aquaculture product. Therefore, this paper develops a multi-objective mixed-integer linear programming model for a marine shrimp farming supply chain network design problem. The problem is to plan production and control inventory according to constraints while maximise total profit surplus and minimise shortest route. A multi-echelon, multi-facility, and multi-period mathematical model is proposed such that real conditions are considered. In the end, some numerical illustrations are provided to show the proper Pareto solutions considering all of the objectives for the decision maker.

Addendum to “FPBH: A feasibility pump based heuristic for multi-objective mixed integer linear programming” [Comput. Oper. Res. 112 (2019) 104760

This is an addendum to the article ’Pal, A. and Charkhgard, H, “A feasibility pump based heuristic for multi-objective mixed integer linear programming”, Computers & Operations Research 112:104760, 2019. In that work, a comparison was made to another method – a multi-directional local search. This was done using a pre-existing code. After the above work was published, evidence emerged that the mentioned pre-existing code contained a bug. In this addendum note, that bug is corrected and updated comparative results are provided.

Designing a sustainable closed-loop supply chain network of face masks during the COVID-19 pandemic: Pareto-based algorithms

This study develops a novel mathematical model to design a sustainable mask Closed-Loop Supply Chain Network (CLSCN) during the COVID-19 outbreak for the first time. A multi-objective Mixed-Integer Linear Programming (MILP) model is proposed to address the locational, supply, production, distribution, collection, quarantine, recycling, reuse, and disposal decisions within a multi-period multi-echelon multi-product supply chain. Additionally, sustainable development is studied in terms of minimizing the total cost, total pollution and total human risk at the same time. Since the CLSCN design is an NP-hard problem, Multi-Objective Grey Wolf Optimization (MOGWO) algorithm and Non-Dominated Sorting Genetic Algorithm II (NSGA-II) are implemented to solve the proposed model and to find Pareto optimal solutions. Since Meta-heuristic algorithms are sensitive to their input parameters, the Taguchi design method is applied to tune and control the parameters. Then, a comparison is performed using four assessment metrics including Max-Spread, Spread of Non-Dominance Solution (SNS), Number of Pareto Solutions (NPS), and Mean Ideal Distance (MID). Additionally, a statistical test is employed to evaluate the quality of the obtained Pareto frontier by the presented algorithms. The obtained results reveal that the MOGWO algorithm is more reliable to tackle the problem such that it is about 25% superior to NSGA-II in terms of the dispersion of Pareto solutions and about 2% superior in terms of the solution quality. To validate the proposed mathematical model and testing its applicability, a real case study in Tehran/Iran is investigated as well as a set of sensitivity analyses on important parameters. Finally, the practical implications are discussed and useful managerial insights are given.

Sustainable, resilient and responsive mixed supply chain network design under hybrid uncertainty with considering COVID-19 pandemic disruption.

The occurrence of the COVID-19 pandemic is a disruption that has adversely affected many supply chains (SCs) around the world and further proved the necessity of combination and interaction of resilience and sustainability. In This paper, a multi-objective mixed-integer linear programming model is developed for responsive, resilient and sustainable mixed open and closed-loop supply chain network design (SCND) problem. The uncertainty of the problem is handled with a hybrid robust-stochastic optimization approach. A Lagrangian relaxation (LR) method and a constructive heuristic (CH) algorithm are developed for overcoming problem complexity and solving large-scale instances. In order to assess the performance of the mathematical model and solution methods, some test instances are generated. The computations showed that the model and the solution methods are efficient and can obtain high-quality solutions in suitable CPU times. Other analyses and computations are done based on a real case study in the tire industry. The results demonstrate that resilient strategies are so effective and can improve economic, environmental and social dimensions substantially. Research findings suggest that the proposed model can be used as an efficient tool for designing sustainable and resilient SCs and the related decision-makings. Also, our findings prove that resilience is necessary for continued SC sustainability. It is concluded that using proposed resilience strategies simultaneously brings the best outcome for SC objectives. Based on the sensitivity analyses, the responsiveness level significantly affects SC objectives, and managers should consider the trade-off between responsiveness and their objectives.

Robust Optimization Model for Probabilistic Protection With Multiple Types of Resources

This paper proposes a robust optimization model for probabilistic protection with multiple types of resources to minimize the required backup capacity for each type of resource against multiple random failures of physical machines in a cloud provider. If random failures occur, the required capacities for virtual machines are allocated to the preplanned backup physical machines, which are determined in advance. Probabilistic protection restricts the probability that the workload caused by failures exceeds the backup capacity by a given survivability parameter. We introduce three survivability parameters for central processing unit (CPU), memory, and the entire cloud provider considering both CPU and memory. By using the relationship between the three survivability parameters, the proposed model guarantees probabilistic protection for each resource, CPU and memory, and the entire cloud provider. By adopting the robust optimization technique, we formulate the proposed model as a multi-objective mixed integer linear programming problem. To deal with the multi-objective optimization problem, we apply the lexicographic weighted Tchebycheff method with which a Pareto optimal solution is obtained. We show that our proposed model reduces the average value between the backup capacity ratios of CPU and memory compared with the conventional model. A multi-objective simulated annealing (MOSA) and nondominated sorting genetic algorithm II (NSGA-II) are adopted to solve larger size problems. By using them, approximate solutions are obtained for larger size problems. In addition, we find that NSGA-II searches for solutions more effectively than MOSA, in our backup capacity allocation problem.

A comprehensive framework for sustainable closed-loop supply chain network design

Many companies face challenges in reducing their supply chain costs while increasing sustainability and customer service levels. A comprehensive framework for a sustainable closed-loop supply chain (CLSC) network is a practical solution to these challenges. Hence, for the first time, this study considers an integrated multi-objective mixed-integer linear programming (MOMILP) model to design sustainable CLSC networks with cross-docking, location-inventory-routing, time window, supplier selection, order allocation, transportation modes with simultaneous pickup, and delivery under uncertainty. An intelligent simulation algorithm is proposed to produce CLSC network data with probabilistic distribution functions and feasible solution space. In addition, a fuzzy goal programming approach is proposed to solve the MOMILP model under uncertainty. Eight small and medium-size test problems are used to evaluate the performance of the proposed model with the simulated data in GAMS software. The results obtained from test problems and sensitivity analysis show the efficacy of the proposed model.

Multi-objective robust optimization for multi-stage-multi-product agile closed-loop supply chain under uncertainty in the context of circular economy

Purpose A circular economy (CE) is an economic system that tries to eliminate waste and continually use resources. Due to growing environmental concerns, supply chain (SC) design should be based on the CE considerations. In addition, responding and satisfying customers are the challenges managers constantly encounter. This study aims to improve the design of an agile closed-loop supply chain (CLSC) from the CE point of view. Design/methodology/approach In this research, a new multi-stage, multi-product and multi-period design of a CLSC network under uncertainty is proposed that aligns with the goals of CE and SC participants. Recycling of goods is an important part of the CLSC. Therefore, a multi-objective mixed-integer linear programming model (MILP) is proposed to formulate the problem. Besides, a robust counterpart of multi-objective MILP is offered based on robust optimization to cope with the uncertainty of parameters. Finally, the proposed model is solved using the e-constraint method. Findings The proposed model aims to provide the strategic choice of economic order to the suppliers and third-party logistic companies. The present study, which is carried out using a numerical example and sensitivity analysis, provides a robust model and solution methodology that are effective and applicable in CE-related problems. Practical implications This study shows how all upstream and downstream units of the SC network must work integrated to meet customer needs considering the CE context. Originality/value The main goal of the CE is to optimize resources, reduce the use of raw materials, and revitalize waste by recycling. In this study, a comprehensive model that can consider both SC design and CE necessities is developed that considers all SC participants.

Course timetabling in medical universities given physicians' educational and clinical tasks

The physician assignment and course timetabling problem at medical universities is a generalized version of the academic timetabling problem. This problem entails assigning courses, educational and clinical tasks to physician faculty members over a semester or academic year. The problem of timetabling academic courses and scheduling physicians in a hospital has been investigated independently in previous studies in this field. These two fields of research are brought together in this article through the presentation of a multi-objective mixed-integer linear programming (MILP) model. The proposed model is based on two optimization criteria: minimizing workload imbalance and maximizing physician preferences. The model is applied to a case study involving the assignment of physicians to courses, educational and clinical tasks at Kurdistan University of Medical Sciences' Department of Infectious Diseases. Pareto solutions are obtained using an enhanced version of the augmented epsilon constraint implemented in the GAMS optimization software; one is selected as the most desirable solution using the TOPSIS method. The proposed model is generic and could be adapted for use in other departments or medical schools.

A simple empirical inventory model for managing the processed corneal tissue equitably in hospitals with demand differentiation

This paper peruses one of the most challenging healthcare concerns related to human organ transplantation. In this regard, a medical system’s health-economic objectives are investigated to (1) achieve a desirable level of health equity in offering healthcare services to patients who are differentiated in terms of medical conditions, and (2) minimize total costs incurred across managing the inventory. This paper presents the first-ever operational research study to manage processed corneal tissue (PCT). Besides, hybrid demand-oriented policies have been proposed to equitably issue and assign specific inventories to demands with distinct medical urgent levels (ULs). In this regard, a practical multi-objective mixed-integer linear programming (MOMILP) model is proposed for a system with multiple products that can be substituted with each other according to medical priorities. A goal programming (GP) approach is utilized to find the optimum solution. The applicability of the model is validated through a real case study. Finally, several sensitivity analyses are conducted to examine the effect of critical parameters on the solutions to gain useful managerial insights. The results show that the proposed health-economic trade-off is well performed and can efficiently handle the real case.

Optimizing an equitable micro‐hydropower deployment: Application of a multi‐objective method for rural Indonesia

AbstractMuch of the developing world is still struggling to provide electricity to rural populations. Extending the grid is frequently not feasible or too expensive in rural and remote areas. In such situations, micro‐hydropower (MHP) can be a cost‐effective source of renewable off‐grid electricity and can be easier to implement and more reliable than a number of other generation technologies. This study employs multi‐objective mixed‐integer‐linear programming (MOMILP) to identify nondominated MHP portfolios to meet rural electricity needs across Indonesia. Besides maximizing the new MHP generation capacity within a fixed budget, this study also incorporates equity as an objective. The equity issue becomes crucial to ensure that government resources are deployed in a manner that considers impacts for the entire population. The MOMILP optimizes a weighted objective function that applies different relative weights to the objectives of generation capacity and equity, subject to several constraints on resource availability and capacity shortfall, as well as budget. In this way, we identify solutions on the Pareto frontier for investment in MHP generation in remote Indonesian rural communities. We illustrate the tradeoffs involved in meeting capacity shortfalls with and without considering equity across provinces and identify non‐dominated MHP portfolios that the Indonesian government could implement to increase rural electrification efficiently.

Optimizing Painting Sequence Scheduling Based on Adaptive Partheno-Genetic Algorithm

In this paper, we formulate and solve a novel real-life large-scale automotive parts paint shop scheduling problem, which contains color arrangement restrictions, part arrangement restrictions, bracket restrictions, and multi-objectives. Based on these restrictions, we construct exact constraints and two objective functions to form a large-scale multi-objective mixed-integer linear programming problem. To reduce this scheduling problem’s complexity, we converted the multi-objective model into a multi-level objective programming problem by combining the rule-based scheduling algorithm and the adaptive Partheno-Genetic algorithm. The rule-based scheduling algorithm is adopted to optimize color changes horizontally and bracket replacements vertically. The adaptive Partheno-Genetic algorithm is designed to optimize production based on the rule-based scheduling algorithm. Finally, we apply the model to the actual optimization problem that contained 829,684 variables and 137,319 constraints, and solved this problem by Python. The proposed method solves the optimal solution, consuming 575 s.

A Study into the Availability, Costs and GHG Reduction in Drop-In Biofuels for Shipping under Different Regimes between 2020 and 2050

In this study, various scenarios were developed that correspond to estimations of future biomass availability and biofuel demand from the maritime industry. These marine biofuel demand scenarios were based on the Greenhouse Gas (GHG) reduction targets of the Renewable Energy Directive II (RED II) and the International Maritime Organization (IMO). A multi-objective Mixed Integer Linear Programming (MILP) model was developed which is used to optimize the Well-to-Tank (WtT) phases of each studied scenario. This resulted in an overview of the most feasible use of feedstocks, deployment of new conversion technologies and trade flows between regions. Additionally, the results provided insight into the costs and emission reduction potential of marine biofuels. By analyzing the results from this study, improved insight into the potential of drop-in biofuels for reaching the proposed emission reduction targets for the maritime sector was developed. A trade-off between costs and emissions was found to result in potential GHG reductions between 68–95% compared to Heavy Fuel Oil (HFO) for 800–2300 EUR/ton. More specifically, 80% GHG reduction compared to HFO can be achieved at fuel costs of between 900–1050 EUR/ton over the studied time period.

Real-time integrated train rescheduling and rolling stock circulation planning for a metro line under disruptions

More and more unexpected events occur in metro systems, which may cause serious disturbances and even disruptions for the operation of trains. This paper studies an integrated train rescheduling and rolling stock circulation planning problem for the complete blockage situations in a metro line. We consider several key practical train operation constraints, including the maximum number of available rolling stocks, the turnaround constraints, the service connection constraints. This problem is viewed as a complex multi-objective mixed integer linear programming (MILP) formulation, where the objectives involve the deviations with respect to the timetable, the (partial) cancellations, and the headway deviations of train services. A two-stage approach is also developed to enhance the computational efficiency, where a smaller-size optimization problem is solved in the first stage, by considering a set of key turnaround stations only, while the original MILP problem is solved in the second stage by fixing some binary variables according to the first stage solution. In addition, we propose a heuristic technique that is based on introducing a new set of constraints to reduce the search space without eliminating potentially good solutions. Comprehensive experiments are investigated based on the practical data of Beijing Subway Lines, where the proposed integrated models and approaches yield much better solutions when compared with a widely used strategy, i.e., holding (waiting at station) strategy and the sequential approach. Moreover, the impacts of the complete blockage locations/durations and the effects of different weight settings in the multi-objective optimization are deeply analyzed.

A robust fuzzy multi-objective programming model to design a sustainable hospital waste management network considering resiliency and uncertainty: A case study.

With the increase in the number of patients and activity of hospitals, the issue of hospital waste management (HWM) is becoming more and more challenging and worrying. In addition to financial losses, there will be irreparable damage to the ecosystem and environment which will create many problems for people (because the job of some people in the area is livestock and agriculture and they have a lot to do with their surroundings). It also doubles the need to pay attention to the issue of sustainable development (simultaneous attention to social, economic and environmental dimensions) in waste management. Moreover, the climatic and geographical conditions and lack of proper waste management in this area lead to major problems. Therefore, in this research, by developing a novel multi-objective mixed integer linear programming model, HWM is addressed in the hospitals of Sari, Iran. The aim is to design an HWM network considering sustainability, resiliency and uncertainty. In order to deal with uncertainty, a robust fuzzy programming approach is employed, and then an improved goal programming technique and Lp-metric method is proposed to solve the model. It was revealed that goal programming outperforms the Lp-metric method in terms of all objectives. Furthermore, the obtained results demonstrate the applicability and efficiency of the proposed methodology to design an efficient sustainable HWM network.

Green dynamic multimodal logistics network design problem considering financing decisions: a case study of cement logistics.

Logistics network is one of the most important parts of supply chains with significant share in achieving sustainability across them. In this paper, we investigate a new multi-objective mixed integer linear programming model for the design of multimodal logistics network. A bi-objective mathematical model is introduced and two conflicting objectives including the minimization of total cost and the total environmental impact are taken into account. Effective environmental life cycle assessment-based method is incorporated in the model to estimate the relevant environmental impacts. Due to budget constraints, financing decisions for facility construction are considered in the proposed model. To cope with the model objective functions, the augmented ε-constraint method is applied. Computational analysis is also provided by using a cement multimodal rail-road logistics network case study to present the significance of the proposed model. Results show that utilizing the proposed multi-period optimization model influences the location of multimodal terminals and their construction time. Also, the results show that the use of the proposed model enhances the efficiency of terminals. On the other hand, computational results indicate that preferences of decision-makers and the importance of environmental objective have significant impacts on the topology of transportation network.

A multi-objective model to optimize country-scale municipal solid waste management with economic and environmental objectives: A case study in Malaysia

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A novel heuristic method for the energy-efficient flexible job-shop scheduling problem with sequence-dependent set-up and transportation time

With the increasing attention on environmental issues, green scheduling in manufacturing industries has become a hot research topic. As a typical scheduling problem, the flexible job-shop scheduling problem (FJSP) has received increasing attention, but research on the FJSP considering set-up and transportation times simultaneously is still rare. To address the energy-efficient FJSP with sequence-dependent set-up and transportation times to minimize makespan and total energy consumption, a multi-objective mixed-integer linear programming model of the problem is formulated and an effective novel heuristic method (NHM) is proposed. To enhance the convergence and distribution of the NHM, three strategies—population initialization, greedy iterative decoding and local intensification—are designed. The performance of the NHM is demonstrated by comparison with three algorithms through 48 instances. The results show that the NHM can obtain a scheduling scheme with lower makespan and total energy consumption than those of the comparison algorithms.

Multi-Objective Optimization to Support the Design of a Sustainable Supply Chain for the Generation of Biofuels from Forest Waste

The production and supply chain management of biofuels from organic waste as raw material has been identified as a promising strategy in the field of renewable energies and circular economy initiatives. This industry involves complex tasks such as strategic land use, feedstock purchasing, production plant location, production capacity strategy, and material flows, which can be solved by mathematical modeling. The study proposed a multi-objective mixed-integer linear programming model to design a sustainable supply chain of biofuels with forest residues from its triple function: economic, environmental, and social. The trade-offs between the proposed objectives were determined with computational results. The proposed objectives were profit maximization, CO2 minimization, and employment generation maximization. Thus, the proposed model serves as a tool for decision-making, allowing the projection of a long-term structure of the biofuel supply chains and contribute to the United Nations Sustainable Development Goals.

Sustainable Scheduling of the Production in the Aluminum Furnace Hot Rolling Section with Uncertain Demand

In order to reduce the energy consumption of furnaces and save costs in the product delivery time, the focus of this paper is to discuss the uncertainty of demand in the rolling horizon and to globally optimize the sustainability of the production in the aluminum furnace hot rolling section in environmental and economic dimensions. First, the triples α/β/γ are used to describe the production scheduling in the aluminum furnace hot rolling section as the scheduling of flexible flow shop, satisfied to constraints of demand uncertainty, operation logic, operation time, capacity and demand, objectives of minimizing the residence time of the ingot in the furnace and minimizing the makespan. Second, on the basis of describing the uncertainty of demand in rolling horizon with the scenario tree, a multi-objective mixed integer linear programming (MILP) optimization model for sustainable production in the aluminum furnace hot rolling section is formulated. Finally, an aluminum alloy manufacturer is taken as an example to illustrate the proposed model. The computational results show that when the objective weight combination takes the value of α=0.7, β=0.3, the sustainability indicators of the environmental and economic dimensions can be optimized to the maximum extent possible at the same time. Increasingly, managerial suggestions associated with the trade-off between environmental and economic dimensions are presented. Scheduling in the rolling horizon can optimize the production process of the aluminum furnace hot rolling section globally, indicating that it is more conducive to the sustainable development of the environment and economic dimensions than scheduling in a single decision time period.

A Hybrid Multi-Objective Evolutionary Algorithm-Based Semantic Foundation for Sustainable Distributed Manufacturing Systems

Rising energy prices, increasing maintenance costs, and strict environmental regimes have augmented the already existing pressure on the contemporary manufacturing environment. Although the decentralization of supply chain has led to rapid advancements in manufacturing systems, finding an efficient supplier simultaneously from the pool of available ones as per customer requirement and enhancing the process planning and scheduling functions are the predominant approaches still needed to be addressed. Therefore, this paper aims to address this issue by considering a set of gear manufacturing industries located across India as a case study. An integrated classifier-assisted evolutionary multi-objective evolutionary approach is proposed for solving the objectives of makespan, energy consumption, and increased service utilization rate, interoperability, and reliability. To execute the approach initially, text-mining-based supervised machine-learning models, namely Decision Tree, Naïve Bayes, Random Forest, and Support Vector Machines (SVM) were adopted for the classification of suppliers into task-specific suppliers. Following this, with the identified suppliers as input, the problem was formulated as a multi-objective Mixed-Integer Linear Programming (MILP) model. We then proposed a Hybrid Multi-Objective Moth Flame Optimization algorithm (HMFO) to optimize process planning and scheduling functions. Numerical experiments have been carried out with the formulated problem for 10 different instances, along with a comparison of the results with a Non-Dominated Sorting Genetic Algorithm (NSGA-II) to illustrate the feasibility of the approach.