Multi-objective Mixed-integer Programming Model Research Articles

Developing a Model for the University Course Timetabling Problem: A Case Study

Over recent years, timetable programming in academic settings has become particularly challenging due to such factors as the growing number of students, the variety of lectures, the inadequacy of educational facilities in some areas, and the incorporation of teachers and students’ preferences into the schedule. Many researchers, therefore, have been formulating the problem of timetabling lectures using different methods. In this research, a multiobjective mixed-integer programming model was developed to provide a timetable for the postgraduate courses at the Industrial Engineering Department of Islamic Azad University, Najafabad Branch (IAUN). The proposed model minimized the violation of the lecturers and educational priorities, the student travel time between classes, and the classes’ surplus capacity. To convert the multiobjective model into a single one, the ε-constraint method was adopted, and the model’s accuracy and feasibility were examined through a real example solved by the CPLEX solver of GAMS software. The results approved the efficiency of this model in preparing a timetable for university lectures.

An automatic multi-objective evolutionary algorithm for the hybrid flowshop scheduling problem with consistent sublots

Lot streaming is the most widely used technique to facilitate overlapping of successive operations. Inspired by real-world scenarios, this paper studies a multi-objective hybrid flowshop scheduling problem with consistent sublots, aiming to simultaneously optimize two conflicting objectives: the makespan and total number of sublots. Considering the setup and transportation operations, a multi-objective mixed integer programming model is developed and the trade-off between the two objectives is evaluated. Because of the NP-hard property of the addressed problem, metaheuristics are suggested. It is well known that the performance of metaheuristics is highly dependent on the setting of algorithmic parameters, referred to as numerical and categorical parameters. However, the traditional design process might be biased by previous experience. To eliminate these issues, an automated algorithm design (AAD) methodology is introduced to conceive a multi-objective evolutionary algorithm (MOEA) in a promising framework. The AAD enables designing the algorithm by automatically determining parameters and their combinations with minimal user intervention. With regard to the problem-specific characteristics and the employed algorithm framework, for the categorical parameters, including decomposition, solution encoding and decoding, solution initialization and neighborhood structures, several operators are designed specifically. Along with the numerical parameters, these categorical parameters are determined and combined using the designed iterated racing procedure. Comprehensive computational results demonstrate that the automated MOEA outperforms other state-of-the-art MOEAs for the addressed problem.

Merging make-to-stock/make-to-order decisions into sales and operations planning: A multi-objective approach

With the advent of mass customization and product proliferation, the appearance of hybrid Make-to-Stock(MTS)/Make-to-Order(MTO) policies arise as a strategy to cope with high product variety maintaining satisfactory lead times. In companies operating under this reality, Sales and Operations Planning (S&OP) practices must be adapted accordingly during the coordinated planning of procurement, production, logistics, and sales activities. This paper proposes a novel S&OP decision-making framework for a flow shop/batch company that produces standard products under an MTS strategy and customized products under an MTO strategy. First, a multi-objective mixed-integer programming model is formulated to characterize the problem. Then, a matrix containing the different strategies a firm in this context may adopt is proposed. This rationale provides a business-oriented approach towards the analysis of different plans and helps to frame the different Pareto-optimal solutions given the priority on MTS or MTO segments and the management positioning regarding cost minimization or service level orientation. The research is based on a real case faced by an electric cable manufacturer. The computational experiments demonstrate the applicability of the proposed methodology. Our approach brings a practical, supply chain-oriented, and mid-term perspective on the study of operations planning policies in MTS/MTO contexts.

The Road to Prosperity: A Study on the Efficiency of Resource Allocation in China’s Expressway Construction

This paper presents a new multi-objective mixed integer programming model to prioritize seven highway infrastructure projects. The proposed model explicitly incorporates socio-economics, uncertainty, resource constraints, and interdependencies to deal with the optimal transportation infrastructure project selection problem. Next, project prioritization is determined based on the ANP results, which reflect the interdependency between criteria and a set of feasible candidate projects. Finally, an empirical study of eastwest highway improvement program is conducted to illustrate how the modeling process proceeds. The results show that the proposed model can effectively support a transportation investment policy that best suits the goal of urban land redevelopment for highly urbanized settings. As such, the model can be generalized for other human settlement studies and illustrate the spatially complex characteristics of transportation networks as well as some of the difficulties raised with respect to priority of national capital improvement projects. The research will provide a useful reference for the study of the relationship between highways and regional economic development.

Multi-objective 3D bin packing problem with load balance and product family concerns

The classical three-dimensional bin packing problem (3D-BPP) orthogonally packs a set of rectangular items with varying dimensions into the minimum number of three-dimensional rectangular bins. While ensuring the minimum number of bins used, the safety of the logistic operations is addressed with the complementary load-balancing objective for which concepts such as orientation and stability are used in the literature though not at the same time. In this study, we extend the load-balanced 3D-BPP by combining both orientation and stability, and introducing a new concept called family unity which encourages packing a family of products (e.g., from the same order and with the same destination) together. Although item related concerns are very common in practice, there are no multi-objective studies in the bin packing literature that includes family unity concept. Therefore, this is the first study that proposes a multi-objective mixed integer programming model for the extended problem to determine the optimal packing plan that minimizes the number of bins used and the deviation of balance from the ideal barycenter while maximizing family unity ratio via a weighted objective function. A numerical example is provided to analyze the performance of the proposed model. Furthermore, a real-life container loading problem is solved and outputs of the study implies the practical advantages of including family unity and load-balance considerations in solving 3D-BPP problems.

A multi-objective optimal decision model for a green closed-loop supply chain under uncertainty: A real industrial case study

Green closed-loop supply chain management is an important topic for business operations today because of increasing resource scarcity and environmental issues. Companies not only have to meet environmental regulations, but also must ensure high quality supply chain operation as a means to secure competitive advantages and increase profits. This study proposes a multi-objective mixed integer programming model for an integrated green closed-loop supply chain network designed to maximize profit, amicable production level (environmentally friendly materials and clean technology usage), and quality level. A scenario-based robust optimization method is used to deal with uncertain parameters such as the demand of new products, the return rates of returned products and the sale prices of remanufactured products. The proposed model is applied to a real industry case example of a manufacturing company to illustrate the applicability of the proposed model. The result shows a robust optimal resource allocation solution that considers multiple scenarios. This study can be a reference for closed-loop supply chain related academic research and also can be used to guide the development of a green closed-loop supply chain model for better decision making.

A multi-objective fuzzy robust stochastic model for designing a sustainable-resilient-responsive supply chain network

This study proposes a multi-objective mixed-integer programming model to configure a sustainable supply chain network while considering resilience and responsiveness measures. The model aims at minimizing the total costs and environmental damages while maximizing the social impacts, as well as the responsiveness and resilience levels of the supply chain network. An improved version of the fuzzy robust stochastic optimization approach is proposed to tackle the uncertain data arising in the dynamic business environment. Furthermore, a new version of meta-goal programming named the multi-choice meta-goal programming associated with a utility function is developed to solve the resulting multi-objective model. A case study in the water heater industry is investigated to illustrate the application of the proposed model and its solution approach. The numerical results validate the proposed model and the developed solution method. Finally, interactions between the sustainability, responsiveness, and resilience dimensions are investigated and several sensitivity analyses are performed on critical parameters by which useful managerial insights are provided.

A multi-objective stochastic programming model to configure a sustainable humanitarian logistics considering deprivation cost and patient severity

As the occurrence of disasters has increased frequently and has resulted in growing concern about their adverse effects on the environment, Sustainable Humanitarian Logistics (SHL) has received great attention recently. SHL aims to reduce disaster damages in an environmentally-friendly manner in the shortest possible time. The terms including ‘environmentally-friendly’ and ‘shortest possible time’ refer to the environmental and social aspects of sustainability. This research proposes a stochastic multi-objective mixed-integer programming model to configure an SHL network during the response phase. Having compared to the research literature, this is the first study that considers economic, social, and environmental aspects of sustainability by incorporating relief cost, deprivation cost, and carbon emissions, respectively. Then, the improved multi-choice goal programming approach is applied to solve the proposed multi-objective model. To indicate the validity of the proposed model, an earthquake that occurred in a region of Kermanshah, Iran, in 2017 is investigated as a real case study. Finally, sensitivity analysis is performed and several managerial and theoretical insights are provided. The results show that exerting environmental issues in humanitarian logistics does not necessarily increase the relief costs, but can be in contrast with the social aspect. Furthermore, a minor increase in the budget of the preparedness phase drastically decreases the response costs.

Integrating data visibility decision in a multi-objective procurement transport planning under risk: A modified NSGA-II

The purpose of this paper is an in-depth investigation of the interplay between suppliers’ data visibility and procurement risks in the supplier selection and procurement planning problem. The role of suppliers’ ability to share high-quality data is incorporated into a decision-making environment. We consider supply chain visibility (as an exogenous decision) to increase the buyer’s awareness of the order status and manage supply chain risks. In doing so, a multi-attribute information visibility index is proposed to measure suppliers’ capability to share the required visible data. A novel multi-objective mixed-integer programming model is then developed to determine the cross-functional policy of purchasing and transportation under risk. A Non-dominated Sorting Genetic Algorithm (NSGA-II) is also tailored to attain Pareto-optimal solutions. Our result indicates the superiority of the proposed NSGA-II algorithm.

A routing and scheduling problem for cross-docking networks with perishable products, heterogeneous vehicles and split delivery

Cross-docking is an effective logistics strategy that has long been employed in supply chains with perishable products, where short processing time of goods is required. In this paper, a new multi-objective mixed-integer programming (MIP) model is proposed for scheduling and routing of heterogeneous vehicles carrying perishable goods across multiple cross-docking systems. Inspired by the actual business operations of a large supermarket chain, multiple cross-docks with simultaneous split pick-up and delivery tasks are considered, each of which processing either general or perishable products. In addition, all pick-up/delivery (P/D) requests for perishable products have a deadline that must be met. The main objectives of the developed model are to reduce distribution costs, accelerate distribution processing time, and maximize the cross-docking network’s capacity utilization rate. To overcome the complexity of the formulated problem, a novel hybrid solution method, namely AUGMECON2-VIKOR is developed and used in the case-study. The results reveal that AUGMECON2-VIKOR outperforms AUGMECON2, particularly when a larger number of grid points are considered in the proposed solution algorithm.

An effective multi-objective whale swarm algorithm for energy-efficient scheduling of distributed welding flow shop

Distributed welding flow shop scheduling problem is an extension of distributed permutation flow shop scheduling problem, which possesses a set of identical factories of welding flow shop. On account of several machines can process one job simultaneously in welding shop, increasing the amount of machines can short the processing time of operation while waste more energy consumption at the same time. Thus, energy-efficient is of great significance to take total energy consumption into account in scheduling. A multi-objective mixed integer programming model for energy-efficient scheduling of distributed welding flow shop is presented based on three sub-problems with allocating jobs among factories, scheduling the jobs in each factory and determining the amount of machines upon each job. A multi-objective whale swarm algorithm is proposed to optimize the total energy consumption and makespan simultaneously. In the proposed algorithm, a new initialization method is designed to improve the quality of the initial solution. And various update operators, as well as local search, are designed according to the feature of the problem. To conduct the experiment, diversified indicators are applied to evaluate the proposed algorithm and other MOEAs performance. And the experiment results demonstrate the effectiveness of the proposed method. The proposed algorithm is applied in the real-life case with great performance compared with other MOEAs.

Physical Internet: First results and next challenges

Physical Internet: First results and next challenges

Allocation and Scheduling of Handling Resources in the Railway Container Terminal Based on Crossing Crane Area

The integrated allocation and scheduling of handling resources are crucial problems in the railway container terminal (RCT). We investigate the integrated optimization problem for handling resources of the crane area, dual-gantry crane (GC), and internal trucks (ITs). A creative handling scheme is proposed to reduce the long-distance, full-loaded movement of GCs by making use of the advantages of ITs. Based on this scheme, we propose a flexible crossing crane area to balance the workload of dual-GC. Decomposing the integrated problem into four sub-problems, a multi-objective mixed-integer programming model (MIP) is developed. By analyzing the characteristic of the integrated problem, a three-layer hybrid heuristic algorithm (TLHHA) incorporating heuristic rule (HR), elite co-evolution genetic algorithm (ECEGA), greedy rule (GR), and simulated annealing (SA) is designed for solving the problem. Numerical experiments were conducted to verify the effectiveness of the proposed model and algorithm. The results show that the proposed algorithm has excellent searching ability, and the simultaneous optimization scheme could ensure the requirements for efficiency, effectiveness, and energy-saving, as well as the balance rate of dual-GC.

Multi-objective migrating bird optimization algorithm for cost-oriented assembly line balancing problem with collaborative robots

Industries are increasingly looking for opportunities at utilizing collaborative robots in assembly lines to perform the tasks independently or assist the human workers due to the advancement of industry 4.0 technologies. Purchasing cost is one of the important factors to be considered by production managers, while designing or redesigning assembly line when collaborative robots are being utilized. Several objectives are to be optimized in an assembly line balancing problem and optimizing line efficiency along with purchasing cost sometimes results in conflicting situation. This paper presents the first study to tackle the cost-oriented assembly line balancing problem with collaborative robots, where several different types of collaborative robots with different purchasing costs are available and selected. A multi-objective mixed-integer programming model is developed to minimize the cycle time and the total collaborative robot purchasing cost. The multi-objective migrating bird optimization algorithm is developed to obtain a set of high-quality Pareto solutions. This algorithm utilizes the fast non-dominated sorting approach to update the population and develops a restart mechanism to select one solution in the permanent Pareto archive to replace the abandoned solution which remains unchanged for several iterations. The computational study validates that the utilization of the multi-objective model is reasonable and developed algorithm produces competing performance in comparison with multi-objective non-dominated sorting genetic algorithm II, multi-objective simulated annealing algorithm and two multi-objective artificial bee colony algorithms.

A location-allocation model of maintenance resources based on fault distribution for agricultural machinery maintenance service network

Aiming at the location-allocation of maintenance resources for agricultural machinery maintenance service network, a multi-objective mixed-integer programming model is established, and an uncertain set is added to ensure the robustness of the results. Given the difference between the service network of agricultural machinery and other emergency service networks, this paper proposes a method to reduce the service cost by adjusting the fault distribution of agricultural machinery. The non-dominated sorting genetic algorithm II is applied to solve the model. Finally, a numerical example and a practical example are given to illustrate the effectiveness of the proposed model.

A Mathematical Model for Course Timetabling Problem With Faculty-Course Assignment Constraints

University course timetabling problem (UCTP) includes the challenging task of generating an automated timetable for courses under resource limitations. Manual generated timetables might hold some errors and consume a long time to create feasible solutions. Thus, there is a need to find optimal and fast solutions for this problem. The difficulty of the timetabling problem is further increased when tackling faculty-related constraints, according to their requirements, preferences, and availability. Thus, student-related constraints are usually the focus of UCTP generated solutions, in which faculty constraints are limited to their teaching load or preferences. This paper proposes a multi-objective mixed-integer programming model for a preregistration UCTP, combined with faculty-related constraints. The goal is to maximize events assignments and faculty-members preferences satisfaction while balancing the university requirements. At the same time, student learning days and unassigned events are minimized. The model is tested with eight real-world instances. Computational experiments are carried out to show the efficiency of the model. The proposed method can generate optimal timetables for all problem instances that satisfy faculty constraints.

A resilient and sustainable closed-loop supply chain using multiple sourcing and information sharing strategies

Abstract The interaction of sustainability and resilience has not been sufficiently addressed in the supply chain literature. Applying sustainability and resilience concepts into a supply chain means the simultaneous optimization of the cost and recourses, including human and environmental ones, for facing possible risks. Thus, the primary motivation of this paper is to consider sustainability and resilience in a closed-loop supply chain simultaneously. For this purpose, the specialists and academics were asked to identify the impacts of supply chain’s strategies on the resilience criteria in linguistic variables. Then, the resulting matrix was solved using fuzzy TOPSIS, and the information sharing and multiple sourcing were selected as the first and second strategies. Accordingly, a new multi-objective mixed-integer programming model was formulated for a closed-loop supply chain. In this research, different dimensions of sustainability have been taken into account through reducing the total cost, energy consumption, and pollution and increasing job opportunities. Information sharing and multiple sourcing strategies have been employed in model development for making supply chain more resilient. The real data of a tire industry was used for validating the proposed model, and the model was solved using the improved version of the augmented e-constraint (AUGMECON2) method. The results emphasized the necessity of combining sustainability and resilience in the closed-loop supply chain.

Optimisation of waste clean-up after large-scale disasters

Disaster waste clean-up after large disasters is one of the core activities at the recovery stage of disaster management, which aims to restoring the normal functioning of the disaster affected area. In this paper we considered a waste clean-up system consists of (i) demolition operation, (ii) collection of waste from customer nodes to temporary disaster waste management sites (TDWMSs), (iii) processing at TDWMSs, and (iv) transportation of the waste to final disposal sites in the recovery of disasters. A multi-objective mixed integer programming model is developed to minimise the total clean-up cost and time. Three different approaches are developed to solve the problem, which are tested with artificial instances and a real case study. Results of artificial instances indicate that the models developed can be used to obtain close to optimal solutions within an acceptable computing time. Results of the case study can facilitate the decision-makers to develop the waste clean-up with minimised total cost and clean-up time by selecting the right location of TDWMSs and setting up the proper waste clean-up schedule.

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 Comparative Study of Scalarization Techniques on the Multi-Objective Single Machine-Scheduling Problem Under Sequence-Dependent Setup Time, Release Date and Due Date Constraints

In this paper, we considered a two-objective machine-scheduling problem under sequence-dependent setup time, release date and due date constraints. The problem is formulated as a multi-objective mixed-integer programming model. Two conflicting objectives are considered as minimization of maximum completion time (makespan) and total tardiness. Despite the most use of metaheuristics in this kind of multi-objective problems, here, we try to solve the problem by transforming the two-objectives as a single objective using scalarization techniques. Test instances are generated as proposed in the scheduling literature. The solutions are obtained using Weighted Sum Scalarization, Benson’s Method and Pascoletti−Serafini Method. In addition, a comparison of scalarization techniques using Δ performance metric is given on the considered problem instances. The obtained results are evaluated and Δ values, which were obtained for Benson’s method, are mostly better than other techniques for the generated test problems.