Mixed-integer Mathematical Model Research Articles

An Internet of Things-Based Production Scheduling for Distributed Two-Stage Assembly Manufacturing with Mold Sharing

In digital product and ion scheduling centers, order–factory allocation, factory–mold allocation, and mold routing can be performed centrally and efficiently to maximize the utilization of manufacturing resources (molds). Therefore, in this paper, a manufacturing resource (molds)-sharing mechanism based on the Internet of Things (IoT) and a cyber-physical production system (CPPS) is designed to realize the coordinated allocation of molds and production scheduling. A mixed-integer mathematical model is developed to optimize the cost structure and obtain a reasonable profit solution. A heuristic algorithm based on evolutionary reversal is used to solve the problem. The numerical results show that based on the digital coordinated production scheduling method, distributed two-stage assembly manufacturing with shared molds can effectively reduce the order delay time and increase potential benefits for distributed production enterprises.

Examination of Provinces in Türkiye about Sectoral Employment Share by Cluster Analysis

The significance of regional dynamics in the process of economic development and regional development has increased as a result of significant factors like competitiveness, human resource development, and observation of the global market. In this study, mathematical programming-based cluster analysis has been conducted to group the regions in Türkiye according to sectoral employment rates. A mixed integer mathematical model is presented that maximizes the smallest of the out-of-cluster distances while minimizing the largest within-cluster distance. Level 2- 26 sub-regions in Türkiye are clustered according to sectoral employment data for 2021 and 2022. As a result, two clusters were obtained for both years in our country according to employment status by gender on a sectoral basis. One of these clusters is where the employment rate of the agricultural sector is higher than other sectors, and the other is where the employment rate of the industrial and service sectors is higher. When the 2021 and 2022 clusters are compared, in total, TR22, TR32, TR33, TRC3; in men, TR21, TR22, TR32, TR52, TR81; In women, it was observed that TRC1 regions were assigned to different clusters. By implementing a successful employment policy as human resource development across the national government, it will be possible to ensure the balanced growth of provinces located in Türkiye's various geographical areas.

Multi-skilled resource-constrained multi-project scheduling problem with dexterity improvement of workforce

In this study, a mixed-integer mathematical model has been presented for the Multi-Skilled Resource-Constrained Multi-Project Scheduling Problem (MSRCMPSP), where the dexterity of workers can be improved via two ways: (1) Cooperating with more proficient co-workers, and (2) Practicing the possessed skills. The model aims to determine the start and finish times of activities considering the dexterity improvement of workforces. This research presents a Modified discrete variant of the Biogeography-Based Optimization (MBBO) algorithm to solve the model and to minimize the total required duration to complete all projects. The MBBO embraces two novel migration procedures, a new mutation process, and a new habitat selection operator. On several test instances and on a case study, the efficacy of the MBBO has been put to examination in comparison to four other meta-heuristics. The MBBO has overpowered other methodologies in terms of most of the assessment criteria. The obtained results have revealed that the dexterity improvement of workers significantly improves the total required duration to complete all projects. This research and its outputs can be helpful for the researchers who work on project scheduling models. Moreover, this study can inspire future project scheduling formulations, where the dexterity of human resources is affected by the learning phenomenon.

A timely efficient and emissions-aware multiobjective truck-sharing integrated scheduling model in container terminals

In line with the development of green port terminals and the necessity of environmentally friendly efficient use of handling and transportation equipment, criteria such as emission reduction, energy minimization, and efficiency in a container terminal are prominent issues, which in recent years, have been the main concern of container terminal managers in developing terminal operating systems. Therefore, in this study, a bi-objective mixed integer mathematical programing model of integrated scheduling for ships’ loading and unloading operation sequencing in container terminals is proposed, which considers the minimization of containers’ flow time, trucks’ emission, and energy consumption as well as sharing trucks among quay cranes and decreasing their empty trips. In this model trucks’ technical specifications and polluting levels are input parameters for estimating emission and energy consumption of operation, which consequently leads to two uniform parallel machine scheduling models. To derive the exact solution of the model, the epsilon-constraint method is applied. Nevertheless, due to the problem’s NP-hardness attribute, two variants of non-dominated sorting genetic algorithm and multiobjective particle swarm optimization metaheuristic algorithms are proposed to identify the approximate Pareto front of solutions. In large-size problems, these algorithms outperform the epsilon-constraint method by finding acceptable results in a reasonable time. This model, which could be embedded in terminal operating software, not only yields a practical optimum operational sequence but also measures the amount of energy and emission from trucks during loading and unloading operations. The results, which utilized the data collected from Shahid Rajaee port in southern Iran, indicate that this practical model as compared to the current procedure in the terminal, results in a significant improvement in energy and emission reduction and terminal flow time.

Efficient last-mile logistics with service options: A multi-criteria decision-making and optimization methodology

The rapid growth of online shopping has intensified the need for cost-effective and efficient delivery systems, posing a significant challenge for businesses worldwide. This study proposes an innovative two-phase methodology that uses a hybrid multi-criteria decision-making (MCDM) approach for efficient last-mile logistics with service options (ELMLSO) such as home delivery, self-pickup, and differently-priced services. This approach aims to streamline last-mile logistics by integrating these service options, resulting in a more comprehensive and effective delivery network that enhances customer satisfaction and maintains a competitive edge. The first phase employs the Ordinal Preference Analysis - Evaluation based on Distance from Average Solution (OPA-EDAS) method to select optimal pickup and delivery centers. The second phase identifies the optimal route using a bi-objective mixed-integer mathematical model, striving to balance cost minimization and customer satisfaction maximization. The Normalized Normal Constraint Method (NNCM) is utilized to solve this model. The application of these methods results in considerable cost savings and improved customer satisfaction, offering valuable insights for managers within the last-mile logistics industry.

Design for Optimally Routing and Scheduling a Tow Train for Just-in-Time Material Supply of Mixed-Model Assembly Lines

With the increase in product varieties, the combination of supermarkets and tow trains is being adopted by more automobile manufacturers for part feeding, especially in mixed-flow assembly lines. This paper focuses on the routing, scheduling, and loading problems of a single towed train that transports parts from one supermarket to the workstation buffer in a mixed-flow assembly line and aims to optimize the loading of the tow train, the optimal delivery schedule and route, and the appropriate departure time to minimize shipping and line inventory costs. To enable part feeding in line with the just-in-time (JIT) principle, a new mixed-integer mathematical model from nonlinearity to linearity and a novel artificial immune genetic algorithm-based heuristic are proposed. Both methods can provide reasonable solutions compared by minimizing the route length and inventory level in terms of speed, and the genetic algorithm shows better performance on a large scale.

Integrated optimization of train stopping plan and seat allocation scheme for railway systems under equilibrium travel choice and elastic demand

This paper examines the integrated optimization of train stopping plan and seat allocation scheme in railway systems, where equilibrium passenger travel choice under elastic demand is considered. The integrated optimization problem is formulated as a non-concave and non-linear mixed-integer mathematical model, where the objective is to maximize the system net benefit considering ticket revenue, consumer surplus, and cost associated with train stoppings. The integrated optimization model can be reformulated into a mixed-integer linear programming (MILP) model based on a series of linearization, relaxation, and outer-approximation techniques, which can then be solved by commercial MILP solvers (e.g., GUROBI). We also compare the integrated optimization approach with that when the train stopping plan and seat allocation are optimized separately and identify the potential benefits. Numerical studies have been conducted on a small-scale example, the Zhengzhou-Xi’an and Shanghai-Beijing high-speed railway corridors to illustrate the proposed model and solution approach.

Improving Energy Consumption and Order Tardiness in Picker-to-Part Warehouses with Electric Forklifts: A Comparison of Four Evolutionary Algorithms

Improving energy consumption (EC) and order tardiness (OT) for a warehouse picker-to-parts system is a challenging task since these two objectives are interrelated in a complex way with forklift activities. Thus, this research aims to minimize EC and OT with a multi-objective mixed-integer mathematical model by considering electric forklift operations. The proposed model addresses a lack of studies by controlling (i) order batching, (ii) batch assignment, (iii) batch sequencing, (iv) forklift routing, and (v) forklift battery charging schedule. The feasibility of the presented mathematical model is validated by solving small-sized examples. To solve medium- to large-sized case studies, we also propose and compare four multi-objective evolutionary algorithms (MOEAs). In illustrative examples, this study identifies the number of battery charging, orders, and forklifts as significant parameters affecting EC and OT. Our analysis also provides regression models connecting EC and OT from Pareto-optimal frontiers, and these results can help industrial practitioners and academic researchers find and investigate the relationship between EC and OT for making relevant decisions in warehouses served by electric forklifts. Among the four MOEAs developed, we show that the NSGA-II non-dominated sorting variable neighborhood search dynamic learning strategy (NSGA-VNS-DLS) outperforms other algorithms in accuracy, diversity, and CPU time.

A Parallel distributed genetic algorithm using Apache Spark for flexible scheduling of multitasks in a cloud manufacturing environment

ABSTRACT Cloud manufacturing is one of the modern manufacturing systems that aim to control and manage production processes through a cloud platform to optimize the usage of resources and achieve customer objectives. Scheduling large-scale problems with diversity in the required tasks and the available services is a significant challenge for any researcher, especially with the possibility of recurring dynamic events, such as the arrival of new tasks. Thus, our first objective is to present a mixed-integer mathematical model that demonstrates the complexity of scheduling problems in a dynamic CMfg environment. We developed a parallel distributed genetic algorithm (PDGA) for optimizing large-scale scheduling problems on Apache Spark. The PDGA adopts a resilient distributed dataset (RDD) to improve the decomposition of the population and also enhance both the performance and the speed of the evolution process. The PDGA then updates the schedule by using a greedy strategy to improve the overall performance. To verify the effectiveness of the PDGA, we evaluated the algorithm on a benchmark and generated 8 large-scale problems based on this benchmark. The experiments show that the PDGA provides better performance and lower computational time compared to the traditional genetic algorithm and particle swarm optimization algorithm.

An exact criterion space search algorithm for a bi-objective blood collection problem

Blood shortages are one of the main challenges in blood supply chains. To supply required blood, blood center managers face conflicting collection objectives involving costs and patients’ lives. Moreover, some challenging decisions must be made, such as routing, blood collection, location of blood stations, transshipment policy and holding inventory. In this study, a bi-objective mixed integer mathematical model is developed to address all the above-mentioned issues in the network. The model focuses on precisely determining the location of collection stations (permanent and temporary), transshipment and inventory of the blood center, routes and the quantity of collected blood to optimize the two objectives of decreasing total blood shortages and costs. Next, a subtour cut generation (SCG) method is introduced to enhance the solution approach of the problem. It leads to solving large instances more efficiently. The problem is critical and complex since missing even a non-dominated solution may lead to both negative financial impact and noncompensable outcomes. To extract all non-dominated solutions, an exact criterion space search method, called the triangle splitting method (TSM), is adopted. Several experiments are investigated for some instances from the literature. In addition, a real case study is considered. Results indicate that designing the network using the proposed mathematical model can significantly reduce total blood costs and shortages. Consequently, by utilizing the proposed methodology, blood center decision makers will have the opportunity to choose the most preferred point among extracted non-dominated solutions. Furthermore, the performance of the adopted TSM was compared with an improved non-dominated sorting genetic algorithm (NSGA-II) and lexmin epsilon constraint (LEPS). The results confirm that the adopted TSM algorithm performs much better than the improved NSGA-II and LEPS, considering bi-objective performance measures.

Integrated mixed-model assembly line balancing and parts feeding with supermarkets

In the automotive industry, decentralized in-house logistic areas called supermarkets are used for parts feeding to mixed-model assembly lines. In the literature, generally, the number of supermarkets and their locations are determined according to a previously balanced assembly line. As a result, supermarket locations have to be completely dependent on the line balance. There may be more than one solution that gives the same performance criterion value in the line balancing. Among these alternative solutions, it is more reasonable to use a solution that provides lower logistics costs than others. For this purpose, in this study, the mixed-model assembly line balancing problem and the supermarket location problem are considered simultaneously. Accordingly, in order to minimize the total costs of the assembly line and supermarkets, a mixed-integer mathematical model is developed, and the developed model is solved by using constraint programming (CP). In addition, a new approach based on Ant Colony Optimization (ACO) and Simulated Annealing (SA) is presented for large-sized problems. An illustrative example problem is solved using both the developed model and the proposed algorithm. The effectiveness of the proposed approach is tested through a new data set of test problems presented to the literature for a computational experiment. The experimental results show that the total costs are reduced meaningfully and a more realistic and applicable structure is achieved by the proposed approach.

Simultaneous response to multiple disasters: Integrated planning for pandemics and large-scale earthquakes

Since the beginning of COVID-19, individuals who have SARS-CoV-2 infectious have brought a heavy burden on the healthcare system. Unavoidably, along with pandemics, large-scale disasters, which are possibly emerging, may double the current health crisis. For a powerful disaster response plan, the health services should be prepared for the overwhelming number of disaster victims and infected individuals The proposed framework determines the appropriate number and location of temporary healthcare facilities for large-scale disasters while considering the burden of ongoing pandemic diseases. In this study, first, a multi-period, mix-integer mathematical model is developed to find the location and number of disaster emergency units and disaster medical facilities. Second, we develop an epidemic compartmental model to stimulate the negative effects of the disaster on disease spread and a mixed-integer mathematical model to find optimal number and the location of pandemic hospitals and isolation centers. To validate the mathematical models, a case study is conducted for a district of Istanbul, Turkey.

Mixed Integer Programming Formulation for Time-Dependent Petrol Station Replenishment Problem: A Real-Life Case in İstanbul

With the increase in the consumption of petroleum and petroleum products, these limited resources must be provided efficiently, accurately, and with minimal damage. Therefore, the accurate and effective distribution of petroleum, and related problems with petroleum distribution have attracted much attention among the practitioners and optimization working researchers over the years. The petroleum distribution problem, as a version of the Vehicle Routing Problem (VRP), deals with the planning of petroleum distribution from the depot(s) to the petrol stations safely and quickly. In this study, the petrol station replenishment problem (PSRP) is handled and a case study is presented for a public company located in İstanbul. The problem is considered as a time-dependent VRP with time windows. A novel mixed integer mathematical model is proposed for the problem. In order to handle the proposed time-dependent problem in a more realistic way, variable tanker speeds are considered based on traffic density. The optimum route is determined in which risks such as environment and marine pollution may occur in case of possible accidents, and these risks are minimized by the proposed mathematical model considering the factors as traffic, vehicle speed, road structure, the road's proximity to the sea and living areas

A Robust Possibilistic Bi-Objective Mixed Integer Model for Green Biofuel Supply Chain Design under Uncertain Conditions

In recent years, concerns regarding issues such as climate change, greenhouse gas emissions, fossil reserve dependency, and petroleum price fluctuation have led countries to focus on renewable energies. Meanwhile, in developing countries, designing an appropriate biofuel supply chain network regarding environmental competencies is an important problem. This paper presents a new bi-objective mixed integer mathematical model aiming to minimize CO2 emission and total costs in the process of the biofuel supply chain, creating a suitable green supply chain network. In this respect, CO2 emission and biofuel demand are regarded as uncertain data to address the real complex cases. Moreover, the SAUGMECON approach was implemented to construct a single objective model, and the obtained Pareto optimal points were depicted and analyzed. Thereby, a robust possibilistic programming approach was implemented to the proposed model to handle existing imprecise data. Furthermore, the applicability and performance of the proposed model were demonstrated based on an experimental example. In this respect, the obtained results from the proposed robust possibilistic programming model were compared with its crisp form to show the robustness and reliability of the proposed uncertain mathematical model.

A Novel Approach for Sustainable Supply Chain Management with Analyzing the Effective Governance under Fuzzy Uncertainty

Nowadays, knowledge has become one of the most important tools of power, distributing public services that accept the audience as citizens and not consumers and provide the principle of services without financial worries. Moreover, the urban products have a specific production and distribution channel that should be assessed. In this research, a mathematical framework is proposed for designing the supply chain network of urban products. The main contribution of this research is to incorporate the effect of public service into urban products’ supply chain planning. In this regard, a mixed-integer mathematical model is proposed. In this mathematical model, an attempt is made to minimize the costs of the product distribution system by considering the effects of production, maintenance, and distribution. Moreover, fuzzy uncertainty has been applied to adapt the mathematical model to real conditions. The numerical results show that if manufacturers and distributors want to strengthen their institutions and maintain their leadership roles as in the past, they can optimize their distribution network structure to achieve the best possible performance. Moreover, technological advances and innovations in production and distribution systems can create a huge leap in profitability.

A multi-objective optimization model for a multi-period mobile facility location problem with environmental and disruption considerations.

The present work addresses a multi-period facility location decision during crisis—Pandemic—situation with highly uncertain demand. Our paper identifies failing distribution centres (DCs) over several periods of time and decides about relocation. Several scenarios arise: DCs can be opened, displaced from one location to another, closed or even reopened during a certain time, using mobile facility. We recommend a multi-objective non-linear mixed-integer mathematical model that identifies, for each period, the best possible location for DCs and their allocation to customers. Our model analyses the trade-off between economic costs and CO_2 emissions generated by facilities operations. We suggest a multi-objective approach based on a Non-dominated Sorting Genetic Algorithm II (NSGA-II). Our simulations demonstrate how mobile facility should be managed to ensure a good balance between economic and environmental criteria.

Resilient Supply Chain Planning for the Perishable Products under Different Uncertainty

In this research, the perishable products’ closed-loop supply chain network design problem is assessed by considering the disruption in production and distribution capacity and taking into account the uncertainty in customer demand. The main contribution of this research is modeling perishable products’ supply chain optimization and providing intelligent solution methods. In this regard, a mixed-integer mathematical model is proposed. This mathematical model consists of three objective functions. The first objective function is related to profit maximization, the second objective function is to minimize delivery time, and the third objective function is to reduce lost business days. Moreover, non-dominated sorting genetic algorithm II (NSGAII) and Multi-Objective Evolutionary Algorithm (MOEA) have been applied to optimize the proposed model. The research results show that the proposed meta-heuristic algorithm can provide a complete set of Pareto solutions in a reasonable amount of time. Moreover, based on different criteria, MOEA provides the non-dominated solutions with a higher quality, while NSGAII presents the Pareto boundary with more solutions than MOEA.

Artificial neural networks integrated mixed integer mathematical model for multi-fleet heterogeneous time-dependent cash in transit problem with time windows

Artificial neural networks integrated mixed integer mathematical model for multi-fleet heterogeneous time-dependent cash in transit problem with time windows

A Multiobjective Mathematical Model for Truck Scheduling Problem in Multidoor Cross-Docking System

Cross-docking is the main operation of unloading products from incoming trucks, regrouping products in relation to their destination, and loading directly onto shipping trucks, reducing warehousing, picking, transportation costs, and delivery times. This is the intended logistics technology. In this paper, we present a new bi-objective mixed-integer mathematical model for truck scheduling problems in cross-docking systems. The goal of the proposed mixed-integer mathematical model is to minimize the total operation time (makespan) and cost of moving cargo within the terminal. The performance of the proposed model is compared with that of the available model to solve small instances. The results showed that in solving small size of problem, the proposed model in this study is more efficient and we found better solutions. An evolutionary algorithm called the nondominated sorting genetic algorithm (NSGA-II) has been proposed to solve larger instances due to computational complexity. To evaluate the proposed algorithm, a comparative analysis of benchmark instances was performed and the efficiency of the above algorithm was compared to the nondominated ranked algorithm (NRGA) based on the index designed in the literature. The statistical hypothesis testing (t-test) is used for determining the best algorithm based on the average runtime and average number of Pareto solutions. Using the Taguchi method, the proposed algorithms are tuned. Considering a temporary storage space and the multiple receiving and shipping docks is the main contribution of the paper. Finally, for evaluating algorithms, multicriteria decision-making (MCDM) technique and statistical method are used. The results show the suitable performance of presented model.

Resilient airline scheduling to minimize delay risks

Airlines tend to design their flights schedules with the primary concern of the minimization of operational costs. However, the recently emerging idea of resilient scheduling defined as staying operational in case of unexpected disruptions and adaptability should be of great importance for airlines as well due to the high opportunity costs caused by the flight cancellations and passenger inconvenience caused by delays in the schedule. In this study, we integrate resilient airline schedule design, aircraft routing and fleet assignment problems with uncertain non-cruise times and controllable cruise times. We follow a data-driven method to estimate flight delay probabilities to calculate the airport congestion coefficients required for the probability distributions of non-cruise time random variables. We formulate the problem as a bi-criteria nonlinear mixed integer mathematical model with chance constraints. The nonlinearity caused by the fuel consumption and CO2 emission function associated with the controllable cruise times in our first objective is handled by second order conic inequalities. We minimize the total absolute deviation of the aircraft path variability’s from the average in our second objective to generate balanced schedules in terms of resilience. We compare the recovery performances of our proposed schedules to the minimum cost schedules by a scenario-based posterior analysis.