Mixed-integer Mathematical Programming Research Articles

The impact of dynamic learning and training on the personnel staffing decision

This paper studies the personnel staffing decision accounting for the planning of workforce training and the inclusion of learning and forgetting, which dynamically change the workforce skill level, influencing the required staffing budget. This contrasts staffing models presented in literature, which determine the required number of workers under the assumption of a fixed and/or predefined skill mix of the workforce. We consider different types of on-the-job and off-the-job training activities, traditional learning associated with execution of regular tasks and forgetting according to which a worker’s efficiency is adapted dynamically throughout the time horizon. The acquired worker’s efficiency level determines the speed at which assigned tasks can be processed, which is modelled via the definition of multiple discrete modes per task. To improve the accuracy of the staffing decision and account for the effect of gradually changing the workers’ skill levels, a baseline schedule is composed that comprises the solving of an integrated days-off scheduling and task assignment problem. We propose a dedicated solution procedure that relies on a constructive heuristic to find an initial solution and subsequently a branch-and-price algorithm to derive a (near-)optimal solution. The branch-and-price algorithm is featured by a multi-stage pricing procedure to find promising columns, alternating between mathematical mixed-integer programming, a single-pass heuristic and a genetic algorithm. The computational experiments validate the performance of the proposed procedure and demonstrate the benefits of different training and learning methods under different conditions.

A Q-learning-based multi-objective evolutionary algorithm for integrated green production and distribution scheduling problems

In recent years, integrated production and distribution scheduling (IPDS) has received growing attention from academia and industry. With increasingly global economic activities, it is vital to extend IPDS to distributed environments. Besides, the production and distribution systems are the main contributors to carbon emissions due to their high energy consumption. Driven by this, this work introduces an integrated green distributed production and distribution scheduling problem with the objectives of total tardiness and total carbon emissions minimization. To provide a clear definition, a mixed-integer mathematical programming model is created. Considering the problem's NP-hard nature, a Q-learning-based multi-objective evolutionary algorithm (Q-MEA) is designed to handle it. To evaluate the performance of Q-MEA, a comparison pool including four variants, five meta-heuristics, and an exact optimizer named CPLEX is constructed to implement numerical experiments. The results demonstrate that Q-MEA has clear advantages over its rivals in tackling our problems. Furthermore, comparing the integrated model with a separate one shows that the former can achieve an average decrease of about 13.10% in total tardiness and 21.02% in total carbon emissions.

A Multi-Objective Mathematical Programming Model for Transit Network Design and Frequency Setting Problem

In this study, we propose a novel multi-objective nonlinear mixed-integer mathematical programming model for the transit network design and frequency setting problem that aims at designing the routes and determining the frequencies of the routes to satisfy passenger demand in a transit network. The proposed model incorporates the features of real-life transit network systems and reflects the views of both passengers and the transit agency by considering the in-vehicle travel time, transfers, waiting times at the boarding and transfer stops, overcrowding and under-utilization of vehicles, and vehicle fleet size. Unlike previous studies that simplify several aspects of the transit network design and frequency setting problem, the proposed model is the first to determine routes and their frequencies simultaneously from scratch, i.e., without using line and frequency pools while considering the aforementioned issues, such as transfers and waiting. We solve the proposed model using Gurobi. We provide the results of what-if analyses conducted using a real-world public bus transport network in the city of Kayseri in Türkiye. We also present the results of computational tests implemented to validate and verify the model using Mandl benchmark instances from the literature. The results indicate that the model produces better solutions than the state-of-the-art algorithms in the literature and that the model can be used by public transit planners as a decision aid.

Variable Neighborhood Search Algorithm for the Single Assignment Incomplete Hub Location Problem with Modular Capacities and Direct Connections

In distribution systems such as airlines and express package delivery, the use of hub-and-spoke networks is common, and flow consolidation at hub facilities is essential for cost reduction. While a constant discount factor is typically used to model cost reduction in interhub links, this paper explores an extension of the incomplete hub location problem with modular capacity that enables direct connections between non-hub nodes. The modified approach, called MHLPDC, aims to locate a set of hub facilities, connect each non-hub node to a hub, and activate hub facility links, access arc links, and direct links between non-hub nodes to minimize network costs. The MHLPDC integrates link activation decisions into the decision-making process and utilizes modular arc costs to model the flow dependence of transportation costs in all arcs. To solve the problem, the paper presents a mixed-integer mathematical programming formulation and heuristic algorithm based on a greedy randomized adaptive search and variable neighborhood search approach. The proposed algorithm produces high-quality solutions, as demonstrated through computational experiments on benchmark instances with up to 40 nodes. Furthermore, a sensitivity analysis of the optimal network structure indicates that increasing the discount factor, by varying hub and access arc capacities as well as the associated variable costs, results in fewer hubs being established and more direct shipments between non-hub nodes being permitted.

A bi-objective integrated mathematical model for blood supply chain: Case of Turkish red crescent

<p style='text-indent:20px;'>Various criteria feature in blood supply chain (BSC) designs, where cost-based and time-based are the most commonly found in the literature. In the current study, total annual cost is used together with a new time-based objective. The total time spent in the transportation of blood products is considered as time lost, and weight is given to that time according to the product amount and then normalized with respect to shelf life. In using cost and time objectives, we developed a bi-objective mixed-integer mathematical programming model for the BSC of Turkish Red Crescent (TRC, the singular authority controlling BSC throughout Turkey), including collection, production, and distribution echelons, and also considering bag-type decisions for whole-blood collection. The objective of the study was to propose a BSC design model and solution approach. With all real-life TRC instances resolved optimally, a linear programming relaxation-based heuristic was developed for large-scale problem sizes. Real-life data were obtained from the TRC and the remainder from open-to-public sources. The study's main finding is that cost and time objectives alone produce significantly different designs, whilst using them together to form efficient-frontier solutions for decision-makers adds practical value.</p>

Maximizing hospital capacity to serve pandemic patient surge in hot spots via queueing theory and microsimulation

This paper presents a mixed-integer mathematical program with embedded equations developed from concepts of queueing theory and Jackson networks for estimating the steady-state maximum potential hospital capacity for COVID-19 patient care in extreme surge conditions, where a hospital must turn nearly all of its existing resources toward the care of pandemic patients. Estimating the potential maximum hospital capacity for pandemic patient care can aid in assessing regional healthcare capacity during surges in pandemic patient demand, predicting shortfalls, and designing preparedness and response actions. To obtain such estimates and inform action, the program determines a best assignment of a heterogeneous staff of nurses and doctors to key units appropriate for their skills to create the optimal allocation of staffed beds. An alternative trial-and-error approach is offered that decision-makers without optimization or software expertise can use to obtain similar estimates. Under a given assignment of resources, a variety of key performance indicators can be obtained through the direct use of the queueing equations. Results of comparisons to outcomes from a detailed discrete event simulation model of an identical hospital design show the accuracy of the equations to be high despite the added simplifications needed for the use of a closed-form equation-based methodology.

Designing a sustainable reverse supply chain network for COVID-19 vaccine waste under uncertainty

The vast nationwide COVID-19 vaccination programs are implemented in many countries worldwide. Mass vaccination is causing a rapid increase in infectious and non-infectious vaccine wastes, potentially posing a severe threat if there is no well-organized management plan. This paper develops a mixed-integer mathematical programming model to design a COVID-19 vaccine waste reverse supply chain (CVWRSC) for the first time. The presented problem is based on minimizing the system's total cost and carbon emission. The uncertainty in the tendency rate of vaccination is considered, and a robust optimization approach is used to deal with it, where an interactive fuzzy approach converts the model into a single objective problem. Additionally, a Lagrangian relaxation (LR) algorithm is utilized to deal with the computational difficulty of the large-scale CVWRSC network. The model's practicality is investigated by solving a real-life case study. The results show the gain of the developed integrated network, where the presented framework performs better than the disintegrated vaccine and waste supply chain models. According to the results, vaccination operations and transportation of non-infectious wastes are responsible for a large portion of total cost and emission, respectively. Autoclaving technology plays a vital role in treating infectious wastes. Moreover, the sensitivity analyses demonstrate that the vaccination tendency rate significantly impacts both objective functions. The case study results prove the model's robustness under different realization scenarios, where the average objective function of the robust model is less than the deterministic model ones’ in all scenarios. Finally, some insights are given based on the obtained results.

The mixed fleet vehicle routing problem with partial recharging by multiple chargers: Mathematical model and adaptive large neighborhood search

We introduce the Mixed Fleet Vehicle Routing Problem with Time Windows and Partial Recharging by Multiple Chargers (MF-VRP-MC). It composes of electric and internal combustion vehicles, and consolidates several aspects in a comprehensive unique model. The MF-VRP-MC considers travelled distance and carried load on vehicles in both emission and energy consumption functions. It deals with the minimization of total cost while satisfying customer delivery demands. First, we develop a mixed integer mathematical programming formulation for the MF-VRP-MC. Because of the NP-hardness of the problem, to solve medium and large-size instances, then we develop an Adaptive Large Neighborhood Search (ALNS) based algorithm with introducing new advanced neighborhood mechanisms to successfully handle complex problem constraints. Meantime, new approaches are tailored for boosting diversification effect in addition to new neighborhood scoring policy and new enhancement procedure. Furthermore, selection of recharging technology among the others at charging station is firstly considered in the solution phase of a mixed fleet problem. Extensive computational results indicate that our ALNS performs quite well on benchmark instances.

Hybrid mathematical and simulation model for designing a hierarchical network of temporary medical centers in a disaster

ABSTRACT The destructions caused by natural disasters have made human societies well aware of the importance of logistical preparedness and precise human resource planning both in the pre- and post-disaster phases. Temporary Medical Centers (TMCs) are one of the most important problems for disaster response. TMCs are established in safe places to treat the injured in times of crisis. In this paper, the optimal locations for the establishment of TMCs are determined using a mixed-integer mathematical programming model. Furthermore, an optimal hierarchical structure is developed for assigning the injured from urban areas to the TMCs, clinics, and hospitals in the event of a disaster. A simulation-based optimisation model is employed to simulate the conditions at the moment the disaster occurs and the ensuing response operations. The findings indicate that the proposed hierarchical location-allocation model reduces the congestion of the injured and minimises total costs and patients’ treatment time.The destructions caused by natural disasters have made human societies well aware of the importance of logistical preparedness and precise human resource planning both in the pre- and post-disaster phases. Temporary Medical Centers (TMCs) are one of the most important problems for disaster response. TMCs are established in safe places to treat the injured in times of crisis. In this paper, the optimal locations for the establishment of TMCs are determined using a mixed-integer mathematical programming model. Furthermore, an optimal hierarchical structure is developed for assigning the injured from urban areas to the TMCs, clinics, and hospitals in the event of a disaster. A simulation-based optimisation model is employed to simulate the conditions at the moment the disaster occurs and the ensuing response operations. The findings indicate that the proposed hierarchical location-allocation model reduces the congestion of the injured and minimises total costs and patients’ treatment time.

Assignment and routing model for the Planning of Food Supply Operation in the South part of Bogota; fruit and vegetable case

Introduction: This article is the product of the research Design of the logistics operation of food distribution in different locations south of Bogotá based on a multistage model, carried out during 2014 in the city of Bogotá.Problem: Bogota City has a big problem in its food supply framed by the inefficiency in the capillary distribution, raising costs to households, which generates difficulties in accessing food mainly to strata 1 and 2.Objective: Define a strategy for the planning of the efficient supply operation of fruits and vegetables to the south of the city.Method: An analysis of the behavior of the system proposed by the the Master Plan for Supply and Food Security of Bogotá was carried out, using a correlational descriptive method for the analysis of the variables, from the characterization of food in 4 locations, and other secondary sources.Results: In the first phase of this model, it was determined the allocations of the load to be distributed from three (3) logistic platforms towards 4 localities based on mixed integer mathematical programming. In the second phase, a basic VRP model was developed that allowed to determine the routing of vehicles with the remaining fruit and vegetables loads to be delivered.Conclusions: The work is relevant as a contribution to the optimal management of food supply through the use of mathematical models, given that it covers fixed costs both for deposits and for the use of vehicles, with a two-phase model. This can contribute to food security through greater access to food with reduced prices and timely availability in the target areas of study.Originality: Staged models that complement each other to define the complete food supply operation.Limitations: The models must be used with a minimum of knowledge on the subject.

COVID19 epidemic outbreak: operating rooms scheduling, specialty teams timetabling and emergency patients' assignment using the robust optimization approach.

The health care system is characterized by limited resources, including the physical facilities as well as skilled human resources. Due to the extensive fixed cost of medical facilities and the high specialization required by the medical staff, the problem of resource scarcity in a health care supply chain is much more acute than in other industries. In the pandemic of the Coronavirus, where medical services are the most important services in communities, and protective and preventive guidelines impose new restrictions on the system, the issue of resource allocation will be more complicated and significantly affect the efficiency of health care systems. In this paper, the problem of activating the operating rooms in hospitals, assigning active operating rooms to the COVID-19 and non-COVID-19 patients, assigning specialty teams to the operating rooms and assigning the elective and emergency patients to the specialty teams, and scheduling their operations is studied by considering the new constraints of protective and preventive guidelines of the Coronavirus. To address these issues, a mixed-integer mathematical programming model is proposed. Moreover, to consider the uncertainty in the surgery duration of elective and emergency patients, the stochastic robust optimization approach is utilized. The proposed model is applied for the planning of operating rooms in the cardiovascular department of a hospital in Iran, and the results highlight the role of proper management in supplying sufficient medical resources effectively to respond to patients and scheduled surgical team to overcome the pressure on hospital resources and medical staff results from pandemic conditions.

Mathematical modeling of inventory cost in a 3-tier supply chain with horizontal cooperation

Inventory together with the transport, location of the production factory, and storage represent important factors that influence the performance of a supply chain. It is thus important for organizations to maintain inventory for efficient and smooth running of their operations. Through cooperation, supply chain players at the same level of the market can work jointly to plan and execute supply chain operations, and achieve greater success than when acting in isolation. Accordingly, this work considers a 3-tier supply chain – Supplier, Manufacturer, and Distributor, and it develops a model for minimizing the cost of inventory across the 3-tiers with horizontal cooperation at the post-production inventory end of manufacturing tier only. A constrained mixed integer mathematical program was developed with the objective of minimizing total inventory cost across the three supply chain tiers. A test problem consisting of 3 suppliers, 3 manufacturers, 3 distributors, and 4 products was used to test the model; the resulting mathematical problem was solved using linear programming with and without post-production inventory horizontal cooperation scenarios. It was found that horizontal cooperation was of immense benefit to supply chain players, and offers great cost savings as against individual operation.

Capacitated multi-objective disassembly scheduling with fuzzy processing time via a fruit fly optimization algorithm.

This work proposes a capacitated fuzzy disassembly scheduling model with cycle time and environmental cost as parameters, which has broad applications in remanufacturing and many other production systems. Disassembly scheduling is not always given accurately as a time quota in a production system, particularly in the obsolete product remanufacturing process. It is important to study novel models and algorithms based on uncertainty processing time to solve uncertainty disassembly scheduling problems. In this paper, a mixed-integer mathematical programming model is proposed to minimize the cycle time and environmental cost, whilst a metaheuristic approach based on a fruit fly optimization algorithm (FOA) is developed to find a fuzzy disassembly scheduling scheme. To estimate the effectiveness of the proposed method, the proposed algorithm is tested with different size cases of product disassembly scheduling. Furthermore, experiments are conducted to compare with other multi-objective optimization algorithms. The computational results demonstrate the proposed algorithm outperforms other algorithms on computational efficiency and applicability to different problems. Finally, a case study is described to illustrate the proposed method. The main contribution of this current work shows the proposed algorithm to solve the problem of disassembly scheduling in an uncertain environment practically and efficiently.

Multi-Objective Modeling of Relief Items Distribution Network Design Problem in Disaster Relief Logistics Considering Transportation System and CO2 Emission

The present study aims to propose a multi-objective mixed integer mathematical programming model for designing a relief items distribution network in sustainable disaster relief logistics. The first objective function minimizes the total network costs. Which are divided into two parts: 1- relief costs including (transportation costs, inventory costs and fixed costs of facilities) 2- social costs (deprivation cost). The second objective function minimizes the amount of pollution generated by the network. Considering the related literature review, this is the first study that to propose a robust fuzzy optimization approach for relief items distribution network design problem considering environmental (CO2 emission), social (deprivation cost) and economic impacts under reliability and uncertainty. Then, the multi-objective model was solved using the multi-choice goal programming. To indicate the validity of the proposed model, a case study was evaluated based on real data (2019 flood in Sari city, Mazandaran Province). Using the proposed model, decision-makers and managers are able to make strategic and tactical decisions with the least cost and time, and in relief planning can enhance the structure of distribution networks and inventory and reduce victims’ dissatisfaction.

Smart control of air conditioning systems in manufacturing systems facing uncertainty

Enhancing energy use efficiency and reducing energy demand are important issues for industry and academe. Studies on the ventilation, and air conditioning (HVAC) system highlighted the optimization of individual devices, but did not fully consider global optimization. The heating and cooling mechanism of an HVAC system in the present study comprises multiple chillers, chilled water pumps, condenser water pumps, and cooling towers. This study proposes a smart control model of heating, ventilation, and HVAC systems in manufacturing systems to deal with dynamic indoor cooling demands and outdoor temperature changes. A stochastic mixed integer mathematical programming model optimizes the heating and cooling decisions of the HVAC system for energy conservation. This study also investigates a case of the HVAC system in a TFT-LCD manufacturing firm. Experiment results indicate that the proposed model saves up to 3.2% of total energy in the target HVAC system.

Collaborative scheduling of operating room in hospital network: Multi-objective learning variable neighborhood search

In this study, the operating room scheduling of hospital networks with virtual alliance has been studied, which at the same time, there is a kind of cooperation and competition among the agents. The main feature in networks with the virtual alliance is the possibility of different objective functions among the agents, which has priority for agents compared to the network’s overall objective. Here, by considering the conditions of emergency arrival, the time of inter-hospital transportation, and the elective patients and non-elective patients in the scheduling, an attempt has been made to bring the problem closer to real-world situations. To solve this problem, first, a mixed-integer mathematical programming model is proposed. Because of its NP-hardness, then, a multi-objective learning variable neighborhood search algorithm is designed to minimize total completion of surgeries, the cost of allocating the patient to the hospital and the surgeon, and the cost of overtime operating rooms throughout the network. Finally, the performance of the proposed algorithm is evaluated in comparison with the NSGA-II and memetic-based algorithm, which due to considering the learning mechanism along with the use of various neighborhood structures in the proposed algorithm, its results are promising. It is expected that by using the proposed algorithms in a cooperative structure, the hospitals are able to achieve optimal/near-optimal solutions in a reasonable time, in which, in addition to more economic activity, patients also benefit due to better use of resources.

Aplicación de métodos cuantitativos en la programación de eventos una aplicación en el carnaval uruguayo

In this work an application of quantitative methods for the programming of artistic shows is presented. In particular, the work carried out for the problem of making the fixture for the contest “Carnaval de las Promesas 2019/2020”. This event is a competition belonging to the Uruguayan carnival that has five different artistic categories, created especially for groups of children and adolescents. A mixed integer mathematical programming model was developed for the problem. The objective was to balance the attendance of the public and comply with the restrictions of the contest regulations, as well as other requirements indicated by the organizers.

Multimodal hub network design with flexible routes

This paper introduces a multimodal hub network design problem with flexible routes. Routes are flexible in the sense that they may contain a mix of hub and non-hub nodes. Nonetheless, commodity transfers can only occur at hubs, while transportation costs are flow-dependent, i.e., scale economies stem from the transport technology chosen to operate the routes. We propose a mixed integer mathematical program, and two metaheuristics based on the adaptive large neighborhood search paradigm to solve the problem. Extensive computational experiments show the performance of the formulation and of the devised algorithms in solving benchmark instances with up to 50 nodes.

Preference elicitation for a ranking method based on multiple reference profiles

Multiple criteria decision aid methodologies support decision makers (DM) facing decisions involving conflicting objectives. DM’s preferences should be captured to provide meaningful recommendations. Preference elicitation aims at incorporating DM’s preferences in decision models. We propose a new preference elicitation tool for a ranking model based on reference points (RMP—Ranking with Multiple Profiles). Our methodology infers an RMP model from a list of pairwise comparisons provided by the DM. The inference algorithm makes use of a Mixed Integer mathematical programming formulation. We prove the applicability by performing extensive numerical experiments on datasets whose size corresponds to real-world problem.

A lateral resupply blood supply chain network design under uncertainties

The vibrant subject of blood banking and blood distribution is addressed where lateral resupply of blood products is allowed. In this paper, we studied a blood supply chain network design consisting of four conventional levels each of which corresponding to one entity in the real world: donors, blood collection facilities, blood centers, and hospitals. The blood supply chain network considered two important properties: ABO-Rh factors and shelf lives of blood products. Moreover, an integrated inventory system for sharing hospitals’ inventory levels is considered to investigate the two performance indicators of the network in terms of cross-matching and outdated units. This type of inventory system is known as “Lateral Resupply” permitting a hospital to satisfy its demand by the other hospitals’ inventories in the absence of the required product at the blood center and its excess in any hospital. The proposed mixed-integer mathematical programming model entails three objectives referring to the three underlying concepts of sustainability, additionally, to cope with uncertainties and multi objectiveness, a scenario-based optimization approach and revised multi-choice goal programming technique were employed, respectively. Finally, the results confirmed that the lateral resupply virtue improved the performance indicators.