Integer Mathematical Programming Research Articles

A Raster-Based Multi-Objective Spatial Optimization Framework for Offshore Wind Farm Site-Prospecting

Siting an offshore wind project is considered a complex planning problem with multiple interrelated objectives and constraints. Hence, compactness and contiguity are indispensable properties in spatial modeling for Renewable Energy Sources (RES) planning processes. The proposed methodology demonstrates the development of a raster-based spatial optimization model for future Offshore Wind Farm (OWF) multi-objective site-prospecting in terms of the simulated Annual Energy Production (AEP), Wind Power Variability (WPV) and the Depth Profile (DP) towards an integer mathematical programming approach. Geographic Information Systems (GIS), statistical modeling, and spatial optimization techniques are fused as a unified framework that allows exploring rigorously and systematically multiple alternatives for OWF planning. The stochastic generation scheme uses a Generalized Hurst-Kolmogorov (GHK) process embedded in a Symmetric-Moving-Average (SMA) model, which is used for the simulation of a wind process, as extracted from the UERRA (MESCAN-SURFEX) reanalysis data. The generated AEP and WPV, along with the bathymetry raster surfaces, are then transferred into the multi-objective spatial optimization algorithm via the Gurobi optimizer. Using a weighted spatial optimization approach, considering and guaranteeing compactness and continuity of the optimal solutions, the final optimal areas (clusters) are extracted for the North and Central Aegean Sea. The optimal OWF clusters, show increased AEP and minimum WPV, particularly across offshore areas from the North-East Aegean (around Lemnos Island) to the Central Aegean Sea (Cyclades Islands). All areas have a Hurst parameter in the range of 0.55–0.63, indicating greater long-term positive autocorrelation in specific areas of the North Aegean Sea.

A multi-objective brain storm optimization for integrated distributed flexible job shop and distribution problems

Production and distribution are critical components of the furniture supply chain, and achieving optimal performance through their integration has become a vital focus for both the academic and business communities. Moreover, as economic globalization progresses, distributed manufacturing has become a pioneering production technique. Via leveraging a distributed flexible manufacturing system, mass flexible production at lower costs can be achieved. To this end, this study presents an integrated distributed flexible job shop and distribution problem to minimize makespan and total tardiness. In our research, a set of custom furniture orders from different customers are processed among flexible job shops and then delivered by vehicles to customers as the due date. To distinctly show the presented problem, a mixed integer mathematical programming model is created, and a multi-objective brain storm optimization method is introduced considering the problem's features. In comparison to the other three advanced methods, the superiority of the algorithm created is showcased. The findings of the experiments demonstrate that the constructed model and the introduced algorithm have remarkable competitiveness in addressing the problem being examined.

Collaborative optimization of routing and storage strategy of multi-period multimodal transport in an uncertain environment

This study uses a storage service strategy to investigate a multiperiod multimodal transport routing and transit planning problem (MPMT-RTP). First, a mathematical integer programming model is used to describe the problem in a deterministic environment. Second, two robust optimization models are established to address the uncertainty of the freight rate fluctuations in each period and the storage space in the total set, thereby improving the solving efficiency of the model through a robust equation transformation. Subsequently, hybrid heuristics are proposed to solve the above problems, and a series of small-scale experiments are conducted to verify the accuracy of the model and effectiveness of the algorithm. Finally, this study conducts case experiments based on survey data. The results show that the total operating cost is reduced by 13.31 % via strategic multiperiod multimodal transport planning. A price fluctuation study shows that under different price fluctuations, the transportation and storage periods of some orders change accordingly, and under three specific price fluctuations, the operating costs are 1085100, 967330, and 948770, respectively. Therefore, the results of this study can provide theoretical guidance for enterprises to optimize their resource allocation paradigms and better adapt to freight rate fluctuations to minimize their operating costs.

Multi Objective and Multi-Product Perishable Supply Chain with Vendor-Managed Inventory and IoT-Related Technologies

With the emergence of the fourth industrial revolution, the use of intelligent technologies in supply chains is becoming increasingly common. The aim of this research is to propose an optimal design for an intelligent supply chain of multiple perishable products under a vendor-managed inventory management policy aided by IoT-related technologies to address the challenges associated with traditional supply chains. Various levels of the intelligent supply chain employ technologies such as Wireless Sensor Networks (WSNs), Radio Frequency Identification (RFID), and Blockchain. In this paper, we develop a bi-objective nonlinear integer mathematical programming model for designing a four-level supply chain consisting of suppliers, manufacturers, retailers, and customers. The model determines the optimal network nodes, production level, product distribution and sales, and optimal choice of technology for each level. The objective functions are total cost and delivery times. The GAMS 24.2.1 optimization software is employed to solve the mathematical model in small dimensions. Considering the NP-Hard nature of the problem, the Grey Wolf Optimizer (GWO) algorithm is employed, and its performance is compared with the Multi-Objective Whale Optimization Algorithm (MOWOA) and NSGA-III. The results indicate that the adoption of these technologies in the supply chain can reduce delivery times and total supply chain costs.

СРАВНЕНИЕ МЕТОДОВ РЕШЕНИЯ ТРАНСПОРТНОЙ ЗАДАЧИ

Mathematical programming is a mathematical discipline that studies various extremal problems and develops algorithms for solving them. Among the problems are those of mathematical integer programming. Integer programming is indispensable for solving mathematical programming problems in which some or all of the variables take on integer values. The problems include the transport problem. The paper considers the transport problem and three linear programming methods for solving it: the method of potentials, the method of differential rents and the simplex method. The paper analyzes and assesses the effectiveness of the three algorithms for optimizing transport problems. Several linear optimization algorithms have been studied and presented. The paper contains the basic concepts, formulas, and algorithms of the methods used. The method of potentials, the method of differential rents and the simplex method are considered. The results of solving the problem using these methods are presented and compared. All calculations were performed using Excel.

Designing Sustainable Flexible Manufacturing Cells with Multi-Objective Optimization Models

Having sustainable and flexible features is crucial for manufacturing companies considering the increasing competition in the globalized world. This study considers three aspects of sustainability, namely economic, social, and environmental factors, in the design of flexible manufacturing cells. Three different multi-objective integer mathematical programming models were developed with the objective of minimizing the costs associated with carbon emissions, inter-cellular movements, machine processing, machine replacement, worker training, and additional salary (bonus). Simultaneously, these models aim to minimize the carbon emission amount of the cells within the environmental dimension scope. The developed models are a goal programming model, an epsilon constraint method, and an augmented epsilon constraint (AUGMECON) method. In these models, alternative routes of parts are considered while assigning parts to machines. The results are obtained using the LINGO 20.0 optimization program with a developed illustrative example. The obtained results are tested and compared by performing sensitivity analyses. The sensitivity analyses include examinations of the effects of changes in part demands, machine capacity values, carbon limit value, and the maximum number of workers in cells.

Using Geopandas for locating virtual stations in a free-floating bike sharing system

Free-floating bike-sharing systems can have a positive influence on the mobility of urban centers and developing efficient localization strategies is crucial to avoid crowding at peak times and increase service availability. Our study aims to efficiently resolve the location of virtual bike stations in a Latin American city through a geospatial data wrangling methodology that allows us to respond opportunely to the potential demand forecasted for the city. This approach is implemented in Python, and it uses the Geopandas and LocalSolver libraries to determine locations for the virtual bike stations that maximize the system coverage. The decision-making process is supported by a binary integer mathematical programming model, and the instances are built from intercity travel surveys that provide realistic data based on travel demand. The developed decision support system prototype provides a recommendation about where virtual bike stations should be located during peak hours and improve general availability by more than 37%. Moreover, when the system's users participate in the relocation of bicycles, the model can eliminate up to 80% of the CO2 emissions and nearly 50% of the operational costs associated with the relocation process.

Multi-criteria optimization of the system for complex processing of oil contaminated waste regarding a set of system quality criteria

The paper proposes a new approach to solving the multicriteria optimization problem for the system for processing man-made waste of the oil and gas complex. The optimization problem is formulated as an integer mathematical programming problem with constraints. The objective function in the optimization problem is formed using a set of efficiency assessments obtained as a result of a multivariate analysis of resource and energy savings in the system for processing industrial waste from oil and gas enterprises based on the Data Envelopment Analysis (DEA) method. As restrictions in the problem, constraints on the maximum duration of the process of processing waste placed in a given group of storage facilities with the help of specialized technological installations are considered. Problem-oriented software has been developed for the numerical solution of the problem of multiobjective optimization.

A mathematical programming model with present value method for optimum design of flexible cellular manufacturing systems

In this article, an integer mathematical programming model for the design problem of flexible cellular manufacturing systems is proposed. The developed mathematical programming model whose objective function is to minimize total design cost including cost of operating parts on machines, cost of using tools on machines, and cost of assigning employees to cells, also contains the present value method. Thus, it is ensured that the operational costs that occur along a certain time period are also taken into account. LINGO 19.0 optimization program software is used for the optimum solution of the integer mathematical programming model with the present value method whose objective function is to minimize the total design cost. In this article, the application of the model and the analysis related to the model are shown using a developed example problem. In addition, by ensuring the optimum design of flexible cellular manufacturing systems, the results of which alternative routes are used for processing parts, which machines are located in which cells, and which employees are assigned to which cells, are obtained. Then, a sensitivity analysis is presented to show the importance of alternative routes of parts.

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.

A Dynamic Colored Traveling Salesman Problem With Varying Edge Weights

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem. In it, each city has one to multiple colors and allows a salesman in the same color to visit exactly once. This work presents for the first time a CTSP whose edge weights among the cities change over time. It can be applied to dynamic routing problems arising in logistic distribution systems with various goods accessibilities to different types of vehicles. A non-linear integer mathematical program is constructed. A Variable Neighborhood Search (VNS) algorithm with a direct-route encoding and random initialization is then presented to solve it. To increase the convergence rate and population diversity of VNS, it is further combined with two-stage greedy initialization and an appropriate population immigrant scheme to perform the population search in a dynamic environment. Then, off-line performance evaluation and Wilcoxon test of the proposed algorithms are performed. The results show that their solution quality is improved by 30% ~ 60% over the basic VNS’s. They can track the environmental changes of CTSP-VEW more rapidly and effectively. In the end, a case study with a practical scenario is conducted.

The on-demand warehousing problem

Warehouses are key elements of supply chain networks, and great attention is paid to increase their efficiency. Highly volatile space requirements are enablers of innovative resource sharing concepts, where warehouse capacities are traded on online platforms. In this context, our paper introduces the on-demand warehousing problem from the perspective of platform providers. The objective prioritises demand–supply matching with maximisation of the number of transactions. If there is a tie, the secondary objective maximises the number of suppliers matched with at least one customer and the number of customers that have matches within a specific threshold with respect to the minimum achievable cost. Besides the mathematical integer programming formulation, a myopic list-based heuristic and an efficient matheuristic approach are presented and benchmarked against the performance of a commercial optimisation solver. The impact of several parameters on the platform's objective is analysed. A particularly relevant finding is that the pricing flexibility on the demand side does not necessarily imply higher payments to the supply side. All data instances are made available publicly to encourage more researchers to work on this timely and challenging topic.

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.

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.

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.

Optimisation of open-pit mine production scheduling considering optimum transportation system between truck haulage and semi-mobile in-pit crushing and conveying

ABSTRACT Despite the upward trend in using semi-mobile in-pit crushing and conveying system (SMIPCC), some mining companies still hesitate to use SMIPCC in their operations. Therefore, a framework is needed to facilitate decision-making between SMIPCC and truck and shovel system (TS) and satisfy the location and relocation time of the semi-mobile crusher (SMC). For this purpose, this paper presents a mathematical integer programming (IP) model considering the operational constraints. The model specifies both the optimum location and optimum relocation time of SMC. Also, it compares the production schedule for the TS and SMIPCC utilised for ore and waste handling over the life of mine. Then, the system with maximum net present value (NPV) is selected as the optimal material handling system. Finally, the model is implemented with a case study. The results show that implementing SMIPCC instead of the TS system for ore and waste materials improves the NPV by 69.77%.

An Integer Mathematical Programming Model for Production Scheduling Problem in Open-Pit Mines under Grade Uncertainty and Solving Using the Firefly Algorithm

Long-term production scheduling in open-pit mines is a crucial issue in mining planning and determines the distribution of cash flow throughout the life of the mine. The purpose of the planning is to maximize the net present value by taking into account all operational constraints such as slope, mixing of different grades, mineral production, and extraction capacity. The uncertainties associated with model data play an important role in optimizing long-term production plans. Among the uncertainties, grade uncertainty plays a major role. In this paper, hybrid models are presented by the Lagrangian relaxation (LR) method, augmented Lagrangian relaxation (ALR) method, and firefly algorithm (FA) to solve the long-term production scheduling problem of open-pit mines with the assumption of deterministic and also considering the grade uncertainty. The firefly algorithm is used to update the Lagrange multipliers. The newly proposed approaches are based on optimizing Lagrangian multipliers and comparing them with the results of combined Lagrangian relaxation method and augmented Lagrangian relaxation with the Genetic Algorithm (GA), and the traditional sub-gradient (SG) method. For solving and validating the obtained model, Chadarmelo iron ore mine is considered as a suitable case study. The results of the case study show that the combined strategy (ALR-FA) can provide a near-optimal solution over other methods such that, over a given period, the net present value using the proposed hybrid approach is 20.11% higher than the traditional method is available. Also, the CPU speed of the proposed model is 4.7% more than the other methods.

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.

Determining the optimal maintenance period in order to minimize the life cycle cost and maximize the performance and reliability index of the bridge

Population growth and development of economic relations have led to increase utilization of transportation infrastructures. The bridge is one of the important components of road construction that always needs special attention during the whole period of design, execution and operation. To ensure that the stairs are regularly inspected, evaluated and operated, management is needed to meet this need in the stairs by performing appropriate maintenance and repairs. Therefore, in this study, a three-objective optimization model includes minimization of maintenance costs, maximization of bridge performance index and reliability of bridges. For this purpose, a complex integer mathematical programming model has been developed. In order to solve the problem, a multi-objective particle mass optimization algorithm has been developed. From the solution of the proposed algorithm, different Pareto answers are obtained so that the decision makers can choose the answer from the obtained Pareto answers that is their priority.Also, after performing a sensitivity analysis on the parameters of failure rate and failure rate during the effect, it has been observed that by increasing the scenario number in two cases, which indicates an increase in failure rate and failure rate during the effect, the amount of costs increases and The overall performance of the system has been declining, which seems natural and correct.