Linear Programming Mathematical Model Research Articles

Efficiency-oriented vehicle relocation of shared autonomous electric fleet in station-based car-sharing system

Long waiting delays for users and significant imbalances in vehicle distribution are bothering traditional station-based one-way electric car-sharing system operators. To address the problems above, a “demand forecast-station status judgement-vehicle relocation” multistage dynamic relocation algorithm based on the automatic formation cruising technology was proposed in this study. In stage one, a novel trip demand forecast model based on the long short-term memory network was established to predict users' car-pickup and car-return order volumes at each station. In stage two, a dynamic threshold interval was determined by combining the forecast results with the actual vehicle distribution among stations to evaluate the status of each station. Then vehicle-surplus, vehicle-insufficient, vehicle-normal stations, and the number of surplus or insufficient vehicles for each station were counted. In stage three, setting driving mileage and carbon emission as the optimization objectives, an integer linear programming mathematical model was constructed and the optimal vehicle relocation scheme was obtained by the commercial solver Gurobi. Setting 43 stations and 187 vehicles in Jiading District, Shanghai, China, as a case study, results showed that rapid vehicle rebalancing among stations with minimum carbon emissions could be realized within 15 min and the users’ car-pickup and car-return demands could be fully satisfied without any refusal.

A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy

PurposeThis paper aims at developing a multi-objective mathematical model of circular economy that integrates key concept of leasing as a strategy in addition to reuse, refurbishing, primary recycling, secondary recycling and disposal.Design/methodology/approachThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.FindingsThe results show that the leasing of the products improves the economic function in addition to the known environmental improvements. The proposed model also shows that the circular economy can generate the jobs for the unskilled people at different locations.Research limitations/implicationsThe proposed model can be further improved by considering the non-linearity due to economy of scale at various centers and in transportation. The model can be further extended to make it multi-period model.Practical implicationsThe proposed model of circular economy can be used by the organizations as a policy tool to decide the optimum number of collection centers, disassembly centers, refurbishing centers, recycling centers and disposal centers and their optimum locations and allocations. The organizations can also trade-off among economic, environmental and social benefits of their proposed decisions in circular economy.Originality/valueThe originality of the proposed mathematical model is consideration of leasing as a strategy to have better control over the supply chain for circularity; considering the training of unskilled people for backward supply chain jobs and accounting for primary recycling and secondary recycling separately for economical computation.

Round-trip hub location problem

In this paper, we introduce a novel network design for the Hub Location Problem, inspired by the round-trip structure commonly used by transport service providers. Our design integrates spoke nodes assigned to a central hub node, creating round-trips where the hub node serves as the starting point, visits all assigned spoke nodes, and returns to the hub. To enhance transportation services and provide additional redundancy, we introduce a new type of nodes called runaway nodes to the network. The motivation for this research arises from two real-life cases encountered during consultancy projects, underscoring the necessity for an optimized network design in transportation services. To address the proposed problem, we introduce a mixed-integer linear programming (MIP) mathematical model. However, due to the problem's complexity, the feasibility of the MIP model is limited to small-scale instances. To tackle medium and large-scale instances, we introduce two hyper-heuristic approaches based on reinforcement learning. These hyper-heuristic approaches harness the power of reinforcement learning to guide the selection of low-level heuristics and improve solution quality. We conduct extensive computational experiments to evaluate the efficiency and effectiveness of the proposed approaches. The results of our experiments affirm the efficiency of the proposed hyper-heuristic approaches, showcasing their ability to discover high-quality solutions for the Hub Location Problem.

Circular closed-loop supply chain network design considering 3D printing and PET bottle waste

AbstractOne of the most critical pillars of Industry 4.0 (I4.0) is Additive Manufacturing (AM) or 3D Printing technology. This transformative technology has garnered substantial attention due to its capacity to streamline processes, save time, and enhance product quality. Simultaneously, environmental concerns are mounting, with the growing accumulation of plastic bottle waste, offering a potential source of recycled material for 3D printing. To thoroughly harness the potential of AM and address the challenge of plastic bottle waste, a robust supply chain network is essential. Such a network not only facilitates the reintegration of plastic bottle waste and 3D printing byproducts into the value chain but also delivers significant environmental, social, and economic benefits, aligning with the tenets of sustainable development and circular economy. To tackle this complex challenge, a Mixed-Integer Linear Programming (MILP) mathematical model is offered to configure a Closed-Loop Supply Chain (CLSC) network with a strong emphasis on circularity. Environmental considerations are integral, and the primary objective is to minimize the overall cost of the network. Three well-known metaheuristics of Simulated Annealing (SA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are employed to treat the problem which are also efficiently adjusted by the Taguchi design technique. The efficacy of our solution methods is appraised across various problem instances. The findings reveal that the developed model, in conjunction with the fine-tuned metaheuristics, successfully optimizes the configuration of the desired circular CLSC network. In conclusion, this research represents a significant step toward the establishment of a circular supply chain that combines the strengths of 3D printing technology and the repurposing of plastic bottle waste. This innovative approach holds promise for not only reducing waste and enhancing sustainability but also fostering economic and social well-being.

Optimization in Territorial Partitioning to Improve the Performance of a Common Building Maintenance Service Contract: A Case Study of a Public Agency in Paraná State, Brazil

All public administration contracts must be evaluated in order to improve their performance while respecting the limits established by laws and regulations. The purpose of this article is to apply an approach to improve the performance of a common building maintenance service contract for the Paraná State Court of Justice (PRCJ), which has a total built area of ​​544 283,79 m² in 224 buildings distributed over 161 counties, by optimizing the territorial partitioning of Paraná State. To partition the state into 14 regions, a binary integer linear programming (BILP) mathematical model is applied to the facilities location problem (FLP) in three scenarios. The results show that Scenario 3 (in which the location of the 14 maintenance offices and the configuration of their areas of activity were optimized) is the best in terms of minimizing the distances traveled by maintenance teams. In this scenario, the total distance traveled would be 9 775 km per day (instead of the current 11 150 km), achieving savings of around 12,3% when compared to the current solution. With this solution, in addition to the distance, the direct and indirect costs associated with the displacement of work teams and the time spent on their corresponding trips would be minimized. Furthermore, the users of maintenance services could be served more quickly, resulting in a higher number of services and greater satisfaction for the target audience of the contract.

A cascaded flowshop joint scheduling problem with makespan minimization: A mathematical model and shifting iterated greedy algorithm

This paper studies a cascaded flowshop joint scheduling problem that has critical applications in the electronic information equipment manufacturing industry but has received limited attention in the scheduling field. The cascaded flowshop joint scheduling problem encompasses both a distributed permutation flowshop scheduling problem and a hybrid flowshop scheduling problem. This paper investigates the efficient scheduling of a set of jobs in two heterogeneous flowshops to minimize the makespan. We present a mixed integer linear programming mathematical model and a shifting iterated greedy algorithm, which constantly changes its search space to explore different solution spaces. Based on the specific characteristics of the problem, a hybrid scheduling approach that combines forward and backward scheduling, a step-by-step destruction and reconstruction operator, and three adaptive reconstructive methods that combine coarse-tuning and fine-tuning are proposed to explore the near-optimal solution. Through comprehensive computational comparison and statistical analysis, the results demonstrate that the proposed shifting iterated greedy algorithm performs significantly better in relative deviation index values at the same CPU running time.

Just‐in‐time scheduling problem with due windows and release dates for precast bridge girders

AbstractAs the prefabrication construction method plays an increasingly important role in the construction of cross‐sea bridges, coordinating the schedule between off‐site prefabrication and on‐site assembly becomes crucial and challenging. This paper studies a just‐in‐time single‐machine scheduling problem with due windows and release dates, which originates from the production and supply process of large segments of precast steel box girders in bridge construction. To solve this problem, we equivalently decompose it into the independent and same type of subproblems and formulate a mixed‐integer linear mathematical programming model. Furthermore, we propose a branch‐and‐bound algorithm with the initialization of a novel linear early and tardy dispatching rule with due windows to solve the problem exactly. The dispatching rule, based on the local dominance criteria with due windows, is designed and used to improve the upper bound. Moreover, a lower bound is obtained by further decomposing and relaxing the subproblems. Finally, the parameter of the dispatching rule is calibrated, and the best search strategy of the branch‐and‐bound algorithm is determined. The comprehensive computational experiments carried out show the efficiency and effectiveness of the proposed branch‐and‐bound algorithm.

A Comparative Study of ε-constraint, LP-metric, and Weighted Sum Multi-objective Optimization Methods in a Circular Economy

Approximately 74.7 Mt (Million Metric Tonnes) of e-waste is expected to be produced in 2030, and laptop e-waste is one of the major constituents of this. The goal of this paper is to develop and optimize a mixed-integer linear programming (MILP) mathematical model for a laptop manufacturer in India, based on a framework that integrates secondary reuse concept associated with traditional circular economy waste avoidance strategies. The multi-objective solution techniques of ε-constraint, LP-metric, and weighted sum methods are used to optimize the circular economy model. The proposed model aids as a policy tool to decide the optimum number of inspection/collection centers, sales/distribution centers, disassembly centers, refurbishing centers, recycling centers, and their optimum locations and allocations. This study results suggest that reuse, secondary customer centers, refurbishing, and recycling of the laptops is not only economically beneficial to the organization but also environment friendly and helps to create more jobs in the rural economy.

Workload balancing and scheduling in picking tower systems considering different storage strategies

Picking tower systems are particularly suitable in the e-commerce distribution field. They permit to stock and pick a wide variety of items by maximizing storage capacity and space utilization. Such types of systems are comparable to zone picking solutions, since pickers work on one floor during the same working shift. However, differences also exist since, for example, once the picking tower system is designed, it is not possible to improve or reduce the area of each floor. Thus, a proper workload balancing is required to avoid an efficiency reduction of this system. This paper proposes a mixed integer linear programming mathematical model to assign pickers to floors and jointly schedule the picking list of each of them aiming to minimize the completion time of all orders. The model is applied to a real case study and first managerial insights are derived by investigating how the number of floors, the storage strategy and the number of pickers allowed on each floor influence the workload and the completion time. The results show that, for the considered case, the most effective configuration is the brand-based storage strategy with four picking levels.

Mathematical modeling and dragonfly algorithm for optimizing sustainable agritourism supply chains

The management of agritourism supply chains plays a pivotal role in promoting sustainable rural development and cultivating economic growth within agricultural communities. The study devises a comprehensive methodology aimed at designing and optimizing agritourism supply chain networks. To achieve this purpose, a two-objective mixed-integer linear programming mathematical model is introduced, tailored to accommodate diverse water consumption priorities across different gardens within the chain. Recognizing the NP-hardness of this intricate problem, a metaheuristic-driven solution approach based on MIN-MAX goal programming and dragonfly algorithm is presented to solve the designed model, aiming to simultaneously maximize the total profit and minimize overall water consumption within the supply chain. To assess the effectiveness of the proposed methodology, we adopted a real-world case study of an agritourism supply chain in China. The obtained results indicate the adoption of the proposed method can efficiently lead to the development and mechanization of agriculture in villages. The numerical analysis highlights that recruitment and production costs significantly influence the total profit of the agritourism supply chain. Additionally, the research underscores the pivotal role of sustainable rural development in creating job opportunities within the agritourism supply chain, thereby stimulating economic growth and fostering more profitable enterprises.

Minimization Implementation of Fuzzy Logic to Optimize a Cashew Nut Production using Simpleks-Duality Theory

Production control of cashew nuts greatly affects the profits earned by the company. When cashew nut raw materials exceed production needs, it results in storing cashews for an extended period, causing the cashew products to lose freshness, and the quality of processed cashews deteriorates. If the raw materials are damaged, the manufacturer must acquire additional costs to procure raw materials again. Another issue is that cashew nut raw materials are seasonal products and are not always available.To solve these problems, a calculation method is needed to control optimal production inventory to minimize the company's expenditures. The method used is to formulate the problem into a Fuzzy Linear Programming mathematical model using a combination of methods: the Simplex algorithm and Duality Theory. The case implementation focuses on the uncertainty of cashew nut production quantities outside the harvest season. Moreover, the calculation of an optimal production quantity to minimize resulting losses is needed. The output generated is an optimal production prediction using the combination of the Simplex Algorithm and Duality Theory in solving Fuzzy Linear Programming.

Optimization of production planning using integer linear programming method (case study of bakpia menik)

Bakpia Menik is a Small and Medium Enterprise (UKM) which operates in the field of bakpia production. Bakpia is one of the local cakes which is the main souvenir from Yogyakarta, so there is a big potential for increasing production. However, SMEs still lack production management planning to optimize resource use. So it is difficult to capture this big opportunity to maximize profits for SMEs. Seeing these problems, this research designed an integer linear programming mathematical model to optimize profits by using existing resources. Integer Linear Programming (ILP) is a mathematical model for maximizing profit and minimizing cost based on a mathematical model involving integer variables represented in a linear relationship. This research produces an integer linear programming model that presents the variables, resources, and constraints of Bakpia Menik. The model output shows that the optimal production amount by maximizing resource use is 31232 units and the maximum profit is IDR 33,431,750. From the model output, it can also show the advantages and disadvantages of Bakpia resources, so that resource availability planning can be carried out which can minimize holding costs.

Sustainable aquafeed development: Incorporating select fruit wastes into Zebrafish diets using mathematical model-based approach

Expensive aquafeed is a major problem in aquaculture, creating the need for a low-cost feed that provides ideal nutritional requirement to maximize growth performances. This study aims to formulate and evaluate two new optimized Zebrafish feeds (F1 and F2) using linear programming mathematical model, one of which incorporates two pigment rich fruit wastes (Pitaya peel and Roselle calyx) in the formulation. The model represents nutritional content and cost of each ingredient into linear equations, with the goal of finding ideal combination that satisfies the specific nutrient requirements. By systematically evaluating ingredient proportions, linear programming ensures that Zebrafish receives adequate nutrients at the lowest possible cost, making the feed development process more efficient and cost-effective. The novel feed formulations derived from the mathematical model were tested on the growth and pigmentation of Zebrafish in comparison to a commercial feed (control). Feed intake of F1 and F2 were generally found to be similar to the control feed, indicating the acceptability of the formulated feeds by the Zebrafish. Body weight and length of Zebrafish fed with F1 and F2 were comparable to Zebrafish fed with control feed (p > 0.05). Similarly, Zebrafish fed with F1 and F2 showed no significant differences in pigment intensity compared to Zebrafish fed with control feed (p > 0.05). The survival rate of fishes in all feeding groups were greater than 70 % with no significant differences (p > 0.05). Results obtained in this study illustrated the potential of mathematic linear programming and effectiveness of utilising pigment-rich fruit wastes in formulating an optimized economic aquafeed.

An effective adaptive iterated greedy algorithm for a cascaded flowshop joint scheduling problem

This paper addresses a novel scheduling problem, namely the cascaded flowshop joint scheduling problem (CFJSP), which has critical applications in the modern electronic information equipment manufacturing industry. The CFJSP is composed of a distributed permutation flowshop scheduling problem and hybrid flowshop scheduling problem. This paper considers how to arrange a variety of jobs for the two flowshops together to minimize total flowtime. We present a mixed integer linear programming mathematical model and an effective adaptive iterated greedy (AIG) algorithm with a decomposition and collaboration mechanism, which optimizes each production phase sequentially and ultimately optimizes the whole process. Combining the problem-specific characteristic, an adaptive inverse bounded heuristic, an adaptive bounded range local search, and an odd/even random insertion reconstruction mechanism are proposed to explore more valuable space. Comprehensive computational experiments and statistical analyses are conducted to verify the effectiveness of the proposed AIG. The experimental results show that the proposed AIG significantly outperforms the state-of-the-art competing algorithms from the literature in relative deviation index values at the same CPU running time.

Multiobjective U-Shaped Disassembly Line Balancing Problem Considering Human Fatigue Index and an Efficient Solution

The progress of science and technology speeds up the replacement of products and produces a large number of end-of-life products. Traditional incineration causes a waste of resources and pollution to the environment. Disassembling and recycling end-of-life products are the recommended way to maximize the utilization of resources and reduce environmental pollution. Disassembly performance is affected by many factors, such as the disassembly posture of the human body, the fatigue of workers on a workstation, disassembly profit, and task precedence relationship. In this article, a mixed integer linear programming mathematical model for U-shaped layout disassembly line balancing problems is developed, in which the balance of workers’ fatigue indices is an optimization objective in addition to disassembly profits. An efficient solution to the problem that uses a collaborative resource allocation strategy of the multiobjective evolutionary algorithm is proposed. The linear programming solver CPLEX is used to verify the accuracy of the model and compared with the proposed algorithm. Experiments demonstrate that the algorithm is significantly superior to the CPLEX solver in handling large-scale cases. The proposed algorithm is also compared with two well-known algorithms, which further verifies its superiority.

A Mathematical Programming Approach for Multi-Objective Optimization in Designing Flexible Manufacturing Cells

The study aims to design flexible manufacturing cells with routing flexibility. A weighted mixed-integer linear mathematical programming model that aims to find optimal routing of parts in flexible manufacturing cells under constraints such as minimum machine utilization rate, maximum machine utilization rate, tool capacities, the utilization rate of workers, and labor-system unbalance is developed. The mathematical programming model aims to minimize the weighted sum of five objective functions: (1) the total number of intracellular movements; (2) the total number of intercellular movements; (3) the total workload unbalance of the machine system; (4) the total number of tools in all machines in the cells; and (5) the total labor-system workload unbalance. The main contribution of this study is to obtain these five objectives simultaneously, which have not been encountered to handle together before. By integrating these factors, the study presents a comprehensive approach to optimizing the design of flexible manufacturing cells. This study also has the potential to enhance system performance by addressing these factors. An illustrative problem tests the developed model, and the LINGO 17.0 optimization program is used to solve the generated mathematical programming model. Moreover, the related sensitivity analysis is performed with some parameters to examine the obtained results.

Health information exchange network under collaboration, cooperation, and competition: A game-theoretic approach.

Health Information Exchange (HIE) network allows securely accessing and sharing healthcare-related information among healthcare providers (HCPs) and payers. HIE services are provided by a non-profit/profit organizations under several subscription plans options. A few studies have addressed the sustainability of the HIE network such that HIE providers, HCPs, and payers remain profitable in the long term. However, none of these studies addressed the coexistence of multiple HIE providers in the network. Such coexistence may have a huge impact on the behavior of healthcare systems in terms of adoption rate and HIE pricing strategies. In addition, in spite of all the effort to maintain cooperation between HIE providers, there is still a chance of competition among them in the market. Possible competition among service providers leads to many concerns about the HIE network sustainability and behavior. In this study, a game-theoretic approach to model the HIE market is proposed. Game-theory is used to simulate the behavior of the three different HIE network agents in the HIE market: HIE providers, HCPs, and payers. Pricing strategies and adoption decisions are optimized using a Linear Programming (LP) mathematical model. Results show that the relation between HIEs in the market is crucial to HCP/Payer adoption decision specially to small HCPs. A small change in the discount rate proposed by a competitive HIE provider will highly affect the decision of HCP/payers to join the HIE network. Finally, competition opened the opportunity for more HCPs to join the network due to reduced pricing. Furthermore, collaborative HIEs provided better performance compared to cooperative in terms of profit and HCP adoption rate by sharing their overall costs and revenues.

Modelling the Slovenian Wood Industry’s Response to the Greenhouse Gas Paris Agreement and the EU “Fit for 55” Green Transition Plan

Almost 200 nations, including the European Union, have signed the Paris Agreement that aims to limit the temperature rise to 1.5 °C above pre-industrial levels by reducing greenhouse gas (GHG) emissions. To meet this target, a significant decrease in GHG emissions by 2030 and net zero by 2050 is necessary. To determine the role of wood products in achieving a 55% reduction in GHG emissions by 2030 compared with 1990 levels, we investigated Slovenia’s potential, which has close to 60% forested areas. Therefore, the country could use wood-based products to achieve the agreed-upon climate goals. Nevertheless, uncertainties remain regarding the extent to which increased tree harvesting, local manufacturing, and the utilization of wood products can aid in substituting fossil-derived materials and reducing GHG emissions. A new model was constructed to increase the understanding of the wood products’ (throughout the forest-based industrial ecosystem, incl. construction) potential contribution to reaching the stated emissions targets. Using this linear programming (LP) mathematical optimisation model and carbon footprint calculations based on life cycle assessment methods, a wood flow distribution, the financial investment needed to process these quantities, and the GHG emissions produced and/or saved were calculated. The findings stipulated that Slovenia has the potential to achieve 55 % less GHG emissions by 2030 by expanding logging to at least 3 million m3 and converting the timber to a larger amount of long service-life wooden items made (and utilised) within the country. Such products accumulate carbon for a long time and decrease the need for materials that cause higher GHG emissions. Concomitantly, a better appreciation of the substitution effects in official carbon accounting would be needed. Moreover, to materialize the potential decrease in emissions would require Slovenia’s construction sector to replace fossil- and mineral-based materials with lignocellulosic products, and to increase the capacity to utilize lower-quality wood in high added value applications, which would require significant investment. This paper offers a comprehensive analysis of diverse optimisation outcomes obtained from the investigation into climate action through the use of wood products in Slovenia.

DRL-assisted joint allocation of antenna, radio, and front-haul resources in TWDM-PON-based NG-RANs with mMIMO-enabled beamforming

The high spectrum efficiency of massive multiple input multiple output (mMIMO)-enabled beamforming is attractive for solving the massive number of connections in next-generation radio access networks (NG-RANs). However, the beamforming based on multiple antenna sub-arrays to support multi-connections would introduce extra 2D antenna sub-array selection and radio resource block (RB) allocation; meanwhile, considering the front-haul bandwidth consumption would reduce as much as possible the redundant data transmitting over front-haul in the NG-RANs. Therefore, a key issue is how to coordinate 2D antenna sub-array selection and radio RB allocation to minimize the front-haul bandwidth and maximize the radio RB utilization when accommodating a set of beam antenna array (BAA) requests. In this paper, we first establish a 3D BAA mapping model to jointly optimize 2D antenna sub-array selection and radio RB allocation, which would in turn affect the allocation of the front-haul wavelength bandwidth in a time and wavelength division multiplexed passive optical network (TWDM-PON)-based front-haul with the mMIMO antenna system. An integer linear programming mathematical model is formulated, and a novel deep reinforcement learning (DRL)-based algorithm is proposed to optimize the front-haul bandwidth and radio RB utilization. Besides, two heuristic algorithms are developed with different antenna sub-array selection policies as the benchmarks. The extensive simulation results show that our proposed DRL-based algorithm can attain the lowest average cost (AC) for different numbers of BAA requests considered by seeking the optimal trade-off between the front-haul bandwidth consumption and the number of the used antennas. Compared with the inter-sub-array benchmark, the DRL-based algorithm can achieve up to 7.5% AC reduction, which is mainly attributed to the 21.2% reduction of the front-haul bandwidth without increasing the number of used antennas.

Dynamic Multi-Compartment Vehicle Routing Problem for Smart Waste Collection

The rapid increase in urbanization results in an increase in the volume of municipal solid waste produced every day, causing overflow of the garbage cans and thus distorting the city’s appearance; for this and environmental reasons, smart cities involve the use of modern technologies for intelligent and efficient waste management. Smart bins in urban environments contain sensors that measure the status of containers in real-time and trigger wireless alarms if the container reaches a predetermined threshold, and then communicate the information to the operations center, which then sends vehicles to collect the waste from the selected stations in order to collect a significant waste amount and reduce transportation costs. In this article, we will address the issue of the Dynamic Multi-Compartmental Vehicle Routing Problem (DM-CVRP) for selective and intelligent waste collection. This problem is summarized as a linear mathematical programming model to define optimal dynamic routes to minimize the total cost, which are the transportation costs and the penalty costs caused by exceeding the bin capacity. The hybridized genetic algorithm (GA) is proposed to solve this problem, and the effectiveness of the proposed approach is verified by extensive numerical experiments on instances given by Valorsul, with some modifications to adapt these data to our problem. Then we were able to ensure the effectiveness of our approach based on the results in the static and dynamic cases, which are very encouraging.