Integer Nonlinear Programming Model Research Articles

A MINP model and hybrid heuristic algorithm for railway cold chain service network design problem: a case study of China

Railway Cold Chain Service Network Design (RCC-SND) aims to optimise resource allocation and utilisation to ensure the efficient transportation of perishable foods. In this study, we propose a Mixed Integer Nonlinear Programming (MINP) model to solve the hub selection, service frequency determination, wagon flow organisation and routing problems in RCC-SND. The application of the model is illustrated using the real network comprising 163 cities in China. The PSO-GA algorithm is proven effective in solving the problem. Furthermore, we introduce two future scenarios to assess the carbon reduction potential and economic costs of railway cold chain operations. There are some main findings: as the hub number increases from 30 to 40, the total cost decreases, as the hub continues to rise, this reduction is offset by the increased hub operational costs. Increasing hubs can enhance direct train frequency while causing railway capacity redundancy, this redundancy can be addressed by freight volume increase, as demonstrated in this study, 4.5 times increase in freight volume can boost train utilisation by up to 12.5%. By 2030, railway cold chain carbon emissions are projected to exceed 1.1 million tons, the adoption of hydrogen as alternative energy is an economically viable solution for emission reduction.

A mathematical model and solution algorithms for optimising system-level configurations of reconfigurable single part flow lines

This study addresses a system-level configuration selection problem for reconfigurable single part flow lines (R-SPFLs) with parallel identical flexible machines at each stage. The problem is to determine the number of stages, the number of machines of a certain type at each stage and the assignment of operations to each stage in order to satisfy the demand of a part type. Precedence relations among the operations and space limitations are also considered. For the objective of minimising the sum of machine purchase and operation processing costs, a nonlinear integer programming model is developed that gives the optimal solutions. Then, due to the problem's complexity, a basic variable neighbourhood search algorithm is proposed that constructs an initial solution using a greedy-type heuristic and improves it using a shaking and a local search improvement methods. Moreover, the basic algorithm is extended to a general one that uses a variable neighbourhood descent method. Computational results show that the two algorithms outperform the previous one significantly in both solution quality and computation times, and the general algorithm improves the basic one significantly. Finally, the applicability of the variable neighbourhood search algorithms is shown by reporting a brief case study.

Optimal emergency hospitals construction in an unexpected epidemic with considering the interactive effect

AbstractConstructing emergency hospitals is one of the most critical measures to defeat an unexpected epidemic. However, existing operations research (OR) studies rarely consider the interactive effect between the construction of emergency hospitals and the dynamics of epidemic transmission. Inspired by this gap, we propose a new modeling framework for decision‐making in emergency hospital construction. In our optimization model, we address the pandemic evolution functions as constraints. We also consider the heterogeneity among infected individuals, distinguishing between those with mild and severe symptoms, each requiring treatment in different types of emergency hospitals. We formulate the problem as a mixed integer nonlinear programming model. Our model can envision the current and future evolution of the epidemic and the impact of different decisions regarding emergency hospital construction on epidemic development. Simultaneously, it provides the optimal strategy to build hospitals and minimize the total number of untreated patients due to the disease. The proposed model is tested using the Covid‐19 outbreak case in Wuhan. The results can provide precise guidelines for emergency hospitals construction, including timing and capacity, and offer decision boundaries for policymakers considering the uncertainty of disease transmission. Furthermore, our decision‐making framework is general and can be adapted to study other epidemics.

Multi-period fourth-party logistics network design from the viability perspective: a collaborative hyper-heuristic embedded with double-layer Q-learning algorithm

In the ‘new normal’ setting of a mega-crisis, the viability becomes the driving force for the fourth party logistics (4PL) network design. In this paper, the viability is characterised in terms of agility, resilience and survival sustainability as the response to changes in demand, disruption and survivability. The fortification and recovery strategies are considered in possible disruptions at transfer centres and third-party logistics providers. A novel mixed integer non-linear programming model is proposed to obtain the multi-period 4PL network solution with minimum total cost under viability constraints. Considering the NP-hard characteristic of problem and the non-convex of proposed model, the hyper-heuristic algorithm is designed. To take advantage of both global optimality seeking and local search ability, a collaborative hyper-heuristic embedded with double-layer Q-learning (CHHDLQL) algorithm is proposed. The effectiveness and efficiency of the proposed algorithm is demonstrated by the promising numerical results. By stress-testing the existing network, appropriate adjustments to fortification and recovery strategies can effectively cope with changes in demand and disruption. Furthermore, the impact of 4PL strategy, fortification and recovery strategies, and viability constraints are investigated. The demand satisfaction, network resilience and capacity can be improved by adjusting agility, resilience and survival sustainability to influence different component network costs. Highlights A novel multi-period 4PL network model under viability constraints is presented. The CHHDLQL algorithm for construction and perturbation coevolution is proposed. The stress tests apply to the 4PL network, including demand, disruption and 3PL. 4PL improves demand satisfaction, resilience and capacity by adjusting viability.

Simultaneous Optimization of Work and Heat Exchange Networks

This paper introduces a simultaneous optimization approach to synthesizing work and heat exchange networks (WHENs). The proposed work and heat integration (WHI) superstructure enables different thermodynamic paths of pressure and temperature-changing streams. The superstructure is connected to a heat exchanger network (HEN) superstructure, enabling the heat integration of hot and cold streams identified within the WHI superstructure. A two-step solution strategy is proposed, consisting of initialization and design steps. In the first step, a thermodynamic path model based on the WHI superstructure is combined with a model for simultaneous optimization and heat integration. This nonlinear programming (NLP) model aims to minimize operating expenditures and provide an initial solution for the second optimization step. In addition, hot and cold streams are identified, enabling additional model reduction. In the second step of the proposed solution approach, a thermodynamic path model is combined with the modified HEN model to minimize the network’s total annualized cost (TAC). The proposed mixed integer nonlinear programming (MINLP) model is validated by several examples, exploring the impact of the equipment costing and annualization factor on the optimal network design. The results from these case studies clearly indicate that the new synthesis approach proposed in this paper produces solutions that are consistently similar to or better than the designs presented in the literature using other methodologies.

신에너지 자동차배터리 산업 공급망 네트워크의 최적화

In this study, an optimization of supply chain network for New Energy Vehicle Power Batteries (NEVPB) from the perspective of resource circulation is proposed. The model consists of seven stages in terms of collection center (CC), repairing center (RC), distribution center (DC), recycling center (RY), part supplier (PS), material supplier (MS), and disposal center (DP). The model is formulated as a nonlinear integer programming model and a comparison of LINGO and genetic algorithm (GA접근법) are conducted respectively. In numerical experiment, it has found a way to repair and recycle NEVPB. Retrieving as many NEVPBs in use demonstrates sustainable power generation benefits by maximizing the use of recovery through resource recycling and searching for recovery classification of batteries as well as shortening lifespan that occur during the process of producing initial parts and modules from raw materials.

An Effective Two-Stage Algorithm for the Bid Generation Problem in the Transportation Service Market

This study designs a two-stage algorithm to address the bid generation problem of carriers when adding new vehicle routes in the presence of the existing vehicle routes to provide transportation service. To obtain the best auction combination and bid price of the carrier, a hybrid integer nonlinear programming model is introduced. According to the characteristics of the problem, a set of two-stage hybrid algorithms is proposed, innovatively integrating block coding within a genetic algorithm framework with a depth-first search approach. This integration effectively manages routing constraints, enhancing the algorithm’s efficiency. The block coding and each route serve as decision variables in the set partition formula, enabling a comprehensive exploration of potential solutions. After a simulation-based analysis, the algorithm has been comprehensively validated analytically and empirically. The improvement of this research lies in the effectiveness of the proposed algorithm, i.e., the ability to handle a broader range of problem scales with less time in addressing complex operator bid generation in combinatorial auctions.

Optimal Sustainable Manufacturing for Product Family Architecture in Intelligent Manufacturing: A Hierarchical Joint Optimization Approach

As consumers and governments prioritize cost-effectiveness and ecological sustainability, the limitations of traditional manufacturing paradigms become apparent in the context of constrained resources. The adverse effects of these paradigms on the environment and society hinder the achievement of a sustainable product life cycle. Intelligent manufacturing processes offer a solution by efficiently gathering meaningful data, such as usage and product recycling information, from previous product generations to enhance product design and subsequent sustainable manufacturing processes (SMPs). Modular product family architecture (PFA) design holds promise in promoting product sustainability and addressing diverse consumer needs. PFA design and SMPs are inherently interconnected within intelligent manufacturing frameworks. This paper aims to integrate the decision-making processes underlying PFA with SMPs. We model integrated PFA and SMP decisions as a Stackelberg game, which involves hierarchical joint optimization (HJO) for assessing product modularity and sustainable manufacturing fulfillment. We develop a bilevel 0–1 integer nonlinear programming model to represent the HJO decision-making process and propose a nested genetic algorithm (NGA) to solve the HJO problem. A case study with a laptop is conducted to validate the feasibility and potential of the proposed HJO model for joint optimization problems in PFA design and SMPs.

Integrated operation models with quay crane maintenance in a container terminal

This paper investigates an integrated optimization problem concerning berth allocation, quay crane assignment, and truck deployment in container terminals, with a specific focus on incorporating quay crane maintenance into the integrated models. A nonlinear integer programming model is proposed, and then a number of equivalent or relaxed models are developed to ease the model. To solve the model on large-scale instances, a SWO-GA is developed to provide a solution. Finally, a set of test instances are randomly generated to access the applicability of the proposed models and the efficiency of the algorithm. The results show that the SWO-GA can obtain a good solution with a small gap within a much shorter computation time than that of CPLEX. Quay crane maintenance significantly affects the operation plans and increases costs. The maintenance time step and the number of berths required for quay crane have a proportional impact on the total cost. It is also found that quay crane maintenance is of great concern for large-sized container terminals. The model and algorithm proposed in this paper provide important insights for operation managers.

Optimizing City-Scale Demolition Waste Supply Chain Under Different Carbon Policies.

In order to establish a green, low-carbon circular development economic system, imperative goals include achieving carbon peaking and carbon neutrality. This research delves into the resource utilization of city-scale demolition waste (C&DW), aligning with environmental protection needs and sustainable development principles. The paper introduces a unique closed-loop supply chain (CLSC) model tailored for C&DW and employs a distinctive mixed integer nonlinear programming (MINLP) model for optimization. Guangzhou serves as a case study for thorough analysis, verification, and practical application of the proposed model, especially under diverse scenarios of carbon price (CP) and carbon trading (CT) policies. The key conclusions drawn from this study include the following: (1) The cost of carbon emissions is intricately influenced by both carbon emissions and carbon price, with the latter effectively regulating the carbon emissions during C&DW recycling. (2) The implementation of a CT policy, with a fixed carbon price, contributes to a further reduction in the cost of C&DW recycling treatment. (3) Under equivalent conditions, the CT policy demonstrates the potential to decrease costs and enhance the economic benefits within the building environmental protection product market. The research outcomes not only contribute to the advancement of management theory in the C&DW recycling supply chain (SC) but also provide a robust theoretical foundation for governmental initiatives aimed at introducing effective C&DW recycling management policies.

Period-dependent pricing methods of multi-type vehicles for BOT highway projects with pavement rehabilitation effects

In the planning stage of a BOT highway project, the future traffic demand plays a pivotal role on designing contract factors. Considering that the traffic demand generally has variations with time, the constant toll during the concession period obviously is not a good choice. And the different toll charges classified by vehicles types definitely affect the traffic composition and maintenance cost. To address this practical issue, this study proposes the mixed integer nonlinear programming models to select the period-dependent toll charges for multi-type vehicles and highway capacity, by considering both the objectives of the government and private firms. Then two solution algorithms are provided to solve our proposed models. Finally, numerical experiments are conducted to assess the applicability and efficiency of our models and algorithms.

Matheuristics vs. metaheuristics for joint lot-sizing and dynamic pricing problem with nonlinear demands

This paper considers a joint dynamic pricing and production planning decisions problem for a profit-maximizing firm that produces and sells multiple products. The objective is to develop a coordinated decision approach for multi-product pricing and lot sizing decisions for a manufacturer considering a limited production capacity. The demand for each product is assumed to be iso-elastic and integrates the complementarity and the substitution effects between the products. First, the problem is formulated as a non-convex mixed integer nonlinear programming model (MINLP) incorporating capacity constraints, setup costs, and nonlinear demand functions. Then, since the model is nonlinear and non-convex, a set of approximate approaches based on the Genetic algorithm, Late Acceptance Hill Climbing and Simulated Annealing methods are designed to solve this problem. Based on this study, the performances of two variants of approximate methods: matheuristics and metaheuristics are discussed and analyzed. The extensive experimental study, performed on real-world inspired instances, shows that matheuristic methods with setup-variables encoding scheme outperform the rest of the methods. The research outcomes show that coordinating a decision-making process by optimizing both prices and production plans simultaneously can result in significant profit for a company. However, one must consider the joint effect of the parameters of the demand function as well as the impact of the production capacity. This comprehensive understanding enables the company to avoid excessive investments in less lucrative products with lower sales potential, thereby ensuring resource allocation aligns with profitability and market demand.

A Two-Phase Approach for Reliability-Redundancy Optimization of a Communication Satellite

The development and launch of communication satellite projects pose significant challenges and costs. The expenses can range from several hundred million dollars, contingent on factors such as mission objectives, satellite system size and complexity including the launch vehicle, and ground infrastructure. Satellites must be designed to withstand harsh conditions in space, such as the extreme temperatures, radiation, and other hazards, while delivering reliable communication services to its users. However, once a satellite is launched, physical maintenance interventions become infeasible in the event of technical problems. Thus, reliability is a critical aspect for these expensive systems. This study aims to minimize the cost of a high-tech communication satellite by addressing design considerations that meet customer reliability requirements without exceeding power and redundant equipment limits. To achieve this goal, we propose an integer non-linear programming model in this research. To solve the satellite design problem, we adopt a two-stage solution approach. Conventional industrial practices in satellite design often involve iterative attempts to determine the redundancy level of onboard units based on customer reliability requirements. These processes rely heavily on the experience of design engineers who evaluate a limited number of alternatives to determine the number of redundant units, resulting in sub-optimal outcomes. In contrast, our proposed approach systematically handles the problem and yields optimal results. Our findings demonstrate that the proposed two-phase approach can achieve optimal redundancy levels within seconds.

Research on Vegetable Pricing and Replenishment Strategy Based on TOPSIS Method and Simulated Annealing Algorithm

By mining the relationship between categories and individual products, this paper puts forward enterprise replenishment and pricing strategies under different conditions. First of all, from the 49 kinds of vegetables sold, the TOPSIS method based on entropy weight is used to select the top 20 important items by taking the market demand and excess income as the first-level index, and taking the historical sales rate, average daily sales volume, variance of sales volume, vegetable loss rate and unit profit as the second-level index. Then, based on the concept of complementary and alternative goods, through the Spearman correlation coefficient, and using the weighted correlation coefficient method, select the top 9 items, such as ginger, garlic, millet pepper combination and so on. Using these selected items, taking the profit maximization of fresh merchants as the objective function and the demand of each category as constraints, a 0-1 integer nonlinear programming model is established. Then, the simulated annealing algorithm is used to simulate the planning for 1000000 times, and the pricing strategy and supply plan of the enterprise on July 1st are obtained, and the maximum profit on that day is 2098.17 yuan.

A bi-objective approach for the multi-skilled worker assignment of a hybrid assembly line-seru production system

The flexibility and responsiveness of seru production have caught the attention of manufacturing and electronics industries. However, multi-skilled worker assignment poses a crucial and challenging decision-making problem for seru production systems. The existing literature on this problem for pure seru production systems primarily focuses on improving efficiency indexes, which often leads to an unbalanced workload among workers. To address this issue, this article investigates multi-skilled worker assignment for a hybrid assembly line-seru production system that comprises divisional serus and a short assembly line. To balance workload and optimize production efficiency, a bi-objective integer nonlinear programming model is developed. This model jointly optimizes worker-to-seru, worker-to-line, batch-to-seru, task-to-worker, and the processing sequence of each batch. A meta-heuristic method, combining Non-Dominated Sorting Genetic Algorithm II (NSGA-II) with Multi-Objective Simulated Annealing (MOSA), NSGA-II-MOSA, is designed to solve the model. The results of numerical experiments demonstrate that the proposed model and solving method can greatly reduce workload imbalance while maintaining production efficiency. Moreover, NSGA-II-MOSA provides better Pareto solutions than three well-known multi-objective optimization approaches.

A flexible train composition strategy with extra-long trains for high-speed railway corridors with time-varying demand

To accommodate the uneven spatio-temporal distribution of passenger demand and improve the maximum transportation capacity for high-speed railway (HSR) corridors, this study proposes a demand-oriented flexible train composition strategy. The proposed strategy allows flexibility in selecting the number of train composition units (e.g., train carriages) for each train to accommodate the demand variations, where extra-long trains (longer than the length of the train station platform) might be utilized. Under such a strategy, a seat allocation method coupled with a train stopping position control strategy is proposed to avoid the need for cross-carriage walking during passenger boarding or alighting (for those extra-long trains). The train stopping position control strategy specifies the carriages that dock at or extend beyond the station platform, while the seat allocation method allocates seats within each carriage to specific origin-destination pairs. The studied problem can be formulated as an integer nonlinear programming model, where the weighted sum of the HSR operating cost and passenger travel time cost is minimized. The proposed model is then reformulated into an integer linear programming model via a series of linearization techniques. A tailored heuristic algorithm based on the variable neighborhood search (VNS) and GUROBI solver is designed to produce high-quality solutions for large-scale problems. Two numerical examples, i.e., a small example and a real-world Shanghai-Hangzhou HSR line example, are presented to illustrate the effectiveness of the proposed approach. The computation results show that, in comparison to traditional fixed and flexible train composition strategies without extra-long trains, the proposed strategy can significantly reduce the total operating cost and total travel time cost.

Study on cruise speed optimization and refueling strategy considering emission control areas

In order to alleviate the cost pressure caused by navigation restrictions and rising fuel prices faced by cruise companies, on the basis of considering the constraints of emission control areas and the arrival time constraints of each port, according to the relationship between the speed and fuel consumption of ships during navigation, a mixed integer nonlinear programming model with the minimum sum of the sum of ship fuel replenishment cost, arrival delay penalty cost and carbon tax cost is established to optimize the speed and refueling strategy of cruise ships. The results show that with the change of fuel price and time constraints, the fuel replenishment strategy will also change.

Optimization and exergoeconomic analysis of a solar-powered ORC-VCR-CCHP system based on a ternary refrigerant selection model

Ternary refrigerants surpass traditional single-component and binary refrigerants in performance, efficiency, and environmental impact in refrigeration systems, but the abundance of combination possibilities makes it challenging to experimentally determine the optimal mixture for a specific system. This research proposes a mechanism model for screening ternary refrigerants, which selects the composition of mixed refrigerants from 24 types of refrigerants and realizes simultaneous optimization of the composition and process parameters of mixed refrigerants. The model is applied to a new ORC-VCR-CCHP (Organic Rankine Cycle- Vapor Compression Refrigeration- Combined cooling, heating and power) system. This system can effectively recover solar energy and convert it into cooling, heat and electricity to meet the energy demand of the university campus to a great extent. Taking the highest exergoeconomic efficiency as the objective function and satisfying excellent economy, environmental protection, thermodynamic stability, and low toxicity at the same time, a mixed integer nonlinear programming (MINLP) model was established. The optimization results show that the optimal exergoeconomic efficiency can reach 42.49 %. The optimal composition with safety and environmental protection in the ORC system and VCR system are R245fa/R41/R1336mzz (z) and R1234ze/R1234yf/R32, with mass fractions of 0.5339/0.4310/0.0351 and 0.2202/0.2073/0.5725 respectively. The article concludes with an Exergoeconomic analysis.

Optimum rescheduling of water networks for batch processes using a goal programming technique

Batch processes are relevant to a wide variety of industries in chemical processes. In batch operations, water sources are almost not directly reused/recycled in process sinks without considering time constraints and storage tanks. However, storage tanks are usually expensive and thus a cost-effective water system has to be synthesized. Rescheduling the water network can contribute to reducing the cost of storage tanks by reducing their number and capacity. In the current research work, a goal programming is used to reschedule the water network in batch processes considering the time and storage tanks. A Mixed Integer Non-Linear Program model is introduced using the Lingo optimization program. This model is used to optimize multiple objectives, which are freshwater usage, wastewater discharge, the number and capacity of tanks, the degree of shifting streams, and the total cost of the water network. Three case studies are presented in this study to demonstrate the effectiveness of the proposed procedure, considering both single and multi-contaminants problems. The results of the first case study show a reduction in the network cost and the freshwater flowrate by 26.4% and 42%, respectively. Regarding the rescheduled water network results of the second case study, the cost is reduced by 24.6% and the freshwater flowrate is decreased by 21.8% with no requirement of storage tanks. The third case study highlights the model’s applicability to multi-contaminants problem, revealing a 15.1% cost reduction and a 25.7% decrease in freshwater flow.

Evaluating the impact of coordinated multiple mobile emergency resources on distribution system resilience improvement

Extreme weather events in recent years have resulted in numerous incidents of major power outages and significant economic losses. Therefore, it is crucial to find potential solutions that can improve the resilience of the distribution system (DS). In this regard, this paper proposes a two-stage resilient restoration model for distribution systems utilizing Electric Vehicles (EVs) and Mobile Energy Resources (MERs) to address the issue. The impact of a transportation network on the two-stage model is represented by the consideration of interdependence between vehicle routes and distribution lines. Initially, the charging and repair stations are strategically placed on the transportation network before an extreme event by considering the distribution lines that have a high probability of failure during the event. An integer nonlinear programming model is used to determine the optimal number and staging locations of the charging and repair stations during the development of the first stage. The second stage involves the design of a mixed integer linear programming model to restore loads and recover the DS via optimizing the dispatch of EVs with MERs on the transportation network. The proposed method is tested on modified IEEE 123-Bus system. The utilization of EVs alongwith MERs under post-disaster conditions helps to reduce the ENS by 42.1038 %. The ENS found to be 7.9150 MWh utilising the proposed method is much less compared to the ENS obtained by existing method and hence this demonstrates the effectiveness of the proposed method.