Bi-objective Programming Model Research Articles

Two-way referral cooperative hospital selection with uncertain information: A two-sided matching decision-making approach

To better rationalize the allocation of medical resources and improve the efficiency of medical resource utilization, researchers have focused on the problem of two-way referral cooperation among hospitals. The selection of an appropriate referral hospital constitutes a crucial aspect of a two-way referral system, which affects the quality of patient treatment and the financial outcome of hospital operations. Within this context, this study regards the collaborative referral hospital selection problem as a two-sided matching decision-making process. Given the hesitance and bounded rationality of decision-makers, a novel two-sided matching framework is developed that integrates hesitant fuzzy linguistic term sets and regret theory to more accurately reflect real-world conditions. Specifically, evaluation information is converted to hesitant fuzzy linguistic term sets via context-free grammar, and new utility functions are introduced to calculate the utility value, regret utility, and rejoice utility through the hesitant degree and score function. Furthermore, an optimization model for calculating the criteria weight is established based on the Euclidean distance and maximization deviation method. Ultimately, the matching satisfaction degree is determined, and a biobjective programming model that maximizes the overall matching satisfaction degree is formulated and solved. The results from experiments and analysis indicate that the proposed framework produces optimal and stable matching solutions, thereby providing a useful reference for hospitals seeking satisfactory referral partners. Moreover, this model could be extended to address large-scale two-sided matching problems or to refine the referral hospital selection problem by considering individual patient needs.

The optimisation of the location of front distribution centre: A spatio-temporal joint perspective

Front Distribution Centre (FDC) is a new terminal warehouse which is closer to customers, with its location selection being crucial for e-commerce and customer time satisfaction. We introduce in this paper a joint distribution function of demand based on time and space, which constructs two spatio-time models: spatio-time clustering model and spatio-time optimisation model. A staged clustering algorithm is designed to obtain the candidate FDCs, and an intelligent algorithm based on NSGA-Ⅱ (Non-dominated Sorting Genetic Algorithm II) is applied to determine the final FDCs, in which the location selection problem is formulated as a bi-objective programming model to minimise total costs and maximise customer time satisfaction. Our results indicate that the model considering spatio-temporal joint attribute of demand performs better than the traditional spatial model. Furthermore, when compared with the k-means clustering algorithm, Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and its improved algorithm Multi-Objective Evolutionary Algorithm based on the Adaptive Neighborhood Adjustment strategy (MOEA/D-ANA), Multi-Objective Particle Swarm Optimisation” (MOPSO) and its enhancing algorithm Competitive Multi-Objective Particle Swarm Optimiser (CMOPSO), the solving method based on staged clustering and NSGA-II absolutely performs more stable and can get a greater number of pareto-optimal solutions with higher qualities. Especially when compared with K-means clustering algorithms, it can reduce total costs by up to 38.84% and improve customer time satisfaction by up to 36.22%.

Crude oil transportation route choices: A connectivity reliability-based approach

The crucial nodes of maritime transportation routes, such as the Strait of Malacca and the Suez Canal, remain vulnerable to various risk events including political instability and military conflict, piracy and terrorism, and vessel incidents. Existing shipping route choice studies often consider transportation costs and environmental effects, but ignore the connectivity reliability of these straits and canals. In this paper, we develop a bi-objective programming model to determine maritime transportation routes for crude oil, taking both transportation costs and connectivity reliability into consideration. We propose a method to measure the connectivity reliability of straits and canals, which captures the dependence structure of risk events. We apply our model to evaluate Gwadar Port using data covering 1999 to 2021, which is being built to enhance the reliability of Chinese oil imports. We find that the Gwadar Port can substitute for the Lombok Strait only if its connectivity reliability can be improved by 2.4%. In order to fully exploit the strategic advantages of Gwadar Port in substituting for other key straits, its connectivity reliability must be improved by 12.2%. Given the varying dependence of risk events identified in our model, our findings provide rich managerial and policy implications for connectivity reliability improvement.

Capacitated Preventive Health Infrastructure Planning with Accessibility-Based Service Equity

Hard-to-access health infrastructure is likely to lead to increased morbidity and mortality. The optimal layout of health facilities is significant for disease control and prevention. This study aims to propose a method to provide equitable access to capacitated preventive health facilities, which captures the key features of the effect of congestion in a competitive choice environment. The problem is formulated as a bilevel nonlinear integer programming model. The upper level is a biobjective programming model subject to investment budget (B) constraint, and the lower level is a user equilibrium analogous model resulting from the users’ choice of facility location. An efficient and operable heuristic algorithm was designed according to the bilevel decision structure where a genetic algorithm (GA) with elite strategy is developed to solve the upper-level problem and the method of successive averages (MSA) is adopted to solve the lower-level problem. A case study is employed to validate the performance of the proposed method. The results show that the method is robust and could reach an equal service quality in a reasonable computation time. However, the sensitivity analysis indicated that the marginal benefit of the investment decreased. There is an optimal B beyond which further increments in investment would not offset the benefits. In addition, the proposed method could be beneficial for other congested public service facilities that users are free to choose from.

An integrated interval-valued intuitionistic fuzzy technique for resumption risk assessment amid COVID-19 prevention

Currently, China has achieved a remarkable achievement on the containment of COVID-19, which creates a favorable condition for the gradual resumption of normal life. However, COVID-19 infections continue to rise in many nations and some sporadic cases occur from time to time in China, which still poses some risks to the resumption. Hence, it is imperative to develop some reasonable techniques to assess the resumption risk. This paper aims to investigate an integrated interval-valued intuitionistic fuzzy (IVIF) technique to adroitly assess the resumption risk based on DEMATEL (decision making trial and evaluation laboratory), BWM (best-worst method) and SPA (set pair analysis). This integrated technique is called IVIF-DBWM-SPA, where the IVIF-DBWM (combined by the IVIF-DEMATEL and IVIF-BWM) is used to determine the global criteria weights and the IVIF-SPA is employed to generate the ranking order of the alternatives. The IVIF-DEMATEL and IVIF-BWM are used to determine the weights of dimensions and the weights of criteria under each dimension, respectively. In this IVIF-BWM, two bi-objective programming models are constructed by regarding experts’ pessimistic and optimistic attitudes, respectively. Combined experts’ intrapersonal and interpersonal uncertainties simultaneously, a bi-objective programming model is proposed to derive the dynamic weights of experts. Based on the determined weights of experts and criteria, an IVIF-SPA is developed to assess the risk levels of all alternatives. The validity of the proposed technique is demonstrated with a real case of college resumption risk assessment amid COVID-19. Some sensitivity and comparison analyses are provided to show the merits of the proposed technique.

A bi-objective green vehicle routing problem with a mixed fleet of conventional and electric trucks: Considering charging power and density of stations

This paper considers a Green Vehicle Routing Problem (GVRP), which includes heavy-duty electric and conventional trucks. We develop a new bi-objective programming model defined on a set of vertices, including a depot, a group of customers, and a set of charging stations. The first objective function is the minimization of the total cost of transportation. To meet the growing environmental concerns, we also consider a second objective function which minimizes total Greenhouse Gas (GHG) emissions. To solve the bi-objective problem, we integrate three multi-objective solution methods (i.e., weighted-sum,ε-constraint, and hybrid methods) with the Adaptive Large Neighborhood Search (ALNS). We thereby generate a set of instances based on real-world locations in the Greater Toronto Area (GTA) and some parts of Ontario in Canada. These instances are then solved by applying the proposed solution methods. The obtained numerical results from the designed experiments revealed that by enhancing the charging power from 90 kW to 350 kW, transportation costs could decrease by up to 5 %. In addition, by doubling the number of stations in the same service area, delivery companies could lower their transportation costs by 2 %. Furthermore, a slight increase (less than 3 %) in transportation costs leads to a remarkable reduction (more than 18 %) in GHG emissions.

A hybrid model for robust design of sustainable closed-loop supply chain in lead-acid battery industry.

Considering supply chain efficiency during the network design process significantly affect chain performance improvement. In this paper, the design process of a sustainable lead-acid battery supply chain network was addressed. Because the design of such networks always involves great computational complexity, in the present study, a two-stage model was proposed to overcome this issue. In the first stage, candidate sites of recycling centers were identified using data envelopment analysis (DEA) and based on their efficiency scores. Unlike the previous studies, not only economic criteria but also technical and geographical criteria were employed to select these locations. In the second stage, a bi-objective programming model was developed to simultaneously determine the tactical and strategic decisions of the chain. Since some data was subject to uncertainty, a robust possibilistic approach was presented. The model ensures that the resulting structure for the chain will be robust to noise and disturbance in parameters. A life cycle assessment model based on the ReCiPe 2008 method was developed in SimaPro software. To evaluate the applicability of the presented method, a case study in the automotive industry was used. The results of implementing the DEA method showed that from among 23 available locations, 11 potential places were selected for construct recycling centers. The final results showed that the inappropriate potential locations of recycling centers were eliminated, and the complexity of the mathematical model proposed in the second stage was reduced. The obtained results of environmental protection costs revealed that this criterion changed from 0 to 8,333,874,332. Moreover, the first objective function resulted in a centralized network to minimize costs, and in contrast, the second objective function tended to decentralize the network to minimize environmental impacts.

First-Train Timetable Synchronization in Metro Networks under Origin-Destination Demand Conditions

This paper focuses on how to synchronize network-wide timetables of first trains in an urban metro system, in which the train-connection-based route can be exactly determined for each first-train-attached origin-destination (OD) demand pair. With the help of even headway scheduling on each line, the problem is actually to adjust the departure times of first trains and connecting trains from their origin stations and the departure interval on each line. Subjected to train operation and connection constraints, a biobjective nonlinear integer programming model is formulated to minimize the total travel time of OD-dependent passenger demands and the deviation between the known and expected schedules. Then, the Nondominated Sorted Genetic Algorithm-II (NSGA-II) is adopted to solve the proposed model, and an improved technique is elaborated to reduce the alternative route choices. Finally, numerical experiments are conducted to demonstrate the effectiveness and availability of the proposed model and methods.

Location of primary health care centers for demand coverage of complementary services

We address the problem of locating primary health care centers integrating the outpatient medical service as a capacitated service and a set of uncapacitated complementary services such as nutrition counseling, dental care, mental health, clinical analysis, and imaging service. The objective is to locate new facilities or upgrade existing ones while the demand coverage of the complementary services is maximized and the total travel distance for the outpatient service allocation is constrained. The cost of opening new facilities and upgrading the existing ones is restricted to a budget. The problem is modeled as a variation of the maximal covering location problem with additional side constraints. In addition, two auxiliary bi-objective integer programming models are introduced to help identify the trade-off between the total travel distance and different budgets. A case study based on the public health care system of the northern zone of the State of Mexico, Mexico, is presented, including an assessment of the trade-off between the total travel distance and the allowed budget. Optimal solutions were found using CPLEX for a set of instances composed of 1,086 demand nodes, 294 current facilities, and 117 candidate locations. The auxiliary bi-objective programming models were solved by an augmented ε-constraint method. The empirical work shows the usefulness of the proposed models.

Transportation of Raw Materials, Recondite Question in Manufacturing Enterprise

Based on the optimization theory, this paper studies the mathematical modeling problem related to the ordering and transportation of raw materials. The paper starts with reasonable assumptions, based on which the following factors are used as index: “average supply”, “order completion rate”, “average order value” and “standard deviation of supply” of each supplier, and the weight of each index is determined by using entropy weight method. On the premise of reasonable weight, the distance method of good-bad solutions (TOPSIS) is used to evaluate and rank each supplier, and finally, the most important supplier is selected. Then, a 0-1 programming model is established, in which “minimum order price” and “minimum loss” are taken as the objective functions, and the two-week inventory of the enterprise is combined with factors such as the loss rate of the forwarder, using MATLAB programming TOPSIS algorithm to solve the model to obtain the optimal ordering and transshipment plan. Considering the possibility that the enterprise needs low utilization of raw materials A and C, a bi-objective programming model is established to determine the weekly ordering and transshipment plan within the target weeks. On the other hand, when the number of suppliers is sufficient, the capacity of the forwarders limits the expansion of the capacity of the enterprise. Therefore, combined with the existing data, a linear programming model with the maximum production capacity as the objective function is established to obtain the maximum production capacity and formulate ordering and transshipment schemes. Finally, the solution process and results are summarized and analyzed.

A goal programming model for the optimization of log logistics considering sorting decisions and social objective

Log logistics include sorting, processing, and transporting of logs from their place of harvest to demand locations. These activities account for a significant portion of the total log procurement costs; therefore, attempts were made in previous studies to optimize some aspects of log logistics. However, operational details, such as sorting decisions, truck compatibility requirements, and social objectives, are often disregarded in the optimization literature. Incorporating these details into the model makes the results more realistic and applicable. To address these gaps, a bi-objective mixed-integer programming model is developed in this paper to optimize log logistics. The first objective is to minimize total logistics costs, and the second objective is to provide a balanced workload for trucking contractors. The bi-objective model is solved using the goal programming approach. The model is applied to log logistics of a large Canadian forest company, where trucking contractors use heterogeneous fleet of trucks to carry various log sorts from cutblocks to sort yards for sorting. The planning horizon is 4 weeks with daily decisions. The goal programming model generates balanced workloads for the contractors with less than 0.4% increase in total costs compared to the single objective model where only the total cost is minimized.

Permutation flow shop energy-efficient scheduling with a position-based learning effect

Severe environmental problems have made green scheduling an emerging research hotspot. In this paper, a permutation flow shop energy-efficient scheduling problem that considers multiple criteria is investigated. The aim is to find the optimal job processing sequence and conveyor speed that minimise both the makespan and total energy consumption. In addition to two types of common criteria, namely, machine-based criterion (i.e. sequence-dependent setup time) and energy-based criteria (including both the transportation time control strategy and machine shutdown strategy), a human-based criterion (i.e. a position-based learning effect) is introduced. A bi-objective programming model is developed, and a multi-objective iterated greedy (MOIG) is designed to reach the Pareto front of the model. Considering that there are two types of decisions in the model (i.e. job sequence and conveyor speed), two algorithm alternatives are designed based on the job sequence and conveyor speed, respectively. Meanwhile, an acceptance criterion with advantages in terms of the convergence speed and solution diversity is proposed. Existing algorithms, including NSGA-II and MOEA/D, are introduced to evaluate the performance of the MOIG. The results emphasise the efficiency of the MOIG. Overall, the model and MOIG effectively improve the green efficiency of enterprises and can reasonably control operating costs.

Strategic reliable supply chain network design: determining tradeoffs between cost and risk

The design of a supply chain network (SCN) should address two conflicting objectives, i.e. inexpensive yet reliable operation. This paper presents models to choose supply facilities and determine distribution options while considering the expected risk of not serving customers attributed to supply shortages. The goal is to design a reliable network with a lower cost under traditional cost objectives. We formulate a stochastic mixed-integer biobjective programming model considering the protection of facilities and solve this problem with a progressive hedging algorithm (PHA). We examine the tradeoff curve between the cost and risk through a case study involving Shanghai in China. The results indicate that substantial improvements in reliability can be reached with a limited increase in the total cost.

Optimization of Multimodal Discrete Network Design Problems Based on Super Networks

In this paper, we investigate the multimodal discrete network design problem that simultaneously optimizes the car, bus, and rail transit network, in which inter-modal transfers are achieved by slow traffic modes including walking and bike-sharing. Specifically, a super network topology is presented to signify the modal interactions. Then, the generalized cost formulas of each type of links in the super network are defined. And based on the above formulas a bi-objective programming model is proposed to minimize the network operation cost and construction cost with traffic flow equilibrium constraints, investment constraints and expansion constraints. Moreover, a hybrid heuristic algorithm that combines the minimum cost flow algorithm and simulated annealing algorithm is presented to solve the proposed model. Finally, the effectiveness of the proposed model and algorithm is evaluated through two numerical tests: a simple test network and an actual multimodal transport network.

A combined intelligent and game theoretical methodology for collaborative multicenter pickup and delivery problems with time window assignment

Collaborative multicenter pickup and delivery problems with time window assignment (CMPDPTWA) are introduced in this paper and formulated and solved as a two-stage optimization problem. First, the collaborative mechanism achieves optimal transportation resource configuration in a multicenter logistics network. Second, open-closed mixed pickup and delivery routes satisfying the demands and time windows of customers are proposed to enhance transportation efficiency and reduce the total logistics operating cost. A set of candidate-time windows is assigned to the corresponding customers through time window assignment (TWA) strategy to increase the operational efficiency of logistics network. A bi-objective programming model for CMPDPTWA is formulated to minimize the number of vehicles and total operating cost. An improved k-means clustering algorithm is used to cluster customers according to their proximities to pickup and delivery centers for reducing the computational complexity to solve the abovementioned problem. A self-learning non-dominated sorting genetic algorithm-II (SNSGA-II) is proposed to optimize the open-closed mixed pickup and delivery routes in CMPDPTWA. An update mechanism for the probabilities of crossover and mutation is devised to improve the efficiency of searching the solution space, and thus to accelerate the convergence of SNSGA-II. The performance of the proposed algorithm is compared with that of other algorithms, and the results indicate that it can generate near-optimal solutions for CMPDPTWA. A game theoretical method involving a cost gap allocation model and the strictly monotonic path strategy is proposed to find the best profit allocation scheme and the optimal coalition sequence for stabilizing the collaborative coalition. Finally, the proposed method is applied to a case study using the real-world logistics network in Chongqing City, China. Six scenarios with and without the collaborative mechanism and TWA strategy are simulated and compared with one another to verify the efficacy of the proposed method. The results show that the collaborative mechanism and TWA strategy can improve the utilization of transportation resources and operational efficiency. Thus, they can facilitate an efficient and sustainable urban logistics network.

Bi-Objective Optimization for Vehicle Routing Problems with a Mixed Fleet of Conventional and Electric Vehicles and Soft Time Windows

With the growing interest in environmental protection and congestion, electric vehicles are increasingly becoming the important transportation means. However, electric vehicles currently face several adoption barriers including high purchasing price and limited travelling range, so the fleets where electric vehicles and conventional vehicles coexist are closer to the current fleet management status. Considering the impact of charging facilities and carbon emission, this paper proposes a vehicle routing problem with a mixed fleet of conventional and electric vehicles and soft time windows. A bi-objective programming model is established to minimize total operational cost and time penalty cost. Finally, the nondominated sorting genetic algorithm II (NSGA-II) is employed to deal with this problem. Furthermore, single-objective optimization is carried out for the two objectives, respectively, and the linear weighting method is also used to solve the problem. Through the contrast of these results and the NSGA-II results, the effectiveness of the algorithm in this paper is further verified. The results indicate that two objectives are contradictory to some extent and decision-makers need a trade-off between two objectives.

A bi-objective programming model for loading finished-vehicles in containers with adjustable brackets

ABSTRACT The containerized transportation mode has attracted more attention from many finished-vehicle (FV) logistics companies and ocean carriers which can provide door-to-door service and organize the multi-model transportation. This paper considers the FV loading problem for a carrier who uses containerized transportation mode. To increase the loading factor of containers and guarantee the safety of vehicles from damage, an adjustable bracket is introduced to place two-layer vehicles by tilting the upper pallet. A bi-objective programming problem is proposed in the sense of maximizing the safety margins of vehicles by setting the configuration of an adjustable bracket and the locations of the vehicles on the pallets. For any given combination of two vehicle types, we proved that the Pareto frontier of the bi-objective programming problem is a line and the Pareto optimal slope of the upper pallet can be determined by a maximization problem. With the Pareto frontier, the general FV loading problem with multiple vehicle types can be modeled as an integer programming problem and calculated by traditional programming algorithms. Areal loading task for the COSCO was adopted to depict our model and method.

Conceptualising a supply and demand resilience methodology: A hybrid DEMATEL-TOPSIS-possibilistic multi-objective optimization approach

Due to the growing globalisation and strategic sourcing, supply chains (SCs) are confronted with potential disruptions. Companies need to make further efforts and investments to improve their supply chain resilience (SCR) in becoming more prepared to minimise disruption risks. Sourcing is one of the main, strategic, key factors towards SCR. Also, organisations require resilience in demand fulfilment to handle volatile marketplaces. This paper presents a methodology towards SCR to both supply and demand variations motivated by a real case study of a manufacturing company that works to improve its SCR. To this end, a hybrid integrated multi-attribute decision making-possibilistic bi-objective programming model (MADM-PBOPM) was developed. First, a new framework presenting pillars to assess suppliers’ resilience was developed based on a thorough literature review and decision makers’ input. Then, a DEMATEL-TOPSIS approach was proposed to quantify existing suppliers’ resilience and assess its performance. It also helped in categorising resilience pillars (RPs) as causes and effects. Thereafter, the obtained weights of suppliers and pillars were integrated into the developed PBOPM. The latter helps the purchasing team to (1) order materials from suppliers based on their resilience and performance efficiency; and (2) elevate the company’s resilience to uncertain demands fulfilment. Therefore, the developed methodology can potentially be used by the purchasing teams to build up SCs that are resilient to supply disruption and demand uncertainty. This MADM-PBOPM model was validated as part of the case study investigation. Furthermore, the suppliers’ assessment output was validated by using two sensitivity analysis approaches including criteria weight variation and other multi-attribute decision making (MADM) approaches.

Optimal Tradable Credit Scheme Design with Recommended Credit Price

As an interesting research topic in transportation field, tradable credit scheme (TCS) has been extensively explored in the latest decade. Existing studies implicitly assumed that travelers are clear about the equilibrium credit price and make their trips accordingly. However, this may not be the case in reality, since the credit price is endogenously determined by the credit-trading behavior, especially in the early stages after the implementation of a TCS. Considering travelers’ uncertainty on the equilibrium credit price, this paper aims to investigate the impacts of perception error on credit price and how to accommodate such errors by an appropriate scheme design. Transferring the perception error on credit price to a given and fixed value released by central authority, we first investigate the impacts of recommended credit price under a given TCS. The numerical results imply that it is necessary to simultaneously consider the choice of recommended credit price and charging scheme in TCS design. Regarding this, we combine the goals of social welfare and public acceptance of the scheme and propose a bilevel biobjective programming (BLBOP) model, by which the net economic benefit is maximized while the gap between the recommended and realized credit prices is minimized. Through two numerical examples, it is found that the rise in perception variance could intensify the contradiction effect between the two objectives. Additionally, a nonnegligible price gap must be allowed to occur to maintain the effectiveness of a TCS.

Modeling Heterogeneous Fleet Vehicle Allocation Problem with Emissions Considerations

Aims: This study proposes a bi-objective linear integer programming model for heterogeneous fleet VAP with emissions considerations. Profit maximization and emissions minimization objectives are employed to handle economic and environmental sustainability purposes. Background: Our literature survey shows that there is no model for the heterogeneous fleet VAP with emissions considerations that simultaneously consider vehicle heterogeneity, penalty costs for unmet demands, and emissions from transportation operations. Objective: The model is employed to also make several scenario analyses on sustainable freight logistics management to understand the trade-offs among economic and environmental objectives. In freight transportation problems, decision-makers need to be able to maintain profitability and to reduce emissions. Methods: In this study, a bi-objective linear integer programming model is proposed for a heterogeneous fleet Vehicle Allocation Problem (VAP) with emissions considerations encountered in the field of sustainable freight transportation. Results: In the numerical analyses, various practical assumptions that can be confronted by decision-makers in real life are discussed. In each analysis, total profit and emissions amounts are revealed along with several other KPIs. The results of the analyses provided in this study could also be useful in terms of understanding the relations among pillars of sustainability in VAPs. Conclusion: It is thought that the proposed model has the potential to aid decision-making processes in sustainable logistics management. In the base case analyses, the total profit obtained under profit maximization is about nine times higher than that obtained under emissions minimization. When the aim is to minimize emissions, the total emissions are found to be nearly one-tenth of that of profit maximization. Supported by also additional scenario analyses, it can be concluded that it might not economically viable to be environmentally-friendly for companies. Therefore, companies have to be encouraged or forced to take environmentally and socially responsible actions through legislation. The analyses demonstrated that various legislative policies on emissions may affect the transportation plans differently in such vehicle allocation systems.