Food supply chain (FSC) management has attracted increasing attention from academics and practitioners in recent years. Although the closed-loop FSC (CLFSC) with returnable transport items (RTIs) has many realistic applications, it is rarely studied. This paper studies a new production-transportation planning problem for a closed-loop perishable FSC with shared RTIs, in which the RTIs can be used by different manufacturers belonging to the same company. The problem consists of determining production, transportation, and inventory quantities for each period of a considered planning horizon to maximize the total profit of the whole supply chain. For the problem, we first formulate it as a mixed-integer linear program (MILP). To efficiently solve the NP-hard problem, we then develop a two-phase heuristic algorithm (TPHA). Experimental results of randomly generated instances show that the performance of the TPHA outperforms the direct use of a commercial solver CPLEX, the differential evolution algorithm, and column generation. Finally, the benefits of the shared RTI strategy and differential price strategy in a CLFSC are verified.

Limited resources are a prevalent and challenging problem in the field of emergency management. Emergency scheduling is an effective way to make full use of resources. However, designing an effective emergency plan to minimize rescue time is a major challenge. This study focuses on large-scale emergency scheduling for fighting forest fires with multiple rescue centers (depots) and limited fire-fighting resources, which aims to determine the optimal rescue route of fire-fighting teams at multiple rescue centers to minimize the total completion time of all fire-fighting tasks. For this problem, we first assign rescue priorities to different fire points according to the speed of the fire spread. Then, we formulate it into a mixed-integer linear programming (MILP) model and analyze its NP-hard complexity. To deal with large-scale problems, a new fast and effective artificial bee colony algorithm and variable neighborhood search combined algorithm is proposed. Extensive experimental results for large-scale randomly generated instances confirm the favorable performance of the proposed algorithm by comparing it with MILP solver CPLEX, genetic algorithms, and particle swarm optimization algorithms. We also derive some management insights to support emergency management decision-making.

Lane reservation optimization is important in intelligent transportation systems. Most existing studies are carried out under deterministic road conditions by assuming constant road travel time. However, road conditions vary due to various factors, resulting in uncertain road travel time. This work addresses a new reliability-based lane reservation and route design problem by considering uncertain road travel time with its known mean and covariance matrix. It aims to decide which road segments in a network should implement reserved lanes and to design routes for special time-crucial transportation tasks. The objective is to maximize transportation service reliability (i.e., the probability of completing the special tasks on time). For this problem, a novel distributionally robust optimization model is first established. To solve it, this work proposes i) an adapted sample average approximation-based approach and ii) a two-stage hierarchical heuristic algorithm based on second-order cone programming. Experimental results on an illustrative example and a real-world case demonstrate that the latter is more effective and efficient than the former. In addition, we conduct a series of parameter sensitivity analysis experiments to reveal the factors affecting lane reservation and provide optimal solutions given different parameter settings.

This study investigates a biobjective integrated parallel machine scheduling and location problem. It aims to place machines on a set of candidate locations, assign jobs dispersed in different locations to the placed machines, and sequence them while minimizing the maximum completion time, i.e., makespan, and the location cost. For the challenging NP-hard problem, we first develop an improved mixed-integer linear program. Then, several inequalities are proposed to further strengthen it. To more effectively and efficiently solve practical-size instances, a new iterative two-stage heuristic algorithm based on$\varepsilon $-constraint is proposed. Extensive experimental results demonstrate that 1) the improved model with valid inequalities can solve 78.4% of 500 benchmark instances, more than 29.8% for the state-of-the-art one and the Pareto solutions obtained by the former are much superior to that of the latter and 2) the proposed iterative two-stage heuristic algorithm can solve all benchmark instances and its performance is significantly superior to the widely adapted nondominated sorting genetic algorithm II in obtaining high-quality Pareto solutions.

We investigate the discrete parallel machine scheduling and location problem, which consists of locating multiple machines to a set of candidate locations, assigning jobs from different locations to the located machines, and sequencing the assigned jobs. The objective is to minimize the maximum completion time of all jobs, that is, the makespan. Though the problem is of theoretical significance with a wide range of practical applications, it has not been well studied as reported in the literature. For this problem, we first propose three new mixed-integer linear programs that outperform state-of-the-art formulations. Then, we develop a new logic-based Benders decomposition algorithm for practical-sized instances, which splits the problem into a master problem that determines machine locations and job assignments to machines and a subproblem that sequences jobs on each machine. The master problem is solved by a branch-and-cut procedure that operates on a single search tree. Once an incumbent solution to the master problem is found, the subproblem is solved to generate cuts that are dynamically added to the master problem. A generic no-good cut is first proposed, which is later improved by some strengthening techniques. Two optimality cuts are also developed based on optimality conditions of the subproblem and improved by strengthening techniques. Numerical results on small-sized instances show that the proposed formulations outperform state-of-the-art ones. Computational results on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations demonstrate the effectiveness and efficiency of the algorithm compared with current approaches. Summary of Contribution: This paper employs operations research methods and computing techniques to address an NP-hard combinatorial optimization problem: the parallel discrete machine scheduling and location problem. The problem is of practical significance but has not been well studied in the literature. For the problem, we formulate three novel mixed-integer linear programs that outperform state-of-the-art formulations and develop a new logic-based Benders decomposition algorithm. Extensive computational experiments on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations are conducted to evaluate the performance of the proposed models and algorithms.

This paper investigates a new multi-objective order assignment and scheduling problem for personal protective equipment (PPE) production and distribution during the outbreak of epidemics like COVID-19. The objective is to simultaneously minimize the total cost and maximize the PPE supply timeliness. For the problem, we first develop a bi-objective mixed-integer linear program (MILP). Then an$\epsilon $-constraint combined with logic-based Benders decomposition method is proposed based on some explored properties. We then extend the proposed model to handle dynamics and randomness. In particular, we design a predictive reactive rescheduling approach to address random order arrivals and manufacturer disruptions. Computational experiments on a real case from China and 100 randomly generated instances are conducted. Results show that the proposed algorithm significantly outperforms an adapted$\epsilon $-constraint method combined with the proposed MILP and the widely used non-dominated sorting geneticalgorithm II(NSGA-II) in obtaining high-quality Pareto solutions.Note to Practitioners—The unprecedented outbreak of COVID-19 and its rapid spread caught numerous national and local governments unprepared. Healthcare systems faced a vital scarcity of PPEs. The urgency of producing and delivering PPEs increases as the number of infected cases rapidly increases. A key challenge in response to the epidemic is effectively and efficiently matching the demands and needs. Performing practical and efficient order assignment and scheduling for PPE production during the COVID-19 outbreak is critical to curbing the COVID-19 pandemic. This work first proposes a bi-objective mixed-integer linear program for optimal order assignment and scheduling for PPE production. The aim is to achieve an economical and timely PPE production and supply. A novel method that combines the$\epsilon $-constraint framework and the logic-based Benders decomposition is proposed to yield high-quality Pareto solutions for practical-sized problems. Computational results indicate that the proposed approaches are practical and feasible, which can help decision-makers to perform acceptable order assignment and scheduling decisions.

This article proposes a risk assessment method based on interval intuitionistic integrated cloud Petri net (IIICPN). The cloud model is widely used in data mining and knowledge discovery, especially in risk assessment problems with linguistic variables. However, the cloud models proposed in the literature do not express interval-valued intuitionistic linguistic satisfactorily, and the reasoning methods based on the cloud models cannot perform risk assessment well. The work in this article includes the definition of IIIC and IIICPN, the method of converting the interval-valued intuitionistic uncertain linguistic numbers into IIIC, and the reasoning method of IIICPN. As proofs, a subway fire accident model is adopted to confirm the feasibility of the proposed method, and comparison experiments between the IIICPN with general fuzzy Petri net and the trapezium cloud model are conducted to verify the superiority of the proposed model.Note to Practitioners—This work deals with the subway fire risk assessment problem. It proposes a cloud model based on interval-valued intuitionistic uncertain linguistic and builds a cloud-based Petri net model. The methods of fire risk assessment use the existing fault trees or aggregation operators to combine all the factors into consideration, but they do not take the interaction of factors. The goal of this work is to assess the risk of subway fire accident of subway, using fuzzy linguistic decision variables. The simulation results indicate that the proposed method is highly effective. The obtained results can help assessors better determine which factors may cause the disaster.

We study a new competitive multi-facility location and quality design problem in a continuous space. The facility location and quality design are considered together because of their interdependence. Especially, new entrant facilities compete for customer demands with existing ones and the latter’s reactions are taken into account. The goal is to maximize the profit of all new entrant facilities by optimally determining their locations and qualities. For this problem, a probabilistic Huff-like gravity model is adopted to analyze the market share to be captured by new and existing facilities, and then a mathematical programming model is provided based on the market share analysis. Since it is shown to be strongly NP-hard, a new iterative solution framework is first proposed to solve it, where at each iteration, new configurations of facility locations are firstly generated, and then the quality decisions of all facilities are modelled as a competitive decision process by a non-cooperative game. The best qualities for new and existing facilities are determined by their Nash equilibrium. Finally, optimal or near-optimal solutions are calculated. Then based on the proposed solution framework, a particle swarm optimization-based approach is developed. Computational results for randomly generated instances indicate that the devised algorithm is able to find suitable locations and qualities of newly entering facilities in a competitive environment and outperforms favorably a genetic algorithm-based approach.

This paper investigates a new lane reservation problem with task merging that consists of optimally determining which lanes in a transportation network have to be reserved and designing reserved lane-based routes in the network for time-crucial transport tasks. Part of the tasks whose destinations are geographically close is merged to reduce the number of vehicles and transport costs. Reserved lanes can reduce the travel time of task vehicles passing through them, while they will generate negative impact on normal traffic, such as traffic delay to the vehicles on adjacent non-reserved lanes. The objective is to minimize the total negative impact of all reserved lanes. For this problem, two new integer linear programming (ILP) models are first developed. The complexity of the problem is proved to be NP-hard. Since commercial solver (like CPLEX) is time-consuming for solving it when the problem size increases, a fast and effective improved differential evolution algorithm (IDEA) is developed based on explored problem properties. Extensive experimental results for a real-life case and benchmark instances of up to 500 nodes in the network and 30 transport tasks show the favorable performance of the IDEA, as compared to CPLEX, differential evolution algorithm and genetic algorithm. Management insights are also drawn to support practical decision-making.

This work investigates the problem of optimally locating an automotive service firm (ASF) subject to stochastic customer demands, varying setup cost and regional constraints. The goal is to minimize the transportation cost while maintaining the specified profit of the ASF. This work studies two variants of the problem: ASF location with known demand probability distributions and with partial demand information, i.e., only the support and mean of the customer demands are known. For the former, a chance-constrained program is formulated that improves an existing model, and then an equivalent deterministic nonlinear program is constructed based on our property analysis results. For the latter, a novel distribution-free model is developed. The proposed models are solved by solver LINGO. Computational results on the benchmark examples show that: i) for the first variant, the proposed approach outperforms the existing one; ii) for the second one, the proposed distribution-free model can effectively handle stochastic customer demands without complete probability distributions; and iii) the results of the distribution-free model are slightly worse than those of the deterministic nonlinear one, but the former is more cost-efficient for the practical ASF location as it is less expensive in obtaining demand information. Moreover, the proposed models and approaches are extended to address a multi-ASF location allocation under demand uncertainty.

Scheduling-location (ScheLoc) problem is a novel problem raised in the manufacturing industry in recent years. It contains two important decision-making issues: location and scheduling. The problem lies in how to determine locations of a group of machines, assign the jobs to be processed to the located machines and sequence the assigned jobs. This paper studies a new bi-objective parallel machine ScheLoc problem to minimize the completion time of the last processed job (i.e., makespan) and the machine location cost, simultaneously. To effectively solve this problem, we first present a bi-objective mixed-integer linear programming model. Then, the ε-constraint method is adopted to obtain its Pareto front. Finally, we use a fuzzy-logic technique to recommend an optimal solution for decision-makers. A case study is conducted to illustrate the trade-off between the makespan and the machine location cost, and some management insights are drawn. Computational results of benchmark instances verify the performance of the proposed method.

With the increase of transport demands, more pressure and challenges are being imparted into efficient transportation. As a conventional and direct congestion alleviation strategy, constructing new roads and lanes are increasingly restricted by limited land resources and high costs. Thus, making full use of existing transport network via appropriate management is critical to realize the sustainable development of transportation systems. As a flexible management strategy, lane reservation strategy has been widely adopted in real life. The reserved lanes can improve the efficiency of special transports, while they bring negative impact such as travel delay for general-purpose transports. In addition, the setting and operating of reserved lanes require a certain amount of cost. This paper proposes a new dual-objective integer linear programming model for optimally determining reserved lanes on a network for time-guaranteed special transports in order to simultaneously maximize the benefits and minimize the negative impact brought by reserved lanes, which incorporates road residual capacity and limited budget to the actual decision. Moreover, an iterative weighted sum-based method is proposed to solve it, in which a new relax-and-optimize algorithm is developed to exactly solve the single-objective optimization problems. Results of extensive numerical experiments show the effectiveness and efficiency of the proposed model and approach.

It is challenging to perform emergency scheduling for fighting forest fires subject to limited rescue resources (i.e., vehicles with fire engines), since extinguishing each fire point should take into account multiple factors, such as the actual fire spreading speed, distance from fire engine depot to fire points, fire-fighting speed of fire engines, and the number of dispatched vehicles. This paper investigates a bi-objective rescue vehicle scheduling problem for multi-point forest fires, which aims to optimally dispatch a limited number of fire engines to extinguish fires. The objectives are to minimize the total fire-extinguishing time and the number of dispatched fire engines. For this problem, we first develop an integer program that is an improved and simplified version of an existing one. After exploring some properties of the problem, we develop an exact dynamic programming algorithm and a fast greedy heuristic method. Computational results for a real-life instance, and benchmark and large-size randomly generated instances confirm the effectiveness and efficiency of the proposed model and algorithms. Besides, a bi-objective integer program is developed to address the multi-depot fire engine scheduling issue.

This paper addresses a new lane reservation problem called bus lane reservation problem (BLRP). The focus of the problem is on optimally selecting lanes to be reserved from an existing transport network and designing reserved lane-based bus paths, such that the rapid and station arrival-time guaranteed bus transit can be ensured, thereby achieving rapid and reliable bus transportation. However, once lanes are reserved, negative impact, such as an increase in travel time on adjacent non-reserved lanes may be caused. For this problem, an improved integer linear program is first formulated to minimize such negative impact. As the existing commercial solvers, e.g., CPLEX, can only solve small-size problems, we develop an exact enhanced cut-and-solve algorithm and an improved kernel search heuristic for solving medium- and large-size problems. Results of extensive numerical experiments confirm the effectiveness and efficiency of the proposed algorithms. In addition, a bi-objective robust BRLP is investigated to study the tradeoff between the negative impact of reserved lanes and the robustness of solution against the uncertainties in the link travel time and the bus dwell time.

This study investigates a new biobjective lanereservation problem, which is to exclusively reserve lanes from an existing transportation network for special transport tasks with given deadlines. The objectives are to minimize the total negative impact on normal traffic due to the reduction of available lanes for general-purpose vehicles and to maximize the robustness of the lane-reservation solution against the uncertainty in link travel times. We first define the robustness for the lanereservation problem and formulate a biobjective mixed-integer linear program. Then, we develop an improved exact ε-constraint and a cut-and-solve combined method to generate its Pareto front. Computational results for an instance based on a real network topology and 220 randomly generated instances with up to 150 nodes, 600 arcs, and 50 tasks demonstrate that the proposed method is able to find the Pareto front and that the proposed cut-and-solve method is more efficient than the direct use of optimization software CPLEX.

This paper studies a lane reservation problem for large sport events in big cities. Such events require organizers to deliver certain people and materials from athlete villages to geographically dispersed venues within a given travel duration. A lane reservation strategy is usually adopted in this circumstance to ensure that time-critical transportation tasks can be completed despite heavy urban traffic congestion. However, it causes negative impact on normal traffic. The problem aims to optimally select and reserve some lanes in a transportation network for the exclusive use of the tasks such that the total traffic impact is minimized. To solve the problem, we first develop an improved integer linear program. Then, its properties are analyzed and used to reduce the search space for its optimal solutions. Finally, we develop a fast and effective quantum-inspired evolutionary algorithm for large-size problems. Computational results on instances with up to 500 nodes in the network and 50 tasks show that the proposed algorithm is efficient in yielding high-quality solutions within a relatively short time.