Medium-sized Instances Research Articles

Formulations, branch-and-cut and a hybrid heuristic algorithm for an inventory routing problem with perishable products

In this paper, we study an inventory routing problem in which goods are perishable. In this problem, a single supplier is responsible for delivering a perishable product to a set of customers during a given finite planning horizon. The product is assumed to have a fixed shelf-life during which it is usable and after which it must be discarded. We introduce four mathematical formulations for the problem, two with a vehicle index and two without a vehicle index, and propose branch-and-cut algorithms to solve them. In addition, we propose a hybrid heuristic based on the combination of an iterated local search metaheuristic and two mathematical programming components. We present the results of extensive computational experiments using instances from the literature as well as new larger instances. The results show the different advantages of the introduced formulations and show that the hybrid method is able to provide high-quality solutions in relatively short running times for small- and medium-sized instances while good quality solutions are found within reasonable running times for larger instances. We also adapted the proposed hybrid heuristic to solve the basic variant of the inventory routing problem. The results using standard instances show that our heuristic is also able to find good quality solutions for this problem when compared to the state-of-the-art methods from the literature.

Exact and heuristic methods to solve a bi-objective problem of sustainable cultivation

This work proposes a binary nonlinear bi-objective optimization model for the problem of planning the sustainable cultivation of crops. The solution to the problem is a planting schedule for crops to be cultivated in predefined plots, in order to minimize the possibility of pest proliferation and maximize the profit of this process. Biological constraints were also considered. Exact methods, based on the nonlinear model and on a linearization of that model were proposed to generate Pareto optimal solutions for the problem of sustainable cultivation, along with a metaheuristic approach for the problem based on a genetic algorithm and on constructive heuristics. The methods were tested using semi-randomly generated instances to simulate real situations. According to the experimental results, the exact methodologies performed favorably for small and medium size instances. The heuristic method was able to potentially determine Pareto optimal solutions of good quality, in a reduced computational time, even for high dimension instances. Therefore, the mathematical models and the methods proposed may support a powerful methodology for this complex decision-making problem.

The inventory routing problem under uncertainty with perishable products: an application in the agri-food supply chain

In this paper, we propose a dynamic and stochastic approach for an inventory routing problem in which products with a high perishability must be delivered from a supplier to a set of customers. This problem falls within the agri-food supply chain ( $${\mathcal {ASC}}$$ ) management field, which includes all the activities from production to distribution. The need for high-quality products that are subject to perishability is a critical issue to consider in the $${\mathcal {ASC}}$$ optimization. Moreover, the demand uncertainty makes the problem very challenging. In order to effectively manage all these features, a rolling horizon approach based on a multistage stochastic linear program is proposed. Computational experiments over medium-size instances designed on the basis of the real data provided by an agri-food company operating in Southern Italy show the effectiveness of the proposed approach.

An Efficient Decision-Making Approach for the Planning of Diagnostic Services in a Segmented Healthcare System

In this paper, we address a decision-making problem related to the requirement of costly equipment by medical diagnostic services in a segmented public healthcare system comprising several institutions and private providers. The problem is motivated by a real-world case of the Mexican healthcare system. The aim of this study is to determine which hospitals can provide the service, their capacity levels, the allocation of demand in each institution, and the referral of patients to other institutions or private providers while minimizing annual investment costs and operating costs required to satisfy demand. A mixed-integer linear programming model that takes into account different characteristics such as patient acuity levels, types of equipment, and demand variation through time is introduced. The model was empirically assessed to evaluate its impact on the decision-making process. A sensitivity analysis to evaluate solution behavior for variations of critical parameters was performed. The results showed that some values could generate a significant effect on the total costs for the service coverage and in the efficiency of the service, whereas overall results indicated the usefulness of the model. While this model is valuable to aid this decision-making problem, it is limited to medium-size instances of up to 90 facilities. To solve the problems with larger instances, a two-phase heuristic algorithm is proposed. In the first phase, the method uses a greedy construction mechanism, and in the second phase, it attempts to improve the solution. Empirical evidence on large instances shows that good solutions with low computing times are reached in comparison with the exact method.

Machine Learning to Support the Presentation of Complex Pathway Graphs.

Visualization of biological mechanisms by means of pathway graphs is necessary to better understand the often complex underlying system. Manual layout of such pathways or maps of knowledge is a difficult and time consuming process. Node duplication is a technique that makes layouts with improved readability possible by reducing edge crossings and shortening edge lengths in drawn diagrams. In this article, we propose an approach using Machine Learning (ML) to facilitate parts of this task by training a Support Vector Machine (SVM) with actions taken during manual biocuration. Our training input is a series of incremental snapshots of a diagram describing mechanisms of a disease, progressively curated by a human expert employing node duplication in the process. As a test of the trained SVM models, they are applied to a single large instance and 25 medium-sized instances of hand-curated biological pathways. Finally, in a user validation study, we compare the model predictions to the outcome of a node duplication questionnaire answered by users of biological pathways with varying experience. We successfully predicted nodes for duplication and emulated human choices, demonstrating that our approach can effectively learn human-like node duplication preferences to support curation of pathway diagrams in various contexts.

Solving the index tracking problem: a continuous optimization approach

Investing vast amounts of money with the goal of fostering medium to long-term growth in returns is a challenging task in financial optimization. A method might be mirroring the market index as closely as possible by choosing from the stocks that make up the index. This approach is known as index tracking and the objective of this paper is to address this problem in order to solve it by means of mathematical programming techniques. In particular, we are interested in investigating the index tracking problem (ITP) as a mixed integer linear program in presence of some real-world constraints known as cardinality constraints as well as transaction costs. These ITP models are NP-hard, and consequently, difficult to solve by classical exact methods even for medium-sized instances. In order to overcome this issue, we propose a method based on nonconvex programming techniques. More precisely, we reformulate the problem as a difference of convex functions (DC) program and solve it by means of an approach known as DC algorithm. In order to evaluate the performance of the proposed algorithm, we conducted numerical experiments using benchmark instances. The results of the algorithm are compared with those provided by the state-of-the-art MILP solver Gurobi. The numerical results confirm the efficiency of the method in solving the ITP.

Exact and Heuristic Solution of the Consistent Vehicle-Routing Problem

Providing consistent service by satisfying customer demands with the same driver (driver consistency) at approximately the same time (arrival-time consistency) allows companies in last-mile distribution to stand out among competitors. The consistent vehicle-routing problem (ConVRP) is a multiday problem addressing such consistency requirements along with traditional constraints on vehicle capacity and route duration. The literature offers several heuristics but no exact method for this problem. The state-of-the-art exact technique to solve VRPs—column generation (CG) applied to route-based formulations in which columns are generated via dynamic programming—cannot be successfully extended to the ConVRP because the linear relaxation of route-based formulations is weak. We propose the first exact method for the ConVRP, which can solve medium-sized instances with five days and 30 customers. The method solves, via CG, a formulation in which each variable represents the set of routes assigned to a vehicle over the planning horizon. As an upper bounding procedure, we develop a large neighborhood search (LNS) featuring a repair procedure specifically designed to improve the arrival-time consistency of solutions. Used as stand-alone heuristic, the LNS is able to significantly improve the solution quality on benchmark instances from the literature compared with state-of-the-art heuristics.

Scheduling a dual-resource flexible job shop with makespan and due date-related criteria

Current struggles for customer satisfaction in make-to-order companies focus on product customization and on-time delivery. For better management of demand-mix variability, production activities are typically configured as flexible job shops. The advent of information technology and process automatization has given rise to very specific training requirement for workers, which indeed turns production scheduling into a dual-resource constrained problem. This paper states a novel dual-resource constrained flexible job-shop problem (DRCFJSP) whose performance considers simultaneously makespan and due date-oriented criteria, where eligibility and processing time are both dependent on worker expertise. Our research comes from an automobile collision repair shop with re-scheduling needs to react to real-time events like due date changes, delay in arrival, changes in job processing time and rush jobs. We have developed constructive iterated greedy procedures that performs efficiently on the large-scale bi-objective DRCFJSP arisen (good schedules in < 5 s), hence providing planners with the required responsiveness in their scheduling of repairing orders and allocation of workers at the different work centres. In addition, computational experiments were conducted on a test bed of smaller DRCFJSP instances generated for benchmarking purposes. Off-the-shelf resolution for an 80% of the medium-sized instances is not fruitful after 9000 s.

Scheduling preemptable position-dependent jobs on two parallel identical machines

A problem of preemptive scheduling of jobs with position-dependent processing times on two parallel identical machines and the schedule length criterion is addressed. Jobs may be preempted but only restricted preemption of a single job is allowed. Several properties of this problem and two exact algorithms for its solution are presented. Computational experiments show that the exact algorithms find optimal schedules for medium size instances in a relatively short time, and that the largest average percentage of nodes discarded by the proposed branch-and-bound algorithm is close to 65%.

A Hierarchical Approach for Solving Simultaneous Lot Sizing and Scheduling Problem with Secondary Resources

This study represents a decomposition heuristic approach for simultaneous lot sizing and scheduling problem for multiple product, multiple parallel machines with secondary resources. The motivation of the study comes from the real-world instance of a plastic injection plant at Vestel Electronics. The plastic injection plant requires plastic injection molds at the planner’s disposal, in order to produce variations of products, by the compatible plastic injection machines. The variations on the molds and the mold changes on the machines bring out sequence dependent major and minor setups. Since each machine requires an operator, we have extended the formulation with workforce and shift planning. Results show that proposed heuristic yields comparable solutions to that of exact model for small and medium size instances; and provides schedules for the large size instances, for which exact model cannot find a feasible solution in the allotted time.

Efficient algorithms under dynamic graphs to solve the Capacitated Arc Routing Problem with feasible sparse graph

In this paper we develop several approaches to approximately solve the capacitated arc routing problem (CARP) on sparse graphs namely sparse CARP. First, we give a mathematical model for the sparse CARP and we present a brief survey about a transformation technique to transform the sparse CARP into a sparse capacitated vehicle routing problem namely sparse CVRP. Later, we propose several approaches to solve the sparse CARP by solving its equivalent obtained sparse CVRP. The first approach is a constructive heuristic (CH) used to construct an initial feasible solution. The second approach is an improving randomized procedure (IRP) used to improve the quality of the initial solution. Finally, we introduce the main adapted tabu search approach (TS) under a sparse dynamic graph. The algorithm starts by applying the first two procedures CH and IRP and attempts to compute a better solution for the sparse CARP. Extensive computational tests on randomly generated problem instances show the effectiveness of the proposed approach. The TS algorithm yields satisfactory results within reasonable computational time. The approach outperformed also the commercial solver Cplex v12.71 which was able to solve only small instances with relatively a big CPU time for medium size instances.

Mathematical model for supply chain design with time postponement

Projetar cadeia de suprimentos é uma importante decisão estratégica e seu impacto influencia diretamente na eficiência e no nível de serviço. O projeto se torna mais complexo quando o objetivo é minimizar o custo de distribuição e utilizar a postergação de tempo na cadeia de suprimentos. Os modelos matemáticos atualmente estudados na literatura de cadeia de suprimentos consideram vários atores. Entretanto, em problemas reais existem diferentes combinações desses atores, criando fluxos próprios de transportes e aumentando a complexidade da cadeia de suprimentos. Este artigo propõe um modelo matemático para projetar a cadeia de suprimentos com postergação de tempo a partir da programação não linear inteira mista para minimizar o custo total, considerando os custos de transportes, abertura de instalações e operacionais. O modelo permite a possibilidade de uma instalação híbrida, ou seja, dois tipos de instalações abertas no mesmo local, sendo uma importante oportunidade de redução de custos. Diferentes conjuntos de instâncias foram simulados para buscar a solução ótima e analisar o comportamento da cadeia de suprimentos em diferentes tamanhos de cenários, os quais foram resolvidos usando um solver comercial e suas performances foram estudadas. O modelo proposto apresenta viabilidade em seu uso para instâncias pequenas e médias com tempo computacional suficiente para auxílio no processo de tomada de decisão.

A Bi-Objective Vehicle-Routing Problem with Soft Time Windows and Multiple Depots to Minimize the Total Energy Consumption and Customer Dissatisfaction

In recent years, the impact of the energy crisis and environment pollution on quality of life has forced industry to actively participate in the development of a sustainable society. Simultaneously, customer satisfaction improvement has always been a goal of businesses. It is recognized that efficient technologies and advanced methods can help transportation companies find a better balance between progress in energy saving and customer satisfaction. This paper investigates a bi-objective vehicle-routing problem with soft time windows and multiple depots, which aims to simultaneously minimize total energy consumption and customer dissatisfaction. To address the problem, we first develop mixed-integer programming. Then, an augmented ϵ -constraint method is adopted to obtain the optimal Pareto front for small problems. It is very time consuming for the augmented ϵ -constraint method to precisely solve even medium-sized problems. For medium- and large-sized problems, two Non-dominated Sorting Genetic Algorithm-II (NSGA-II)-based heuristics with different rules for generating initial solutions and offspring are designed. The performance of the proposed methods is evaluated by 100 randomly generated instances. Computational results show that the second NSGA-II-based heuristic is highly effective in finding approximate non-dominated solutions for small-size and medium-size instances, and the first one is performs better for the large-size instances.

Job shop scheduling with consideration of floating breaking times under uncertainty

There are several practical cases in where the attendance of operators during performance of operations is mandatory. In such cases, during the resting times, the operators cannot leave the jobs until the relevant operations are finished. On the other hand, usually, some fixed time-frames are assigned to resting purposes during a working day, and therefore the operations must be scheduled in such a manner that the operators could have enough time to rest in the arranged time-frames. Moreover, the processing times are under uncertainty, in real conditions. The present paper intends to deal with a new variant job shop scheduling problem. For this reason a mathematical model is presented, and the robust modifications are discussed. Next a branch and bound algorithm, and two heuristic algorithms based on the Beam Search (BS), and Particle Swarm Optimization (PSO) which are well adjusted to scheduling problems are employed to solve the practical cases. The effectiveness of the proposed algorithms are then validated by comparing with optimum solution using small, and medium-size instances and simulated annealing algorithm as the most common one for scheduling problems, and a strong lower bound, using medium and large-size instances.

Upper and lower bounds for the vehicle-routing problem with private fleet and common carrier

The vehicle-routing problem with private fleet and common carrier (VRPPC) extends the capacitated VRP by considering the option of outsourcing customers to subcontractors at a customer-dependent cost instead of serving them with the private fleet. The VRPPC has important applications in small package shipping and manufacturing, but despite its relevance, no exact solution approach has been introduced so far. We propose a branch-price-and-cut algorithm that is able to solve small to medium-sized instances and provides tight lower bounds for larger instances from the literature. In addition, we develop a large neighborhood search that shows a decent solution quality and competitive run-times compared to the state-of-the-art on instances with homogeneous as well as heterogeneous vehicle fleet. In addition, several new best known solutions are found.

A Joint Vehicle Routing and Speed Optimization Problem

Classic vehicle routing models usually treat fuel cost as input data, but fuel consumption heavily depends on the travel speed, which leads to the study of optimizing speeds over a route to improve fuel efficiency. In this paper, we propose a joint vehicle routing and speed optimization problem to minimize the total operating cost including fuel cost. The only assumption made on the dependence between fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set-partitioning formulation and a branch-cut-and-price algorithm to solve this problem. We introduce new dominance rules for the labeling algorithm so that the pricing problem can be solved efficiently. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0810 .

Optimising online review inspired product attribute classification using the self-learning particle swarm-based Bayesian learning approach

Bowing to the burgeoning needs of online consumers, exploitation of social media content for extrapolating buyer-centric information is gaining increasing attention of researchers and practitioners from service science, data analytics, machine learning and associated domains. The current paper aims to identify the structural relationship between product attributes and subsequently prioritise customer preferences with respect to these attributes while exploiting textual social media data derived from fashion blogs in Germany. A Bayesian Network Structure Learning model with the K2score maximisation objective is formulated and solved. A self-tailored metaheuristic approach that combines self-learning particle swarm optimisation (SLPSO) with the K2 algorithm (SLPSOK2) is employed to decipher the highest scored structures. The proposed approach is implemented on small, medium and large size instances consisting of 9 fashion attributes and 18 problem sets. The results obtained by SLPSOK2 are compared with the particle swarm optimisation/K2score, Genetic Algorithm/K2 score and ant colony optimisation/K2 score. Results verify that SLPSOK2 outperforms its hybrid counterparts for the tested cases in terms of computational time and solution quality. Furthermore, the study reveals that psychological satisfaction, historical revival, seasonal information and facts and figure-based reviews are major components of information in fashion blogs that influence the customers.

A new box selection criterion in interval Bernstein global optimization algorithm for MINLPs

Mixed-integer nonlinear programming (MINLP) problems are known to be challenging due to the involvement of nonlinear mathematical relations and combinatorial complexities. In this paper, an interval form-based Bernstein global optimization algorithm is presented to solve polynomial MINLP problems. The major contribution of this paper is a new box selection criterion for this interval form-based Bernstein global optimization algorithm. This new box selection criterion promotes fast convergence of the Bernstein algorithm. Moreover, the new box selection criterion allows the construction of a hybrid branch-and-bound framework for the Bernstein algorithm, wherein a local search method is used to obtain a good upper bound on the global minimum, and the Bernstein form is employed to obtain a valid lower bound on the global minimum. We show with numerical results that it is possible to obtain a significant reduction in the number of subdivisions required with this new box selection criterion. Furthermore, the Bernstein algorithm with this new box selection criterion is evaluated numerically on a variety of small- to medium-size MINLP problem instances and its performance is compared with the previously reported Bernstein global optimization algorithm as well as with a few state-of-the-art MINLP solvers. The results of the numerical studies demonstrate satisfactory performance in terms of the chosen performance metrics. Finally, the trim-loss minimization problem from the paper industry is solved to demonstrate the practical applicability of the Bernstein algorithm.

Branch-and-Price for the Pickup and Delivery Problem with Time Windows and Scheduled Lines

The Pickup and Delivery Problem with Time Windows and Scheduled Lines (PDPTW-SL) consists of routing and scheduling a set of vehicles, by integrating them with scheduled public transportation lines, to serve a set of freight requests within their time windows. This paper presents an exact solution approach based on a branch-and-price algorithm. A path-based set partitioning formulation is used as the master problem, and a variant of the elementary shortest path problem with resource constraints is solved as the pricing problem. In addition, the proposed algorithm can also be used to solve the PDPTW with transfers (PDPTW-T) as a special case. Results of extensive computational experiments confirm the efficiency of the algorithm: it is able to solve small- and medium-size instances to optimality within reasonable execution time. More specifically, our algorithm solves the PDPTW-SL with up to 50 requests and the PDPTW-T with up to 40 requests on the considered instances. The online appendix is available at https://doi.org/10.1287/trsc.2017.0798 .

The gateway hub location problem

We introduce the Gateway Hub Location Problem (GHLP) to design global air transportation systems. Relying on a three-level hub network structure and on having nodes located in different geographic regions, the GHLP consists of locating international gateways and domestic hubs, activating arcs to induce a connected gateway and hub network, and routing flows within the network at minimum cost. Most previous studies focus on a typical hub-and-spoke network, in which local and global flows are not differentiated. Here to better represent a world wide air transportation system, global flows can only leave or enter a given geographic region by means of a gateway, while local flows can only use hubs within their respective region. As routing local or global flows involved different agents, this study presents a mixed integer programming formulation that exploits these differences to model both the local and global flows. Due to the formulation's characteristics, two algorithm variants based on Benders decomposition method are devised to solve the problem. A new repair procedure produces optimality Benders cuts whenever feasibility Benders cuts would rather be expected. While the monolithic version failed to solve medium size instances, our algorithms solved lager ones in reasonable time.