Real-size Instances Research Articles

The Dial-a-Tour Problem

This article delves into the Dial-a-Tour Problem (DATP) frequently encountered in local travel agencies, known for their personalized and hands-on customer service. In the DATP, multiple tourist groups are efficiently matched with different vehicles using vanpooling, maximizing vehicle occupancy while ensuring seamless transfers to the local attractions included in their booked tours. Each tourist group is picked up from and returned to their respective hotels after their journey. The predetermined locations and the sequence of visits for each tour are known in advance. Therefore, the primary objective is to minimize the number of vehicles required to fulfill all requests and maintain the desired level of service.To tackle this challenge, the article presents a comprehensive approach. It introduces a mixed-integer linear model, two constraint programming formulations, and a novel operator called the k-buffer insertion operator. This operator serves as the centerpiece of a descent heuristic proposed in the study.Extensive evaluation across a diverse range of randomly generated instances underscores the superiority of the proposed constraint programming formulations over the mixed integer linear programming model. However, it is noteworthy that the proposed heuristic surpasses even the most effective constraint programming formulation. This highlights its remarkable efficiency in solving real-size instances within notably brief computation times. Such prowess underscores the practical utility of this heuristic in effectively tackling the complexities inherent in the Dial-a-Tour Problem.

Reinforcement learning approaches for the stochastic discrete lot-sizing problem on parallel machines

This paper addresses the stochastic discrete lot-sizing problem on parallel machines, which is a computationally challenging problem also for relatively small instances. We propose two heuristics to deal with it by leveraging reinforcement learning. In particular, we propose a technique based on approximate value iteration around post-decision state variables and one based on multi-agent reinforcement learning. We compare these two approaches with other reinforcement learning methods and more classical solution techniques, showing their effectiveness in addressing realistic size instances.

Exploring fairness in food delivery routing and scheduling problems

Demand for delivery of take-away meals to customers has been growing worldwide, with deliveries often performed by non-specialised gig economy couriers working for online platform operators such as Deliveroo or Just Eat. This has led to the introduction of the ‘meal delivery problem’, characterised by a series of individual pickup and delivery tasks to be assigned to available couriers. While there is a vast set of algorithms proposed in the literature that aim to minimise total workload, very little attention has been given to equitably distributing work between couriers. We propose a new multi-objective problem that is aiming at distributing orders equitably between couriers as well as minimising total workload, where all information is known upfront. We propose an integer linear programming (ILP) model with a weighted objective function that is used to derive the Pareto front in small-scale problems by exploiting the ϵ−constraint approach. This formulation has been proven to solve in a reasonable time for problems with up to 60 orders, however, the optimal Pareto front can only be computed within a reasonable time for problems up to 30 orders. For problems with more orders, we propose a Variable Neighbourhood Search (VNS) algorithm, for which the fitness evaluation evolves in order to explore a wider set of the solution space. The VNS is compared against the ILP and also tested on more realistic size instances with up to 3123 orders, improving the performance over the business as usual and shows that equitable distribution of work can be achieved alongside reducing the total travelled distance.

Drop-and-pull container drayage with flexible assignment of work break for vehicle drivers

Consideration of driver-related constraints, such as mandatory work break, in vehicle scheduling and routing is of extraordinary importance for safety driving and guaranteeing the interests of vehicle drivers. Drop-and-pull transportation is an efficient mode in container drayage services and creates interdependencies between the routes of vehicle drivers. The situation becomes even more complicated when the drivers must comply with requirements of the mandatory work break. This paper addresses a drop-and-pull container drayage problem with flexible assignment of work break. The time and location of work break for drivers can be flexibly chosen based on scheduling, routing and optimization requirements. The transportation vehicle is comprised of two parts as a tractor and a trailer. The tractor can drag at most one trailer at a time, and is separable from the trailer when executing drayage activities. The problem is formulated as a mixed-integer programming model, which is then strengthened by proposing several families of valid inequalities. To efficiently solve realistic-sized instances, a backtracking adaptive threshold accepting algorithm with a mixed-integer programming model specially coping with the assignment of work break is proposed. Mechanisms of tabu search are incorporated to enhance the searching ability of the algorithm. Experiments indicate that the proposed algorithm can efficiently handle the vehicle scheduling and routing as well as the work break assignment and outperforms the mathematical programming approach. Sensitivity analyses about different policies and varied length of the work break are also conducted with some managerial insights presented.

Appointment scheduling in surgery pre-admission testing clinics

Pre-admission testing clinics are care units serving outpatients prior to surgical operation and performing procedure-specific tests to prepare them. Patients may need multiple tests, each performed by a specialized operator and delivered in any order. Exam rooms act as renewable resources: rooms are limited, tests are administered to patients inside the rooms, individually, and patients occupy the room until all the required tests are completed.Careful scheduling of patient appointments is essential in clinic management for both the patient and the provider: on the one hand, minimizing patient waiting time improves service quality, on the other hand, minimizing completion time (makespan) improves system efficiency.In this paper, we propose offline policies for the daily scheduling of pre-admission test appointments. As a benchmark, we consider two online scheduling policies widely used in common practice. Each of these offers a different compromise between complexity and resource exploitation.The proposed optimization-based offline booking policy is identified as a new problem in the machine scheduling literature, for which we propose a network-flow model representation. A family of matheuristics based on different variable fixing criteria is provided to circumvent the high computational effort required to solve the mathematical model to optimality on real-size instances. The performance, advantages and disadvantages of each of the online and offline policies are compared in a variety of scenarios based on realistic data.Through this work, decision-makers have a new set of tools they can choose from according to their priorities.

Electric Vehicle Charge Scheduling with Flexible Service Operations

Operators who deploy large fleets of electric vehicles often face a challenging charge scheduling problem. Specifically, time-ineffective recharging operations limit the profitability of charging during service operations such that operators recharge vehicles off duty at a central depot. Here, high investment cost and grid capacity limit available charging infrastructure such that operators need to schedule charging operations to keep the fleet operational. In this context, flexible service operations, that is, allowing delayed or expedited vehicle departures, can potentially increase charger utilization. Beyond this, jointly scheduling charging and service operations promises operational cost savings through better utilization of time-of-use energy tariffs and carefully crafted charging schedules designed to minimize battery wear. Against this background, we study the resulting joint charging and service operations scheduling problem accounting for battery degradation, nonlinear charging, and time-of-use energy tariffs. We propose an exact branch-and-price algorithm, leveraging a custom branching rule and a primal heuristic to remain efficient during the branch-and-bound phase. Moreover, we develop an exact labeling algorithm for our pricing problem, constituting a resource-constrained shortest path problem that considers variable energy prices and nonlinear charging operations. We benchmark our algorithm in a comprehensive numerical study and show that it can solve problem instances of realistic size with computational times below one hour, thus enabling its application in practice. Additionally, we analyze the benefit of jointly scheduling charging and service operations. We find that our integrated approach lowers the amount of charging infrastructure required by up to 57% besides enabling operational cost savings of up to 5%. Funding: This work was supported by the German Federal Ministry for Economic Affairs and Energy [Grant 01MV21020B]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0272 .

Modelling the forest harvesting tour problem

In a globalized market, forest management plans play an important role in the sustainability of forest enterprises. Several optimization processes have therefore been developed to support decision-making in forestry operations. However, important issues remain to be addressed, such as planning the allocation of harvesting areas and scheduling the harvesting teams that are contracted for these purposes. Harvesting schedules include different time scales and natural constraints, so that finding optimal or even good quality ones constitutes a highly complex combinatorial optimization problem. Efficient planning of harvesting operations can significantly reduce the costs associated with logistics and improve the economic performance of companies in the sector. In Uruguay, almost 75\% of total forest harvesting operations for pulp production are carried out by contractor companies, so they are an important player in the supply chain. This study aims to optimize the allocation and routing of the harvesting equipment of forest contractors, which must be located at the sites to be harvested during the year. Numerical experiments over a case study based on realistic data have shown that realistic-sized instances can be resolved by standard mathematical programming software in a reasonable time. The mathematical programming model can also be useful to evaluate potential gains in joint planning by several contractors with respect to the costs incurred by separate planning; as illustrated also with numerical examples over the same case study. This model can be used to support annual forest harvest scheduling and equipment allocation for corporate contractors, leading to better quality plans and improvement opportunities.

Multi-class pilot dispatching problem with stochastic pilotage duration

In most seaports, pilotage is compulsory for incoming and outgoing vessels to use pilotage services. Maritime pilots play a critical role in providing local knowledge and assistance to ensure the safety of vessels and seafarers. Typically, pilots are classified into multiple classes on the basis of their experiences and qualifications. Moreover, pilotage duration is usually stochastic due to various factors, including harsh weather conditions, visibility, and traffic changes. In this study, we address a multi-class pilot dispatching problem with stochastic pilotage duration. We formulate this problem as a stochastic programming model that considers the expected penalty cost for late arrival at each task's location. To solve this problem, we develop a branch-and-price algorithm that integrates column generation within the branch and bound framework. Additionally, we develop a novel labelling algorithm and several effective acceleration techniques to enhance the efficiency of the proposed algorithm. Extensive numerical experiments demonstrate the effectiveness of the proposed algorithm and show that it can handle realistic-sized instances while outperforming a metaheuristic search method.

An Adaptive Large Neighbourhood Search algorithm for a real-world Home Care Scheduling Problem with time windows and dynamic breaks

This paper presents a Home Care Scheduling Problem (from now on HCSP) based on a real case of a care company for elderly and dependent people located in the North of Spain. The problem incorporates many of the common features addressed in the HCSP literature, such as soft and hard time windows for the services, available working time of the caregivers or affinity levels between users and caregivers. However, it also includes other novel characteristics that increase the difficulty of the problem significantly, since the breaks between services will play a key role in the quality of the solutions. To evaluate the solutions, the users welfare will be prioritized over the cost associated with the schedule.The problem has been formulated as a Mixed Integer Linear Programming (MILP) one but, due to the complexity of the model, it is not possible to solve it for real size instances. Therefore, we have designed a method that combines the Adaptive Large Neighbourhood Search (ALNS) methodology with a heuristic approach necessary to evaluate the objective functions. To analyse the behaviour of the algorithm, a set of computational experiments are carried out under different configurations. First, the MILP formulation and the algorithm have been compared over some standard instances from the literature. Finally, the performance of the algorithm is evaluated over a real case study based on the timetables of the company during some weeks from 2016 to 2017.

The balanced maximally diverse grouping problem with integer attribute values

The paper considers the assignment of items to groups according to their attribute values such that the groups are as balanced as possible. Although the problem is in general NP-hard, we prove that it can be solved in pseudo-polynomial time if attribute values are integer. We point out a relation to partition and more general to multi-way number partitioning. Furthermore, we introduce a mixed-integer programming (MIP) formulation, a variable reduction technique, and an efficient lower bound for the objective value. Our computational results show that the lower bound meets the optimal objective value in the most of our instances of realistic size. Hence, the MIP solves instances with several thousand items within seconds to optimality.

Exact methods for the Oven Scheduling Problem

The Oven Scheduling Problem (OSP) is a new parallel batch scheduling problem that arises in the area of electronic component manufacturing. Jobs need to be scheduled to one of several ovens and may be processed simultaneously in one batch if they have compatible requirements. The scheduling of jobs must respect several constraints concerning eligibility and availability of ovens, release dates of jobs, setup times between batches as well as oven capacities. Running the ovens is highly energy-intensive and thus the main objective, besides finishing jobs on time, is to minimize the cumulative batch processing time across all ovens. This objective distinguishes the OSP from other batch processing problems which typically minimize objectives related to makespan, tardiness or lateness. We propose to solve this NP-hard scheduling problem using exact techniques and present two different modelling approaches, one based on batch positions and another on representative jobs for batches. These models are formulated as constraint programming (CP) and integer linear programming (ILP) models and implemented both in the solver-independent modeling language MiniZinc and using interval variables in CP Optimizer. An extensive experimental evaluation of our solution methods is performed on a diverse set of problem instances. We evaluate the performance of several state-of-the-art solvers on the different models and on three variants of the objective function that reflect different real-life scenarios. We show that our models can find feasible solutions for instances of realistic size, many of those being provably optimal or nearly optimal solutions.

Forwarding containers to dry ports in congested logistic networks

This work investigates the impact of container arrival flow rate on the port surrounding network and proposes a mixed integer programming model to optimize their forwarding towards dry port destinations. A novel efficient model with limited network capacity and time period dependent travel cost function is proposed. The aim is to give a decision support for operational planning with limited capacity of both the terminal yard and the logistic network, with respect to the quantity of containers transferred per time unit. The model considers time dependent costs and traveling times to reduce congestion. As a further novel issue of the model, arc costs and traveling times change during specific time slots. More precisely, new linear functions are derived as tangents to the nonlinear convex components of a classical traveling time function proposed in the literature. The aim is to produce a light model which can be effectively used for macro planning of forwarding operations. The model is proved to be fast in real case instances also if compared to classical literature approaches. The model is used to study the container dispatching process in a terminal which is going to be the main Italian container terminal equipped to manage mega-ship traffic. Results obtained from real-size instances are reported. We tested the behavior of the model under different scenarios. Our tests confirmed model efficiency and its of supporting the management of peak events also by controlling shut-down time slots to lower congestion.

Heuristic and metaheuristic procedures for the buffer sizing problem in parallel assembly lines balancing problem with multi-line workstations and different cycle times

In the parallel assembly lines balancing problem (PALBP) there is the possibility that the operators can perform the tasks assigned to their multi-line workstation on two adjacent lines. As a result, the line efficiency can be increased. In a PALB system, the assembly lines can work with the same or different cycle times. In the latter case, the lines may produce in batches, and thus the use of buffers (existence and sizing) in multi-line workstations is needed. Exact procedures have been proposed to solve the buffer sizing problem (BSP) in a multi-line workstation, but only small-size instances can be solved in a viable computational time. The BSP is an unresolved problem for real-size instances. This paper presents the first non-exact procedures to solve real-size instances of the BSP in a multi-line workstation for a given set of tasks. The problem is detailed and described in the paper, and several heuristics and metaheuristic procedures are developed to solve it. Finally, several computational experiments are carried out to evaluate the procedures presented.

Scheduling personalized study plans considering the stress factor

ABSTRACT Learning path generation involves the computation of learning trajectories to personalize academic instruction to prevent school problems. The Educational Planning Problem ( EPP ) considers generating personalized learning paths by scheduling activities that satisfy expected grades while minimizing plans makespan. In this work, we propose two scheduling models with two new activity duration functions incorporating student stress and sequence dependence to mimic learning effects and increase personalization. We also developed a metaheuristic algorithm to solve real-size instances composed of a greedy randomized adaptive search procedure enhanced by a variable neighborhood search. Experimental results validate the efficiency of our approach and the importance of considering stress in learning trajectories personalization.

Application of decomposition techniques in a wildfire suppression optimization model

Resource assignment and scheduling models provides an automatic and fast decision support system for wildfire suppression logistics. However, this process generates challenging optimization problems in many real-world cases, and the computational time becomes a critical issue, especially in realistic-size instances. Thus, to overcome that limitation, this work studies and applies a set of decomposition techniques such as augmented Lagrangian, branch and price, and Benders decomposition’s to a wildfire suppression model. Moreover, a reformulation strategy, inspired by Benders’ decomposition, is also introduced and demonstrated. Finally, a numerical study comparing the behavior of the proposals using different problem sizes is conducted.

Efficient GRASP solution approach for the Prisoner Transportation Problem

Every day, resources are allocated to the transportation of prisoners to and from services such as hospitals and court proceedings. The optimal allocation of the resources – such as protected vehicles, drivers, and guards – is a complex task that requires significant efforts of human planners. For this reason, a recent paper described the Prisoner Transportation Problem (PTP), that aims to optimize the transportation of convicts between origin–destination pairs within pre-defined time windows. In addition to the similarities with the Vehicle Routing Problem with Time Windows, the PTP presents many additional challenges induced by the use of multi-comparted vehicles and incompatibility constraints, related to the safety of both prisoners and personnel.To efficiently solve the PTP, this paper proposes a GRASP approach, that was tested on a dataset of real-size instances, and the results show significant improvements with respect to the only competing approach proposed in the literature, both in terms of solution quality and computational times required to find them.

A relax-and-fix Pareto-based algorithm for a bi-objective vaccine distribution network considering a mix-and-match strategy in pandemics

Mass vaccination in pandemics is one of the most effective strategies to halt disease transmission. A well-organized vaccination plan is essential for guaranteeing its success in cases with limited vaccines. On the other hand, most vaccines need more than one dose for appropriate immunity, intensifying the vaccine shortage probability and complicating decision-making. This study presents a bi-objective mixed-integer linear model for a vaccine distribution chain problem, simultaneously considering economic and social objectives, with multi-dose vaccination adaptable even for booster doses. Moreover, the compatible vaccines in each vaccination process are considered a mix-and-match strategy to diversify vaccination alternatives and alleviate the vaccine shortage risk. It is shown that the problem is NP-hard, and we develop two heuristic and meta-heuristic algorithms to solve real-size instances in a reasonable time. Both algorithms use problem size reduction and problem decomposition techniques to produce an approximate Pareto front for the problem. The heuristic algorithm employs relax-and-fix and fix-and-optimize techniques, and an epsilon-constraint method to solve the multi-objective problem. The proposed meta-heuristic algorithm is based on the hybrid of two well-known evolutionary algorithms, particle swarm optimization, and genetic algorithm. It also uses a multi-objective framework called PESA-II to generate the Pareto front. Both proposed heuristic and meta-heuristic algorithms can employ parallel computing, which significantly reduces computational time. Finally, we investigate the proposed algorithms’ performance using 30 random problem instances and a case study from Iran. The results demonstrate that heuristic and meta-heuristic algorithms have obtained a reasonable solution with a maximum of 6.9% and 16.3% cost objective function gap respectively. The heuristic algorithm is superior to the meta-heuristic in terms of Pareto front quality metrics.

Minimizing patients total clinical condition deterioration in operating theatre departments

The operating theatre is the most crucial and costly department in a hospital due to its expensive resources and high patient admission rate. Efficiently allocating operating theatre resources to patients provides hospital management with better utilization and patient flow. In this paper, we tackle both tactical and operational planning over short-term to medium-term horizons. The main goal is to determine an allocation of blocks of time on each day to surgical specialties while also assigning each patient a day and an operating room for surgery. To create a balance between improving patients welfare and satisfying the expectations of hospital administrators, we propose six novel deterioration rates to evaluate patients total clinical condition deterioration. Each deterioration rate is defined as a function of the clinical priorities of patients, their waiting times, and their due dates. To optimize the objective functions, we present mixed integer programming (MIP) models and two dynamic programming based heuristics. Computational experiments have been conducted on a novel well-designed and carefully chosen benchmark dataset, which simulates realistic-sized instances. The results demonstrate the capability of the MIP models in finding excellent solutions (maximum average gap of 4.71% across all instances and objective functions), though, requiring large run-times. The heuristic algorithms provide a time-efficient alternative, where high quality solutions can be found in under a minute. We also analyse each objective function’s ability in generating high quality solutions from different perspectives such as patients waiting times, the number of scheduled patients, and operating rooms utilization rates. We provide managerial insights to the decision makers in cases where their intention is to meet KPIs and/or maintaining trade-offs between patients and administrators expectations, more fair assignments, or ensuring that the most urgent patients are taken care of first.

Dock assignment and truck scheduling problem; consideration of multiple scenarios with resource allocation constraints

The notion of ‘resource’ plays an important role in the overall efficiency and performance of most cross-docks. The processing time can often be described in terms of the resources allocated to different trucks. Conversely, for a given processing time, different combinations of resources can be prescribed. We study the problem of truck scheduling and dock assignment in the presence of resource constraints. In the absence of a closed-form (or well-defined) linear formulation describing the processing times as a function of resources, expert’ knowledge has been mobilized to enable modelling of the problem as an integer linear model. Two cases are taken into account: In the first one, the expert believes in his/her estimation of the processing time for every truck and only proposes a different combination of resources for his/her estimation, while in the second one the expert proposes a limited number of resource deployment scenarios for serving trucks, each of which has a different combination of resources and different processing times. We propose a novel compact integer programming formulation for the problem, which is particularly designed with an embedded structure that can be exploited in dual decomposition techniques with a remarkably computationally efficient column generation approach in this case. The case in which a scenario with invariant processing time is considered and modelled as a special case of the proposed model. Since a direct application of commercial solvers such as CPLEX to solve instances of this problem is not realistic, we propose a branch-and-price framework and, moreover, several classes of valid inequalities. Our extensive computational experiments confirm that the proposed exact solution framework is very efficient and viable in solving real-size instances of the practice and in a reasonable amount of time.

Multi-Trip Multi-Trailer Drop-and-Pull Container Drayage Problem

This paper addresses a novel and interesting container drayage problem in which a tractor can pull multiple trailers and can perform multiple trips during a working day. A state-based method and an IF-THEN method are proposed to model the multi-trip feature. The problem is mathematically formulated as two mixed-integer programming models. Three families of valid inequalities are introduced to strengthen the models. An adaptive large neighborhood search (ALNS) algorithm with an embedded decoding mathematical model is proposed to solve realistic-sized instances of the problem. Numerical experiments based on a large number of benchmark instances indicate that the inequalities are valid and that the model based on IF-THEN constraints shows excellent performance. The ALNS algorithm outperforms the strengthened mathematical model considering large-sized instances. The multi-trailer mode is more suitable if customers are clustered in the area far away from the depot when compared to the single-trailer mode.