Small Instances Research Articles

Optimal and heuristic solutions for placing multiple finite-size rectangular facilities in an existing layout

In a companion paper (Date, K., and R. Nagi. [(2023) Optimal Placement of Multiple Finite-size Rectangular Facilities in an Existing Layout. International Journal of Production Research, THIS ISSUE]) we investigated a new problem of optimal placement of multiple finite-size rectangular facilities with known dimensions in the presence of existing rectangular facilities. We introduced the requisite theory to arrive at a solution by dividing the feasible region into sub-regions whose boundaries provide the candidates for the optimal placement. In this paper, we focus on developing optimal and heuristic solution methods for solving problem instances with various facility counts. To solve small instances with fewer facilities, we develop two optimal methods: (1) efficient explicit enumeration based on a tree state-space representation and (2) an implicit enumeration scheme that uses a flow-decomposition-based lower bound to reduce the search space and time. To solve industrial-sized instances, we have to resort to a family of construction and improvement heuristics given that the problem is NP-hard. The heuristic procedures perform well for non-pathological cases with an acceptable optimality gap. The main contribution of this paper is a range of optimal to heuristic methods that can be applied by the practitioner depending on their problem characteristics and desired efficiency.

Customized GRASP for rehabilitation therapy scheduling with appointment priorities and accounting for therapist satisfaction

Physical therapy in acute care hospitals plays an important role in the rehabilitation of patients. Nevertheless, the profession must deal with staff shortages caused by a lack of potential employees and absenteeism which are results of high physical and mental workloads. The therapist shortage negatively affects the total number of daily appointments the department can fulfill. For appointments that can be successfully scheduled, continuity of care with the same therapist cannot be guaranteed for individual patients. Lack of continuity of care negatively influences the therapist's satisfaction. Therapist preferences for individual appointments in general cannot always be guaranteed when designing schedules, which also hurts satisfaction. This paper develops a multi-criteria model for the daily therapy appointment-scheduling problem. The primary objective is to minimize the total sum of priority violations for unscheduled appointments. To improve therapist satisfaction, we consider therapist preferences including continuity of care as a secondary objective. Here, our integer programming formulation aims to minimize the total sum of preference violations for scheduled appointments. We are dealing with an operational planning problem with a daily planning horizon. The operational objective is to achieve therapist schedules in at most two hours. The therapists’ schedules together need to include several hundred appointments for a planning day. Due to intractability, the developed integer program cannot provide schedules for such problem sizes. Therefore, we develop a customized Greedy Randomized Adaptive Search Procedure (GRASP) with six innovative local search operations to improve an initially constructed solution. We test the heuristic algorithm on realistic data instances. The metaheuristic provides high-quality schedules for various problem sizes in short runtimes, i.e., within minutes. Comparisons with the optimal solutions for small problem instances show very good results of the GRASP with a similar number of scheduled appointments and good adherence to continuity of care and therapist preference requirements.

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.

A Metaheuristic Framework for Energy-Intensive Industries With Batch Processing Machines

Batch processing machines, which operate multiple jobs at a time, are commonly used in energy-intensive industries. A significant amount of energy can be saved in such industries using production scheduling as an approach to enhance efficiency. This study deals with an energy-aware scheduling problem for parallel batch processing machines with incompatible families and job release times. In such an environment, a machine may need to wait until all the jobs in the next batch become ready. During waiting time, a machine can be switched <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> or kept <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> standby for more energy-efficient scheduling. We first present a mixed-integer linear programming (MILP) model to solve the problem. However, the presented MILP model can only solve small problem instances. We therefore propose an energy-efficient tabu search (ETS) algorithm for solving larger problem instances. The proposed solution framework incorporates multiple neighborhood methods for efficient exploration of the search space. An energy-related heuristic is also integrated into the ETS for minimizing energy consumption during the waiting time. The performance of our proposed ETS algorithm is validated by comparing it with CPLEX for small problem instances and with two other heuristic algorithms for larger problem instances. The contribution of different components in ETS is also established in our experimental studies. The proposed solution framework is expected to bring many benefits in energy-intensive industries both economically and environmentally.

The Flexible Job Shop Scheduling Problem with Setups and Operator Skills: an application in the textile industry

The Flexible Job Shop Scheduling Problem (FJSSP) is one of the most studied problems in the literature thanks to its practical relevance. Many industrial production scheduling problems can be seen as a FJSSP with different constraints and objectives. The studied problem arises in a textile factory, precisely in the sewing process. Multiple real-world constraints are tackled. Individual skills of operators and different types of setup times are considered: machine-change setup time for operators, colour-change setup times and configuration-change setup times. The objective is to minimize the total tardiness. To the best of the authors’ knowledge, this is the first study that tackles this variant of the problem. This paper presents a preliminary study to validate the approach and evaluate the tractability of the industrial problem. A mixed-integer linear programming (MILP) model is proposed and solved using a commercial solver. Real-world data are used to generate more than 1000 problems that are clustered in 4 groups based on the number of jobs to be scheduled, the number of operators and flexibility of their skills. The results show that the proposed MILP model can reach optimality for the small size instances but it is intractable for most large-sized instances. Moreover, the results highlight how diversifying the operators’ skills can help find better solutions.

Multi-Objective Workforce and Process Planning For Socio-Economic Sustainable RMS: Lp-metric vs Epsilon Constraint

As a new manufacturing paradigm, reconfigurable manufacturing system (RMS) has shown promising results when dealing with market changes. This study explores the issue of integrating workforce planning and process planning within RMS. The idea is to consider socio-economic sustainable manufacturing by investigating new KPIs from the social aspect. The choice of workforce flexible work hours and the accident risk are concurrently viewed as social aspects. This challenge has been approached by using a new mixed integer linear model. Furthermore, the model considers other objectives, including operational cost and total completion time. The ϵconstraint and Lp-metric are used to solve the multi-objective model for five small and medium-sized instances. The findings demonstrate a 60% variation in reconfiguration time, and processing time contributes to 5% and 7.8% changes in makespan and 25% and 56% in total cost. Finally, some in-depth analysis is performed to illustrate and verify the performance of the suggested solution approach.

Minimizing the maximum tardiness for a permutation flow shop problem under the constraint of sequence independent setup time

In this work, we will study a permutation flow shop scheduling problem under the constraint of sequence independent setup time. In our case, each machine requires a certain setup time to process all the different jobs assigned to it. Hence, this setup time will be independent of sequence of jobs, but will depend only on the nature of machine. The optimization objective is to minimize the maximum tardiness criterion. To solve this optimization problem, an exact method, heuristics and metaheuristics are the three main resolution methods that we have used. The exact method is represented by the mixed integer linear programming (MILP) model. In terms of the second category of resolution methods, we have been focused on two methods, the first is a modified heuristic based on Johnson rule (HBJR) while the second is based on the Nawaz–Enscore–Ham (NEH) algorithm. Finally, three metaheuristics have been used, namely the iterated local search (ILS) method, the iterated greedy (IG) algorithm and the genetic algorithm (GA). Our numerical results indicate that for the problems with small size instances, the NEH heuristic outperforms HBJR approach, while for relatively large size instances, the developed IG algorithm gives best results than both other metaheuristics ILS and GA.

A multi-objective two-echelon vehicle routing problem with multiple delivery options

The classical two-echelon vehicle routing problem (2E-VRP) has commodities transported from depots to intermediate facilities and then delivered to customers from these facilities. In this study, we consider another type of 2E-VRP, in which vehicles from both echelons can be used for home delivery. We also present a sustainable model, which considers customers' preferred delivery locations, economic and environmental costs. Also, we present a meta-heuristic algorithm to solve real-world size instances in a timely manner. The computational results demonstrate that the proposed solution method can effectively solve small instances with a minimal gap when compared to an exact solver, and it can also handle large instances in a timely manner.

Optimizing Segregated Waste Collection Routes as a Decision-Making Problem in the Municipal Solid Waste Management System in Small Town

Routing vehicles is a generic decision-making problem of strategic management in any business serving customers in distributed locations with a limited fleet including municipal solid waste collection. This paper introduces an approach tailored for optimizing waste collection routes in small towns and rural areas where dead-end streets are typical in the road network. Leveraging the Traveling Salesperson Problem (TSP), the approach employs optimal route determination taking advantage of the specific character of a road network with many dead-end streets. The service area for waste collection was aggregated, so the graph representing the map results in a relatively small data instance. This facilitated the application of the exact method, i.e. Mixed-Integer Programming using the OpenSolver tool in Excel. Conducted in collaboration with a municipal agency in southeastern Poland, this study outlines a comprehensive methodology, emphasizing the reduction of complex dead-end streets into singular nodes within the graph for effective route optimization. A comprehensive methodology is outlined alongside the solutions attained. Computational experiments focused on minimizing total travel distance during waste collection operations, demonstrating the methodology's success. Beyond efficiency gains, optimized routes hold potential for significant environmental impact reduction. The reduced travel distances result in decreased fuel consumption and emissions, aligning with sustainability goals. Developing an Excel-based decision support tool for municipal solid waste management is a significant contribution, particularly for decision-makers less familiar with Operations Research. The tool's compatibility within the spreadsheet environment streamlines waste management processes for municipal units, enhancing decision-making efficiency in optimizing waste collection routes.

An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines the piecewise-linear approximations and iteratively solves convex approximation problems. The convergence analysis provides a bound on the optimality gap as a function of approximation errors. Based on this bound, we prove that the proposed B&B algorithm terminates in a finite number of iterations and the worst-case bound to obtain an ϵ-optimal solution reciprocally depends on the square root of ϵ. Numerical experiments on Cobb–Douglas production efficiency and equitable resource allocation problems support that the algorithm efficiently finds a highly accurate solution while significantly outperforming the benchmark algorithms for all the small size problem instances solved. A modified branching strategy that takes the advantage of non-linearity in convex functions further improves the performance. Results are also discussed when solving a dual reformulation and using a cutting surface algorithm to solve distributionally robust counterpart of the Cobb–Douglas example models.

Power on the Go: A Solution to Address Electric Vehicle Charging Challenges

In this article, we propose a novel solution to address the current challenges related to charging an Electric Vehicle (EV). The Power on the Go: Single-drop and Double-drop problems allow an EV to be charged at a convenient location, where a service vehicle (drone), which is launched from a nearby charging station, can bring a compatible power bank at the request of the driver through an app. The objective is to reduce the cumulative wait time between service requests and the start of charging. We present mathematical formulations and two order-first split-second-based heuristic approaches for both problems. While the mathematical formulations can generate optimal solutions for small instances in a reasonable amount of time, the heuristics are fast and perform very well, with gaps &lt; 5% for up to 20 node instances. Moreover, the formulations highlight the mean savings in wait time (29.37%) when the power bank can charge two EVs consecutively before a replacement is needed. The implications of the proposed model can be extensive, as we seek to overcome the availability and technological challenges of EV charging while advocating its adoption.

Effect of surface roughness and morphology on the adsorption and transport of CH4/CO2 mixtures in nanoporous carbons

We report here molecular simulations of the adsorption and transport behaviour of CH4/CO2 mixtures in two types of non-ideal carbon nanopores. One model decorates an otherwise slit pore with surface imperfections which disrupt the smooth walls; a second model considers a disordered media, formed of randomly arranged coronene flakes, resulting in significant tortuosity. Boundary-Driven Non-Equilibrium Molecular Dynamics (BD-NEMD) and External Force Non-Equilibrium Molecular Dynamics (EF-NEMD) are used to study adsorption and transport properties in both types of pores with varying degrees of rugosity and tortuosity. Intermolecular interactions and bulk fluid properties are described by the statistical associating fluid theory (SAFT) coarse-grained Mie potential and equation of state respectively. Strong CO2 adsorption and fast CH4 transport are observed in smooth slit pores. Small instances of surface rugosity change the dynamics significantly, reducing the transport diffusivity by over an order of magnitude. The fast plug-like flow reported in slit pores dissipates with increasing rugosity, indicating a fundamental change in the flow pattern. Furthermore, rugose pores exhibit a lower capacity for CO2 adsorption, suggesting the performance of CO2 -enhanced oil recovery may be overestimated by the smooth pore models. A pore characteristic factor is shown to be appropriate to correlate the transport diffusivities in nano-pores.

The regular language-constrained orienteering problem with time windows

Several application domains of the Orienteering Problem (OP) entail the categorization of graph nodes. Specific categories of nodes may be preferred to be included in the solution, while nodes of other categories should be limited to a certain extent or even excluded. Additionally, precedence constraints may apply among nodes from different categories. We contend that regular expressions, which describe patterns of node categories and specify constraints for solution paths, can effectively capture practical tourist tour planning aspects. Hence, we introduce the Regular Language-Constrained OP with Time Windows (RLC-OPTW) as an extension of the OP, where regular expressions are utilized to describe the admissible category patterns in solution paths. Our approach leverages the simplicity, elegance, and expressive power of regular languages, which excel in applications involving pattern recognition and matching. Given that RLC-OPTW is NP-hard, we initially provide an exact solution for small instances of the problem. Then, we present two efficient heuristic approaches: The first heuristic iteratively appends nodes to the solution to generate an initial feasible (i.e., regular expression-constrained) solution and then replaces nodes in search of higher quality solutions. The second heuristic iteratively inserts nodes at any point within the solution and then replaces sets of consecutive nodes upon reaching a local optimum. The efficiency of our proposed algorithms has been assessed using publicly available datasets. We have also showcased the effectiveness of our methods in generating meaningful tourist trips that adhere to practical user constraints using a real dataset with tourist attractions in Athens (Greece) as a case study. Although our algorithmic approaches and experimental evaluation of RLC-OPTW primarily focus on tourist trip planning, the proposed algorithms can be applied to finding paths under constraints in numerous other application domains of the OP.

Truck-Drone Pickup and Delivery Problem with Drone Weight-Related Cost

Truck-drone delivery is widely used in logistics distribution for achieving sustainable development, in which drone weight greatly affects transportation cost. Thus, we consider a new combined truck-drone pickup and delivery problem with drone weight-related cost in the context of last-mile logistics. A system of integer programming is formulated with the objective of minimizing the total cost of the drone weight-related cost, fixed vehicle cost and travel distance cost. An improved adaptive large neighborhood search algorithm (IALNS) is designed based on the characteristics of the problem, several effective destroy and repair operators are designed to explore the solution space, and a simulated annealing strategy is introduced to avoid falling into the local optimal solution. To evaluate the performance of the IALNS algorithm, 72 instances are randomly generated and tested. The computational results on small instances show that the proposed IALNS algorithm performs better than CPLEX both in efficiency and effectiveness. When comparing the truck-drone pickup and delivery problem with drone weight-related cost to the problem without drone weight-related cost, it is found that ignoring the drone weight constraints leads to an underestimate of the total travel cost by 12.61% based on the test of large instances.

Modeling and solving the multi-objective energy-efficient production planning and scheduling with imperfect maintenance activities

PurposeThe purpose of this study is to propose a new mathematical model that integrates strategic decision-making with tactical-operational decision-making in order to optimize production and scheduling decisions.Design/methodology/approachThis study presents a multi-objective optimization framework to make production planning, scheduling and maintenance decisions. An epsilon-constraint method is used to solve small instances of the model, while new hybrid optimization algorithms, including multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm, multi-objective harmony search and improved multi-objective harmony search (IMOHS) are developed to address the high complexity of large-scale problems.FindingsThe computational results demonstrate that the metaheuristic algorithms are effective in obtaining economic solutions within a reasonable computational time. In particular, the results show that the IMOHS algorithm is able to provide optimal Pareto solutions for the proposed model compared to the other three algorithms.Originality/valueThis study presents a new mathematical model that simultaneously determines green production planning and scheduling decisions by minimizing the sum of the total cost, makespan, lateness and energy consumption criteria. Integrating production and scheduling of a shop floor is critical for achieving optimal operational performance in production planning. To the best of the authors' knowledge, the integration of production planning and maintenance has not been adequately addressed.

Learning heuristics for arc routing problems

Solid waste collection and street sweeping can each be formulated as a capacitated arc routing problem (CARP) in which the streets of a city require service by a fleet of vehicles at minimum total cost. Heuristic and meta-heuristic methods have been used to solve CARP because the problem is known to be NP-Hard. In this paper we introduce Splice, a novel machine learning framework that learns heuristics to solve routing problems, such as CARP, defined on the edges (rather than vertices) of a non-euclidean graph representation of the problem. Splice uses a message passing graph neural network to generate a graph embedding, and deep Q-learning feed-forward layers to learn heuristics to construct a giant tour that results in minimum total cost after applying the splitting procedure, iterating until all tasks are serviced. Compared to the two AI-driven approaches to CARP, Splice has a simpler network architecture and does not require a supervised learning method for training. The total costs of the solutions found by Splice are from 11-30% lower than those found by a path scanning heuristic and a memetic meta-heuristic algorithm. When trained on small instances, the heuristics learned by Splice generalize well, i.e., can be used to solve larger instances without retraining. Due to the route-first split-second form of heuristic learned, the Splice framework may be applied to solve other variants of routing problems by adapting the splitting procedure.

An effective approach for bi-objective multi-period touristic itinerary planning

Planning effective itineraries for tourists is a major problem that has been gaining attention over the last years. This paper proposes a new bi-objective integer linear programming model for this problem. Decisions include the choice of the best itinerary to be performed considering multi-period routing, time windows for the visited attractions and the choice of restaurants and hotels. The conflicting objectives considered are: (i) maximizing the level of service offered by the itinerary, and (ii) minimizing the total distance traveled. The problem resolution, even for small instances by exact methods, is limited. This motivated the proposition of a new customized MIP-heuristic based on decomposition, fix-and-optimize and MIP-start, to produce good-quality solutions with moderate computational effort. Tchebycheff’s scalarization method was coupled to this heuristic and multiple compromise solutions were obtained. Extensive results with problem instances of different sizes and characteristics showed a good performance of this approach, capable of producing effective solutions within short runtimes. The analysis of the solutions indicated a strong conflict between the objectives, allowing the user to quantify the losses and gains when one criterion is prioritized over the other. A brief sensitivity analysis of some model parameters revealed interesting managerial insights. Some examples include quantifying the negative impacts in terms of the level of service offered by concentrating hotels and restaurants in the center of tourist attractions, increasing visit and transfer times between attractions and reducing the planning horizon for the entire itinerary. These aspects validate the potential of using this MIP model and applying this MIP-heuristic in real situations.

Scale-aware dimension-wise attention network for small ship instance segmentation in synthetic aperture radar images

Scale-aware dimension-wise attention network for small ship instance segmentation in synthetic aperture radar images

DANet: Dual-Branch Activation Network for Small Object Instance Segmentation of Ship Images

In maritime scenes, instance segmentation of small object ships is of vital importance. Small ship objects in images have the characteristics of smaller size, lower image cover rate and fewer appearance features. However, existing instance segmentation methods fail to recognize and segment them and can cause missed ship segmentation. To this end, we propose a dual-branch activation network (DANet) for small object instance segmentation of ship images. DANet consists of a Feature Encoding, a Dual Mask Branch, and a Dual Activation Branch. The Feature Encoding adopts feature refinement and a pyramid structure to obtain more fine-grained features. The proposed Dual Mask Branch extracts dual-path mask features for encoding small object information. We propose a Dual Activation Branch to activate more small object regions and generate instance features. Furthermore, we build the Small ShipInsSeg dataset from a total of 5,256 images and 11,612 instances. The experiments show that DANet outperforms the SparseNet baseline and achieves state-of-the-art performance. Additionally, our method achieves a good trade-off between accuracy and speed.

Integrated planning and scheduling of engineer-to-order projects using a Lamarckian Layered Genetic Algorithm

This paper presents a new mathematical formulation for planning and scheduling activities of Engineer-To-Order (ETO) projects. It includes a new ETO strategy to reduce two principal impacts of the design uncertainty inherent in the ETO context: waste (of time and resources) and schedule instability. Our optimization approach is based on a two-level decision process to address, either sequentially or separately, the initial planning and the rescheduling stages. We also propose a hybrid Layered Genetic Algorithm combined with an adaptive Lamarckian learning process (LLGA). LLGA uses a new genetic representation (encoding format and decoding method) and a new cycle-avoidance procedure that guarantees solutions feasibility. LLGA is compared to the branch-and-cut procedure of CPLEX run on the proposed mathematical model on randomly generated instances with up to 340 operations. Our mathematical model shows a good performance for small and medium-sized instances, especially for the rescheduling stage. This performance deteriorates for larger instances (larger computing times and out-of-memory problems). However, the proposed heuristic is computationally stable and yields good-quality solutions in a reasonable computing time without requiring a large memory space. Our experiments also demonstrate the merits of our new ETO strategy in improving the robustness of the solutions.