Heuristic Solution Methods Research Articles

Multi-product multi-region supply chain optimisation for seasonal crops

There is a large demand for seasonal crops year-round within Australia, even when they are considered out of season. The demand is satisfied by continually moving production throughout the year to climates where the crops are in season. Management of the supply chain for a major national grower is challenging for several reasons. Due to the large number of planting decisions, it is standard practice for a team of production planners to create the annual production plan. For fresh food production, the supply chain does not contain intermediate storage requiring that the production plan is carefully timed not to waste resources with overproduction. In this paper, we develop a supply chain model that simultaneously manages the production of multiple crops across many growing regions. Production is set to satisfy the demand of multiple end-products while considering the packing plants' throughput capacity, each growing region's harvest capacity, and farm capacity. A time delay may be applied when moving between stages of the supply chain due to the geographic scale being modelled. A deterministic Mixed Integer Program is used to find the optimal planting plan, which minimises the deviation from demand for all products year-round at a minimal cost. Due to the excessive runtime for solving the model, a heuristic solution method is introduced. Numerical experiments demonstrate the advantage of the proposed model over the current manual planning process, which can solve the problem faster and with less deviation across the planning horizon.

Attractiveness factors in retail category space location-allocation problem

We study the problem of category space location-allocation in the retail industry. We introduce a new attractiveness factor to reflect the product-based visibility level in designing the optimal allocation policy. This factor will be determined for each aisle by the lineup of product categories allocated to that aisle and all other aisles sharing a shopping path with it. We explore how considering the classical location-based attractiveness and the proposed product-based attractiveness can improve a retailer's overall space profitability. We develop a modelling framework that integrates both location-based and product-based attractiveness factors in a mixed-integer nonlinear program. Due to the non-linearity and non-convexity of the proposed model, large-scale instances are computationally challenging to solve using the state-of-the-art commercial solvers. We thus introduce a two-stage heuristic solution method that generates a near-optimal solution in a reasonable amount of time. Using the two-stage model, we explore the optimal store design for an illustrative case study. The results couple the optimal category space allocation to customers' shopping paths and create a profitability-maximising balance between the placement of high-demand and high-impulse product categories. We show that focussing on product-based attractiveness exposes the store to congestion risks, which can be prevented by adding constraints limiting congestion in different aisles of the store.

Resilient mixed open and closed-loop supply chain network design under operational and disruption risks considering competition: A case study

This study addresses the problem of resilient mixed open and closed-loop supply chain network design under operational and disruption risks as a fundamental domain in supply chain management. To deal with disruption risks, several resilience strategies (including multiple sourcing, facility fortification, adding extra production capacity, multi-channel distribution, and pricing) are applied. A model with the objective of maximizing the profit is proposed, which uses a two-stage stochastic programming approach. In order to cope with the problem's complexity, a constructive heuristic method and two metaheuristics, including an improved genetic algorithm (IGA) and an improved particle swarm optimization (IPSO) are developed. After tuning the parameters of metaheuristics via the Taguchi method, various numerical instances are utilized to test the validity and efficiency of the model and solution methods. Further, a real industrial case study is provided and analyzed. Results show that the constructive heuristic outperforms other solution methods and the performed analysis indicates that utilizing resilient strategies has a remarkable effect on reducing losses originating from risks and maintaining market share against competitors.

The consistent production routing problem

AbstractThis article introduces the consistent production routing problem in a setting with multiple plants and products. The problem consists in finding minimum‐cost production‐routing plans that also meet specific consistency requirements. In our context, consistency is defined as the degree to which some specified features of the solution remain invariant over time. We consider four forms of consistency, namely: driver, source, product, and plant consistency. For each of these consistency requirements, there is a target maximum value defining the decision‐maker's tolerance to deviations from a perfectly consistent solution. These targets are enforced as soft constraints whose violations need to be minimized when optimizing the integrated production and routing plan. We present a mathematical formulation for the problem and an exact branch‐and‐cut algorithm, enhanced with valid inequalities and specific branching priorities. We also propose a heuristic solution method based on iterated local search and several mathematical programming components. Experiments on a large benchmark set of newly introduced instances show that the enhancements substantially improve the performance of the exact algorithm and that the heuristic method performs robustly for production routing problems with different consistency requirements as well as for standard versions of the problem. We also analyze the cost‐consistency trade‐off of the solutions, confirming that it is possible to impose consistency without excessively increasing the cost. The results also reveal the impact of the first time period when optimizing and measuring the consistency features we study.

Stochastic RWA and Lightpath Rerouting in WDM Networks

In a telecommunication network, routing and wavelength assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity because of stranded bandwidth. At this point, service providers try to recover the capacity via a defragmentation process. We study this setting from two perspectives: (i) while granting the connection requests via the RWA problem and (ii) during the defragmentation process by lightpath rerouting. For both problems, we present the first two-stage stochastic integer programming model incorporating incoming request uncertainty to maximize the expected grade of service. We develop a decomposition-based solution approach, which uses various relaxations of the problem and a newly developed problem-specific cut family. Simulation of two-stage policies for a variety of instances in a rolling-horizon framework of 52 stages shows that our stochastic models provide high-quality solutions when compared with traditionally used deterministic ones. Specifically, the proposed provisioning policies yield improvements of up to 19% in overall grade of service and 20% in spectrum saving, while the stochastic lightpath rerouting policies grant up to 36% more requests, using up to just 4% more bandwidth spectrum.Summary of Contribution: For handling the intrinsic uncertainty of demand in the telecommunications industry, this paper proposes novel stochastic models and solution methodology for two fundamental problems in telecommunications at operational level: (i) routing and wavelength assignment (RWA) and (ii) lightpath rerouting problem. Despite the vast literature on the RWA problem, stochastic optimization has not been considered as a viable solution for resource allocation in optical networks. We propose two-stage stochastic programming models for both problems and design efficient decomposition-based solution methods that use various relaxations of the models and a new family of cutting planes. Our extensive and rigorous numerical experiments show the significant merit of incorporating uncertainty into decision making, as well as the effectiveness of the decomposition framework and our newly designed family of cuts in enhancing the solvability of both models. This work opens new avenues to explore where the powerful stochastic programming literature can be leveraged to make operational decisions in telecommunications problems, a field that currently relies mostly on deterministic and heuristic solution methods.

A Markov decision process approach for managing medical drone deliveries

Drone delivery is a fast and innovative method for delivering parcels, food, and medical supplies. Furthermore, this low-contact delivery mode contributes to reducing the spread of pandemic and vaccine-preventable diseases. Focusing on the delivery of medical supplies, this paper studies optimizing the distribution operations at a drone hub that dispatches drones to hospitals located at different geographic locations. Each hospital generates stochastic demands for medical supplies to be covered. This paper classifies stochastic demands based on the distance between hospitals and the drone hub. Satisfying the demands requires flying over different ranges, which is directly related to the amount of charge of the drone batteries. We develop a stochastic scheduling and allocation problem with multiple classes of demand and model the problem using a finite Markov decision process approach. We provide exact solutions for the modest sizes instances using backward induction and discuss that the problem suffers from the curses of dimensionality. Hence, we provide a reinforcement learning method capable of giving near-optimal solutions. We perform a set of computational tests using realistic data representing a prominent drone delivery company. Finally, we analyze the results to provide insights for managing drone hub operations and show that the reinforcement learning method has high performance compared with the exact and heuristic solution methods.

Network-level control of heterogeneous automated traffic guaranteeing bus priority

Guaranteeing the quality of transit service is of great importance to promote the attractiveness of buses and alleviate urban traffic issues such as congestion and pollution. Emerging technologies of automated driving and V2X communication have the potential to enable the accurate control of vehicles and the efficient organization of traffic to enhance both the schedule adherence of buses and the overall network mobility. This study proposes a novel network-level control scheme for heterogeneous automated traffic composed of buses and private cars under a full connected and automated environment. Inheriting the idea of network-level rhythmic control proposed by Lin et al. (2021b), an innovative rhythmic control scheme for heterogeneous traffic, i.e., RC-H, is established to organize the mixed traffic in a rhythmic manner. Realized virtual platoons are designed for accommodating vehicles to pass through the network, including dedicated virtual platoons for buses to provide exclusive right-of-ways (ROWs) on their trips and regular virtual platoons for private cars along with an optimal assignment plan to minimize the total travel cost. A mixed-integer linear program (MILP) is formulated to optimize the RC-H scheme with the objective of minimizing the weighted travel costs of both buses and private cars. A bilevel heuristic solution method is designed to relieve the computational burden of MILP. Numerical examples and simulation experiments are conducted to evaluate the performance of the RC-H scheme under different scenarios. The results show that the bus punctuality can be guaranteed and the traveler delay can be minimized under various demand levels with transit priority. Moreover, compared with traffic signal control (TSC) strategies, including those with fixed timing and those with bus priority, the RC-H scheme shows significant advantages in handling heavy traffic demand, in terms of both reducing vehicle delay and enhancing network throughput.

A two-level off-grid electric distribution problem on the continuous space

We introduce a two-level distribution network design problem to serve a set of demand points. At the higher level, primary facilities with source capabilities feed secondary facilities over tree networks. At the lower level, both the primary and secondary facilities serve customers within a coverage distance over star networks. The problem has wide applications especially in the spatial planning of energy distribution networks, where the coverage distance constraints may be associated with the loss of electric power over distance. The facilities can be located anywhere on the continuous space in our greenfield development problem. We formulate an optimization problem that determines the number, types, and locations of the facilities as well as the lower and higher-level networks to minimize a distribution cost. We also propose a heuristic solution method that solves a discrete counterpart and then improves its solution by moving facilities around on the continuous space. When the number of demand points is large, the discrete counterpart is also hard to solve. Therefore, we propose a decomposition method for its solution: We first solve a decentralized single-level problem with secondary facilities and then form the higher-level network. We perform numerical experiments to demonstrate the benefits of our discrete problem decomposition and facility location adjustments on the continuous space.

An Evaluation Method of Renewable Energy Resources’ Penetration Capacity of an AC-DC Hybrid Grid

With increasingly more renewable energy being integrated into the AC-DC hybrid grid, the grid shows more complex dynamic characteristics due to the mutual coupling of HVDC and renewable energy. To evaluate the renewable energy resources’ penetration capacity of the AC-DC hybrid grid, this paper proposes an evaluation method of the renewable energy resources’ penetration capacity of an AC-DC hybrid grid, which considers both economy and safety. Firstly, indicators are proposed for an evaluation of the economy and safety of the AC-DC hybrid grid integrated with renewable energy, where both static and transient stability indicators are considered. Secondly, to maximize the renewable energy penetration capacity and minimize the network loss, an optimization model of the renewable energy penetration capacity of the AC-DC hybrid grid is established considering the static and transient stability constraints. Then, a heuristic solution method for solving the renewable energy penetration capacity optimization model is proposed. Finally, based on the improved IEEE 39 node system, a case analysis is carried out. The simulation results verify the correctness and effectiveness of the proposed method.

A Clustering-based Simulated Annealing Algorithm with Taguchi Method for the Discrete Ordered Median Problem

Researchers have studied discrete location problems for a long time because of their importance in practice. The Discrete Ordered Median Problem (DOMP) generalizes discrete facility location problems. The DOMP generalizes the main facility location problems' objective functions such as the p-median, p-center and p-centdian location problems. As these problems, also known as the problems of location-allocation, have NP-hard structure, it is inevitable to use heuristic methods for solution. In this study, a metaheuristic algorithmic suggestion will be put forward by examining the DOMP to find optimal solutions. For that purpose, we proposed a Simulated Annealing (SA) metaheuristic with K-means Clustering Algorithm in initialization for the DOMP. Novel approaches for initial solution and K-exchange algorithm-based neighborhoods for local search were analysed. In addition, best level of selected parameters were determined by Taguchi method. Forty common p-median instances derived from OR-LIB were used to test the SA performance, and the results were compared with three state-of-art algorithms in the literature. According to the computational results, 21 best solutions were obtained on instances despite gap values and CPU times increasing proportionally to the scale of the instances. In a conclusion, the proposed clustering-based SA algorithm is competitive and can be a robust alternative for the DOMP.

Composing Vessel Fleets for Maintenance at Offshore Wind Farms by Solving a Dual-Level Stochastic Programming Problem Using GRASP

Background: Dual-level stochastic programming is a technique that allows modelling uncertainty at two different levels, even when the time granularity differs vastly between the levels. In this paper we study the problem of determining the optimal fleet size and mix of vessels performing maintenance operations at offshore wind farms. In this problem the strategic planning spans decades, while operational planning is performed on a day-to-day basis. Since the operational planning level must somehow be taken into account when making strategic plans, and since uncertainty is present at both levels, dual-level stochastic programming is suitable. Methods: We present a heuristic solution method for the problem based on the greedy randomized adaptive search procedure (GRASP). To evaluate the operational costs of a given fleet, a novel fleet deployment heuristic (FDH) is embedded into the GRASP. Results: Computational experiments show that the FDH produces near optimal solutions to the operational day-to-day fleet deployment problem. Comparing the GRASP to exact methods, it produces near optimal solutions for small instances, while significantly improving the primal solutions for larger instances, where the exact methods do not converge. Conclusions: The proposed heuristic is suitable for solving realistic instances, and produces near optimal solution in less than 2 h.

A Novel Model for Transfer Synchronization in Transit Networks and a Lagrangian-Based Heuristic Solution Method

A Novel Model for Transfer Synchronization in Transit Networks and a Lagrangian-Based Heuristic Solution Method

Some structural results for the problem of Min-Time Coverage in Constricted Environments

In a recent work, we introduced a new set of problems in the area of networked robotic systems that concern the time-optimal execution of certain coverage tasks taking place in constricted environments. That work provided the detailed problem definitions, a complete representation of these problems in terms of Mathematical Programming (MP) formulations, and a formal analysis of their worst-case computational complexity. The current work establishes some structural results for the considered problems that are useful for the strengthening of the aforementioned MIP formulations and for the further development of pertinent heuristic solution methods for these problems. We demonstrate the first possibility in this paper, and we defer the second one to future work.

A heuristic for two-echelon urban distribution systems

The negative impacts of urban freight transport have fostered the design of new distribution systems for inner city deliveries. One of the proposed city logistics solutions is the establishment of two-echelon distribution systems, where freight originating from the periphery of the city is transferred at intermediate locations (satellites) from larger vehicles (urban freighters) to smaller more environmentally friendly vehicles (city freighters), deemed more suited to operate in the city centre. In this paper, we address a variant of the two-echelon (capacitated) vehicle routing problem (2E-CVRP) arising in the context of city logistics encompassing characteristics such as a heterogeneous fleet of city freighters, time windows, vehicles synchronisation at satellites, direct deliveries, the possibility of freight transfers at customers, and multiple trips by city freighters. We propose a heuristic solution method for this problem based on a Variable Neighbourhood Search (VNS) heuristic, as well as a set of auxiliary evaluation metrics designed to support the decision making process. Preliminary results show the flexibility of the proposed heuristic to account for different problem characteristics, as well as the impacts of considering different best insertion criteria for the initial solution construction. Additionally, the proposed evaluation metrics have allowed for an improved assessment of the trade-offs between different city logistic solutions, and may be considered when developing decision support systems.

A large neighborhood search approach for the paint shop scheduling problem

Minimizing the setup costs caused by color changes is one of the main concerns for paint shop scheduling in the automotive industry. Yet, finding an optimized color sequence is a very challenging task, as a large number of exterior systems for car manufacturing need to be painted in a variety of different colors. Therefore, there is a strong need for efficient automated scheduling solutions in this area. Previously, exact and metaheuristic approaches for creating efficient paint shop schedules in the automotive supply industry have been proposed and evaluated on a publicly available set of real-life benchmark instances. However, optimal solutions are still unknown for many of the benchmark instances, and there is still a potential of reducing color change costs for large instances. In this paper, we propose a novel large neighborhood search approach for the paint shop scheduling problem. We introduce innovative exact and heuristic solution methods that are utilized within the large neighborhood search and show that our approach leads to improved results for large real-life problem instances compared to existing techniques. Furthermore, we provide previously unknown upper bounds for 14 benchmark instances using the proposed method.

Picker Routing in AGV-Assisted Order Picking Systems

To reduce unproductive picker walking in traditional picker-to-parts warehousing systems, automated guided vehicles (AGVs) are used to support human order pickers. In an AGV-assisted order-picking system, each human order picker is accompanied by an AGV during the order-picking process. AGVs receive the picked items and, once a picking order is complete, autonomously bring the collected items to the shipping area. Meanwhile, a new AGV is requested to meet the picker at the first storage position of the next picking order. Thus, the picker does not have to return to a central depot and continuously picks order after order. This paper addresses both the routing of an AGV-assisted picker through a single-block, parallel-aisle warehouse and the sequencing of incoming orders. We present an exact polynomial time routing algorithm for the case of a given order sequence, which is an extension of the algorithm of Ratliff and Rosenthal [ Ratliff HD, Rosenthal AS (1983) Order-picking in a rectangular warehouse: A solvable case of the traveling salesman problem. Oper. Res. 1(3):507–521], and a heuristic for the case in which order sequencing is part of the problem. In addition, we investigate the use of highly effective traveling salesman problem (TSP) solvers that can be applied after a transformation of both problem types into a standard TSP. The numerical studies address the performance of these methods and study the impact of AGV usage on picker travel: by using AGVs to avoid returns to the depot and by sequencing in (near-) optimal fashion, picker walking can be reduced by about 20% compared with a traditional setting. Sharing AGVs among the picker workforce enables a pooling effect so that, in larger warehouses, only about 1.5 AGVs per picker are required to avoid picker waiting. Summary of Contribution: New technologies, such as automatic guided vehicles (AGVs) are currently considered as options to increase the efficiency of the order-picking process in warehouses, which is responsible for a large part of operational warehousing costs. In addition, picker-routing decisions are more and more often based on algorithmic decision support because of their relevance for decreasing unproductive picker walking time. This paper addresses both aspects and investigates routing algorithms for AGV-assisted order picking in parallel-aisle warehouses. We present a dynamic programming routine with polynomial runtime to solve the problem variant in which the sequence of picking orders is fixed. For the variant in which this sequence is a decision, we show that the problem becomes NP-hard, and we propose a greedy heuristic and investigate the use of state-of-the-art exact and heuristic traveling salesman problem solution methods to address the problem. The numerical studies demonstrate the effectiveness of the algorithms and indicate that AGV assistance promises strong improvements in the order-fulfillment process. Because of the practical relevance of AGV-assisted order picking and the presented algorithmic contributions, we believe that the paper is relevant for practitioners and researchers alike.

Two-machine scheduling with aging effects and variable maintenance activities

This paper presents models and solution algorithms for a two-machine scheduling problem with position-dependent job processing times subject to both aging and maintenance effects. Aiming to minimize the overall makespan for two identical parallel machines, two cases are analyzed. In the first case, no maintenance is scheduled. In the second case, maintenance is scheduled within the job processing sequence, restoring the machine to as-new condition. Assuming the number and the positions of maintenance stops to be variable, machine maintenance and job processing are scheduled simultaneously. Integer linear programming (ILP) models are formulated to determine the optimal maintenance and job processing sequence on each machine. To solve large-size problems, six heuristic solution methods are developed and compared. The maximum delay penalty (MDP) heuristic is best for the no-maintenance case, while the variable neighborhood search (VNS) metaheuristic is best for the with-maintenance case. Both methods quickly produce near-optimal solutions for large-size problems.

A mathematical programming model to select maintenance strategies in railway networks

This paper presents a nonlinear integer programming model to support the selection of maintenance strategies to implement on different segments of a railway network. Strategies are selected which collectively minimise the impact of sections’ conditions on service, given network availability and budget constraints. Different metrics related to the network topology, sections’ availability, service frequency, performance requirements and maintenance costs, are combined into a quantitative approach with a holistic view. The main contribution is to provide a simple yet effective modelling approach and solution method which are suitable for large networks and make use of standard solvers. Both an ad hoc heuristic solution and relaxation methods are developed, the latter enabling the quality of the heuristic solution to be estimated. The availability of railway lines is computed by exploiting the analogy with series–parallel networks. By varying the model parameters, a scenario analysis is performed to give insight into the influence of the system parameters on the selection of strategies, thus enabling more informed decisions. For its simple structure, the model is versatile to address similar problems arising in the maintenance of other types of networks, such as road and bridges networks, when deciding on the strategic allocation of maintenance efforts.

Robust dynamic tariff method for day-ahead congestion management of distribution networks

With the large-scale deployment of distributed energy resources (DERs) in distribution networks, network congestion could occur due to the non-coordinated operation of DERs. The dynamic tariff (DT) method as a decentralized day-ahead congestion management method has been widely studied. In the DT method, it is assumed that the distribution system operator (DSO) and aggregators use the same energy requirement parameters, which is impractical due to the DSO’s forecast error. The discrepancy between the DSO’s forecast parameters and aggregator’s accurate parameters leads to a certain level of uncertainty that needs to be handled when employing the DT method. Therefore, a robust DT method is proposed for day-ahead congestion management while dealing with the uncertainty in the DT framework. A three-level robust DT model is formulated to obtain a robust DT solution, based on which the network constraints are respected even in the worst-case scenario. Moreover, due to the nonconvexity of the three-level robust DT model, the robust DT model is reformulated as a two-level optimization model, and a heuristic solution method is developed to obtain the robust DT solution with an iterative procedure. The Roy Billinton Test System (RBTS) was used to conduct case studies to validate the effectiveness of the proposed robust DT method for day-ahead congestion management in distribution networks. The case study results demonstrate that the deterministic DT method may be ineffective due to the DSO’s forecast errors whereas the proposed robust DT method can resolve congestion efficiently under the uncertain condition.

Managing mobile production-inventory systems influenced by a modulation process

The objective of this paper is to investigate the potential added value of being able to relocate production capacity, relative to fixed production capacity, in a network of multiple, geographically distributed manufacturing sites. There is a growing number of examples of production capacity that can be geographically relocated with a modest amount of effort; e.g., 3D printers, bioreactors for cell and gene manufacturing, and modular units for pharmaceutical intermediates. Such a capability shows promise for enabling the fast fulfillment of a distributed network with a reduction in the total inventory and total production capacity of a distributed network with fixed production capacity without sacrificing customer service levels or total system resilience. Allowing also for transshipment, we model a production-inventory system with L production sites and Y units of relocatable production capacity, develop efficient and effective heuristic solution methods for dynamic relocation and multi-location inventory control, and analyze the potential added value and implementation challenges of being able to relocate production capacity. We describe the (L, Y) problem as a problem of sequential decision making under uncertainty to determine transshipment, mobile production capacity relocation, and replenishment decisions at each decision epoch. To enhance model realism, we use a partially observed stochastic process, the modulation process, to model the exogenous and partially observable forces (e.g., the macro-economy) that affect demand. We then model the (L, Y) problem as a partially observed Markov decision process. Due to the considerable computational challenges of solving this model exactly, we propose two efficient, high quality heuristics. We show for an instance set with five locations that production capacity mobility and transshipment, relative to the fixed production capacity case, can improve systems performance by as much as 41% on average over the no-flexibility case and that production capacity mobility can yield as much as 10% more savings compared to when only transshipment is permitted.