Computers & Operations Research最新文献

When dynamic production capacity is considered in production lot-sizing plans, it becomes very challenging to efficiently determine the optimal production plan. Many papers apply “at most one fractional production period” to develop efficient algorithms, but those algorithms are still time consuming. In this paper, in a special situation where costs are non-speculative, we provide a novel proposal based on “at least one balance period”, in which the products made in this period not only satisfy the demands in this period but also backlogged demands and some demands after this period, to obtain an efficient algorithm. This algorithm complexity is one level lower than the algorithm without non-speculative cost assumptions in the literature regarding the number of periods in their time complexity function. Then, in a general situation, we propose a combination of two complementary algorithms as an efficient heuristic method. Moreover, in the literature, the estimation of computation time complexity in searching for the optimal production plan considers only the number of capacity levels and production periods on theoretical view. However, with numerical experiments, we observe that demand variation could also have significant effects on the computation time in practice.

In response to the government’s heightened focus on recycling and remanufacturing, as well as the growing awareness among consumers about environmental security, manufacturing companies are currently required to establish efficient closed-loop supply chain networks in order to improve their social reputation and competitive advantage. This study investigates the optimization of a Closed-Loop Supply Chain (CLSC) network that involves multiple products, multiple periods, and uncertain returns, which also considers the influence of many factors, such as carbon cap-and-trade policy, raw part procurement discounts, and facility capacity constraints, on the supply chain. Simultaneously, customer demand is sensitive to both product pricing and product greenness, and product greenness can be improved by investing in emission reduction technologies. To address the uncertainty in the returns, we propose a two-stage distributionally robust chance-constrained optimization model, which is transformed into a mixed integer linear programming model. To efficiently address the complex problem, we design an improved Benders decomposition (IBD) algorithm. The experimental results confirm that the IBD algorithm has significant advantages when compared to the Benders decomposition algorithm. Additionally, this study conducted a sensitivity analysis on key parameters and proposed operation suggestions of practical importance.

We study risk-averse multistage stochastic programs with expected conditional risk measures (ECRMs). ECRMs are attractive because they are time-consistent, which means that a plan made today will not be changed in the future if the problem is re-solved given a realization of the random variables. We show that the computational burden of solving the risk-averse problems based on ECRMs is the same as the risk-neutral ones. We consider ECRMs for both quantile and deviation mean-risk measures, deriving the Bellman equations in each case. Finally, we illustrate our results with extensive numerical computations for problems from two applications: hydrothermal scheduling and portfolio selection. The results show that the ECRM approach provides higher expected costs in the early stages to hedge against cost spikes in later stages for the hydrothermal scheduling problem. For the portfolio selection problem, the new approach gives well-diversified portfolios over time. Overall, the ECRM approach provides superior performance over the risk-neutral model under extreme scenario conditions.

Designing efficient heuristics for the different variants of vehicle routing problems and customising the heuristics to various input distributions is a time-consuming and expensive task. In recent years, end-to-end machine learning techniques have been developed because they are easy to modify for different problem variants, thereby saving on the design time to develop new efficient heuristics. These learning techniques, such as the transformer-based constructive methods, struggle to provide high quality solutions on problem instances with hundreds to thousands of customers in a reasonable time. Furthermore, many of the end-to-end heuristics also do not guarantee that solutions obey fleet-size constraints. We propose a heuristic for solving large capacitated vehicle routing problem (CVRP) that carefully integrates a machine learning heuristic with Integer Linear Programming techniques. To address the issue of solutions with poor objective function values generated by end-to-end machine learning approaches on larger instances, we dynamically partition the CVRP problem instance into smaller sub-problems and apply a machine heuristic on the smaller sub-problems. This allows the machine learning heuristic to always operate on smaller problems similar in size to those for which it was trained. The machine learning heuristic generates many solutions for each sub-problem which are then combined using a set partitioning approach based on a ILP formulation. The set partitioning ILP also guarantees that solutions obey fleet-size constraints.

We evaluate the performance of our heuristic on a difficult set of benchmark instances with hundreds to thousands of nodes, achieving small gaps (less than 3% on average) with respect to best known solutions, significantly improving upon the solution quality of the existing learning heuristics. Furthermore, we demonstrate that our results generalise well to other vehicle routing problems, such as green vehicle routing problem.

This paper introduces the two-level vehicle routing and loading problem (2L-VRLP), an innovative model integrating the two-level bin packing and vehicle routing problems to address real-world logistics challenges that require simultaneous packing and transportation decisions. By capturing the essence of dual-level packing (boxes onto pallets, pallets onto vehicles) and optimising vehicle routing, the 2L-VRLP offers an integrated framework that outperforms traditional separated models, demonstrating superior solutions that align closely with practical logistics operations. We propose a set of heuristic algorithms tailored for the 2L-VRLP’s unique requirements and explore automated algorithm selection using an artificial neural network (ANN), marking a step towards incorporating machine learning in logistics optimisation. This work not only showcases the 2L-VRLP model’s potential to enhance logistics management but also sets the groundwork for future research and applications in this domain.

Data structures are the main ingredient to strengthen both the time complexity and the filtering power of algorithms in Constraint-Based Scheduling. The TimeTable and the Profile are well-known data structures applied to filtering algorithms for cumulative constraint. The two data structures in this paper are applied simultaneously to overload checking and edge-finding rules. The resulting rules named TimeTable Horizontally Elastic Overload Checker and TimeTable Horizontally Elastic Edge Finder rules respectively subsume the enhancement of the overload checking rule and the edge-finding rule with the individual data structure. This new edge-finding rule is relaxed after a successive application of Profile on well-selected task intervals, then TimeTable on the new horizontally elastic edge-finding rule. Potential task intervals for the edge-finding rule are selected based on two criteria (specified later in the paper) and the strong detection rule of the horizontally elastic edge finder rule of Fetgo Betmbe and Djamegni (2022) is then applied to those selected task intervals. The new horizontally elastic edge-finder rule subsumes the edge-finding rule and is not comparable to the timetable edge-finding rule. A two-phase filtering algorithm of complexity $O\left(n^2\right)$ each (where $n$ is the number of tasks sharing the resource) is proposed for the new rule. Improvements based on the TimeTable are obtained by considering fixed parts of external tasks that overlap with the potential task intervals. The improved rule subsumes the timetable edge-finding rule, and a quadratic algorithm is derived from the previous algorithm. Experimental results, on a well-known suite of benchmark instances of Resource-Constrained Project Scheduling Problems, show that the propounded algorithms are competitive with the state-of-the-art algorithms regarding running time and tree search reduction.

In this paper, we consider a bay design problem in a less-than-unit-load production warehouse, which is motivated by a real-world problem in a semiconductor company. The objective is to maximize the utilization of the vertical space in bays by considering several practical storage requirements. To solve the problem, a non-linear integer programming model is first formulated. Since the problem is similar to a two-stage cutting stock problem (CSP), a column-and-row generation (CRG) method is developed, in which the original problem is decomposed into a restricted master problem and three subproblems, including two classical column generation subproblems and a row generation subproblem. The two former subproblems are solved as unbounded knapsack problems and for the latter, a two-stage approach is applied. The results of computational experiments on randomly generated instances show that the proposed CRG method is more efficient than the classic column-generation-based method, solving the non-linear model directly and solving a cut model in the literature directly. The results of a case study show that our strategy can improve the utilization of the existing warehouse storage space significantly by about 24%. The CRG method is also tested on basic two-stage two-dimensional CSP benchmarks and its performance is compared to those of other pattern-based methods. The results show its potential for effectively solving the basic two-stage two-dimensional CSPs.

The minimum sum coloring problem (MSCP) is an important extension of the graph coloring problem with wide real-world applications. Compared to the classic graph coloring problem, where lots of methods have been developed and even massive graphs with millions of vertices can be solved well, few works have been done for the MSCP, and no specialized MSCP algorithms are available for solving massive graphs. This paper explores how to solve MSCP on massive graphs, and then proposes a fast local search algorithm for the MSCP based on three main ideas including a coarse-grained reduction method, two kinds of scoring functions and selection rules as well as a novel local search framework. Experiments are conducted to compare our algorithm with several state-of-the-art algorithms on massive graphs. The proposed algorithm outperforms previous algorithms in almost all the massive graphs and also improves the best-known solutions for some conventional instances, which demonstrates the performance and robustness of the proposed algorithm.

Adaptive Large Neighbourhood Search (ALNS) is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 18 years of intensive research into ALNS, the design of an effective adaptive layer for selecting operators to improve the solution remains an open question. In this work, we isolate this problem by formulating it as a Markov Decision Process, in which an agent is rewarded proportionally to the improvement of the incumbent. We propose Graph Reinforcement Learning for Operator Selection (GRLOS), a method based on Deep Reinforcement Learning and Graph Neural Networks, as well as Learned Roulette Wheel (LRW), a lightweight approach inspired by the classic Roulette Wheel adaptive layer. The methods, which are broadly applicable to optimisation problems that can be represented as graphs, are comprehensively evaluated on 5 routing problems using a large portfolio of 28 destroy and 7 repair operators. Results show that both GRLOS and LRW outperform the classic selection mechanism in ALNS, owing to the operator choices being learned in a prior training phase. GRLOS is also shown to consistently achieve better performance than a recent Deep Reinforcement Learning method due to its substantially more flexible state representation. The evaluation further examines the impact of the operator budget and type of initial solution, and is applied to problem instances with up to 1000 customers. The findings arising from our extensive benchmarking bear relevance to the wider literature of hybrid methods combining metaheuristics and machine learning.

Making accurate predictions of the true production frontier is critical for reliable efficiency analysis. However, canonical deterministic methods like Data Envelopment Analysis (DEA) provide approximations of the production frontier that cannot accommodate noise satisfactorily and suffer from overfitting. This study combines machine learning techniques known as Least Squares Boosting (LSB) and Multivariate Adaptive Regression Splines (MARS), to introduce a new methodology that improves the accuracy of production frontiers predictions and overcomes previous limitations. The new method fits pairwise regression splines to the data while ensuring that the predicted production frontiers satisfy certain the required regularity conditions: envelopmentness, monotonicity, and concavity. The method, termed LSB-MAFS, is implemented through computational algorithms, and we illustrate its applicability by performing simulations with several data generating processes. We also compare its performance against the most popular alternatives, considering both deterministic and stochastic scenarios: DEA, bootstrapped DEA, Corrected Concave Non-Parametric Least Squares (C²NLS) and Stochastic Frontier Analysis (SFA). The new method outperforms these alternatives in the most complex scenarios, including stochastic settings where parametric methods like SFA should perform better in principle. We conclude that our approach to production frontier prediction is a valid and competitive alternative for dependable efficiency analysis.