An optimization approach for the lot sizing and scheduling problem in the brewery industry

This study considers a production lot sizing and scheduling problem in the brewery industry. The underlying manufacturing process can be basically divided into two main production stages: preparing the liquids including fermentation and maturation inside the fermentation tanks; and bottling the liquids on the filling lines, making products of different liquids and sizes. This problem differs from other problems in beverage industries due to the relatively long lead times required for the fermentation and maturation processes and because the “ready” liquid can remain in the tanks for some time before being bottled. The main planning challenge is to synchronize the two stages (considering the possibility of a “ready” liquid staying in the tank until bottling), as the production bottlenecks may alternate between these stages during the planning horizon. This study presents a novel mixed integer programming model that represents the problem appropriately and integrates both stages. In order to solve real-world problem instances, MIP-based heuristics are developed, which explore the model structure. The results show that the model is able to comprise the problem requirements and the heuristics produce relatively good-quality solutions.     

Variable neighborhood search based approaches to a vehicle scheduling problem in agriculture

A vehicle scheduling problem (VSP) that arises from sugar beet transportation within minimum working time under the set of constraints reflecting a real‐life situation is considered. A mixed integer quadratically constrained programming (MIQCP) model of the considered VSP and reformulation to a mixed integer linear program (MILP) are proposed and used within the framework of Lingo 17 solver, producing optimal solutions only for small‐sized problem instances. Two variants of the variable neighborhood search (VNS) metaheuristic—basic VNS (BVNS) and skewed VNS (SVNS) are designed to efficiently deal with large‐sized problem instances. The proposed VNS approaches are evaluated and compared against Lingo 17 and each other on the set of real‐life and generated problem instances. Computational results show that both BVNS and SVNS reach all known optimal solutions on small‐sized instances and are comparable on medium‐ and large‐sized instances. In general, SVNS significantly outperforms BVNS in terms of running times.     

An integer programming column generation principle for heuristic search methods

There is an increasing interest in integrating column generation and heuristic approaches to efficiently solve large‐scale discrete optimisation problems. We contribute in this direction. Based on the insights from Lagrangian duality theory, we present an auxiliary problem that can be used for finding near‐optimal solutions to a discrete column‐oriented model. The structure of this auxiliary problem makes it suitable for being addressed with a heuristic search method involving column generation. To this end, we suggest a large neighbourhood search strategy where the repair step is to solve a column generation type subproblem. The suggested search strategy and mathematical models involved need to be tailored to the problem structure. To illustrate important design options and computational behaviour, four applications are studied: bin packing, generalised assignment, a resource allocation problem and the fixed‐charge transportation problem.     

A new ILS algorithm for parallel machine scheduling problems

This paper addresses the non-preemptive scheduling problem of scheduling jobs on identical parallel machines to minimize the maximum completion time or makespan. The problem has been proved to be NP-hard in the strong sense. The NP-hardness of the problem motivates us to develop a new methodology to obtain near-optimal solutions. We formulate the problem as an integer programming and then propose a new iterated local search (ILS) algorithm based on a variable number of cyclic exchanges to solve it. The properties of the solutions are derived and the results are used to improve the computational efficiency of our algorithm. Computational experiments show that the cyclic exchange neighborhood embedded in an iterated local search framework is effective for solving the scheduling problems with up to 1000 jobs and 40 machines within a reasonable amount of computation time. Received: April 2005 / Accepted: January 2006     

化工工业多品种成批轮番生产的集成分批与调度

针对化工工业流程式多品种成批轮番生产集成分批与调度问题,分析多阶段、共享设备、物料输入输出变动转化率、库存限制和品种切换调整时间的工艺特点,建立连续时间表示的混合整数线性规划模型,提出二维粒子群优化算法。设计粒子编码为生产设备的加工状态,通过有效的解码程序将粒子解释为分批和调度。算法采用收缩算子提高局部求精能力,并引入发散算子和速度扰动策略保持种群的多样性。实验结果表明了所提出的算法具有良好的性能。     

求解零空闲流水线调度问题的改进蚁群算法*

在研究蚁群算法的基础上,解决零空闲流水线调度问题的最大完工时间。改进了蚁群算法中信息素密度的初始化方法和更新规则,结合快速邻域搜索算法,解决算法易陷入局部收敛的缺点,提出了该算法解决零空闲调度问题的最佳求解策略。仿真实验表明,该算法具有高效性和优越性。     

A heuristic to solve the synchronized log-truck scheduling problem

We present a synchronized routing and scheduling problem that arises in the forest industry, as a variation of the log-truck scheduling problem. It combines routing and scheduling of trucks with specific constraints related to the Canadian forestry context. This problem includes aspects such as pick-up and delivery, multiple products, inventory stock, multiple supply points and multiple demand points. We developed a decomposition approach to solve the weekly problem in two phases. In the first phase we use a MIP solver to solve a tactical model that determines the destinations of full truckloads from forest areas to woodmills. In the second phase, we make use of two different methods to route and schedule the daily transportation of logs: the first one consists in using a constraint-based local search approach while the second one is a hybrid approach involving a constraint programming based model and a constraint-based local search model. These approaches have been implemented using COMET2.0. The method, was tested on two industrial cases from forest companies in Canada.     

Integer linear programming for a cutting problem in the wood-processing industry: a case study

In this paper, the authors present a case study from the wood-processing industry. It focuses on a cutting process in which material from stock is cut down in order to provide the items required by the customers in the desired qualities, sizes, and quantities. In particular, two aspects make this cutting process special. Firstly, the cutting process is strongly interdependent, with a preceding handling process, which, consequently, cannot be planned independently. Secondly, if the trim loss is of a certain minimum size, it can be returned into stock and used as input to subsequent cutting processes. In order to reduce the cost of the cutting process, a decision support tool has been developed that incorporates an integer linear programming model as a central feature. The model is described in detail, and experience from the application of the tool is reported.     

Multi-start iterated local search metaheuristic for the multi-mode resource-constrained project scheduling problem

In this paper a multi-start iterated local search (MS-ILS) algorithm is presented as a new and effective approach to solve the multi-mode resource-constrained project scheduling problem (MRCPSP). The MRCPSP is a well-known project scheduling NP-Hard optimization problem, in which there is a trade-off between the duration of each project activity and the amount of resources they require to be completed. The proposed algorithm generates an initial solution, performs a local search to obtain a local optimum, subsequently, for a certain number of iterations, makes a perturbation to that local optimum and performs a new local search on the perturbed solution. This whole process then restarts with a different initial solution for a certain number of restarts. The algorithm was tested on benchmark instances of projects with 30, 50 and 100 activities from well-known libraries. The obtained results were compared to recent benchmark results from the literature. The proposed algorithm outperforms other solution methods found in related literature for the largest tested instances (100 activities), while for smaller instances it shows to be quite competitive, in terms of the average deviation against known lower bounds.     

带释放时间的并行机调度问题的ILS & SS算法

研究工件带释放时间的两类并行机最小化总完成时间的调度问题.针对问题提出了一种新的基于变深度环交换邻域结构的Iterated local search(ILS)算法.1)提出了变深度环交换邻域结构.2)基于变深度环交换和传统Swap的混合邻域,提出了带有两种kick策略的ILS算法.3)为了加强ILS逃出局部最优的能力,将Scatter search (SS)搜索方法引入了ILS算法中;算法将当前最好解和次好解进行分散处理,再从处理后的解开始继续迭代.为了验证算法的有效性,对两类并行机问题分别随机产生100组数据进行试验.实验结果表明:对于同构并行机问题,引入SS的ILS算法的计算结果与下界的平均偏差为0.99%,而没有引入SS的ILS算法的为1.06%;对于无关并行机问题,引入SS搜索方法后,ILS算法的计算结果 改进了6.06%,并明显优于多点下降算法.     

An effective heuristic for flexible job-shop scheduling problem with maintenance activities

Most production scheduling problems, including the standard flexible job-shop scheduling problem (FJSP), assume that machines are continuously available. However, in most realistic situations, machines may become unavailable during certain periods due to preventive maintenance (PM). In this paper, a flexible job-shop scheduling problem with machine availability constraints is considered. Each machine is subject to preventive maintenance during the planning period and the starting times of maintenance activities are either flexible in a time window or fixed beforehand. Moreover, two cases of maintenance resource constraint are considered: sufficient maintenance resource available or only one maintenance resource available. To deal with this variant FJSP problem with maintenance activities, a filtered beam search (FBS) based heuristic algorithm is proposed. With a modified branching scheme, the machine availability constraint and maintenance resource constraint can be easily incorporated into the proposed algorithm. Simulation experiments are conducted on some representative problems. The results demonstrate that the proposed filtered beam search based heuristic algorithm is a viable and effective approach for the FJSP with maintenance activities.     

On the asymptotic optimality and improved strategies of SPTB heuristic for open-shop scheduling problem

This article investigates the open-shop scheduling problem with the optimal criterion of minimising the sum of quadratic completion times. For this NP-hard problem, the asymptotic optimality of the shortest processing time block (SPTB) heuristic is proven in the sense of limit. Moreover, three different improvements, namely, the job-insert scheme, tabu search and genetic algorithm, are introduced to enhance the quality of the original solution generated by the SPTB heuristic. At the end of the article, a series of numerical experiments demonstrate the convergence of the heuristic, the performance of the improvements and the effectiveness of the quadratic objective.     

The distributed permutation flowshop scheduling problem

This paper studies a new generalization of the regular permutation flowshop scheduling problem (PFSP) referred to as the distributed permutation flowshop scheduling problem or DPFSP. Under this generalization, we assume that there are a total of F identical factories or shops, each one with m machines disposed in series. A set of n available jobs have to be distributed among the F factories and then a processing sequence has to be derived for the jobs assigned to each factory. The optimization criterion is the minimization of the maximum completion time or makespan among the factories. This production setting is necessary in today's decentralized and globalized economy where several production centers might be available for a firm. We characterize the DPFSP and propose six different alternative mixed integer linear programming (MILP) models that are carefully and statistically analyzed for performance. We also propose two simple factory assignment rules together with 14 heuristics based on dispatching rules, effective constructive heuristics and variable neighborhood descent methods. A comprehensive computational and statistical analysis is conducted in order to analyze the performance of the proposed methods.     

Optimal cyclic single crane scheduling for two parallel train oilcan repairing lines

Crane is widely used to move a heavy object from one place to another not only in manufacturing industry but also service industry. As an important resource in the train oilcan repairing, crane scheduling affects directly the productivity of the systems. In this paper, we study cyclic single crane scheduling problem with two parallel train oilcan repairing lines, where jobs are loaded into the line at one end and unloaded at the other end. The processing time at each workstation must be within a given range. There is no buffer between these stations. A crane is used to move jobs between the workstations in two parallel lines. The objective is to schedule the moves to minimize the production cycle. We proposed a time way diagram for two parallel lines and developed a mixed integer linear programming model. Then we extended the model to the scheduling problem with multi-station to eliminate the bottleneck in lines. Examples are given to demonstrate the effectiveness of the model.     

A genetic algorithm-based approach for solving the resource-sharing and scheduling problem

We introduce a heuristic that is based on a unique genetic algorithm (GA) to solve the resource-sharing and scheduling problem (RSSP). This problem was previously formulated as a continuous-time mixed integer linear programming model and was solved optimally using a branch-and-bound (B&B) algorithm. The RSSP considers the use of a set of resources for the production of several products. Producing each product requires a set of operations with precedence relationships among them. Each operation can be performed using alternative modes which define the subset of the resources needed, and an operation may share different resources simultaneously. The problem is to select a single mode for each operation and accordingly to schedule the resources, while minimizing the makespan time. The GA we propose is based on a new encoding schema that adopts the structure of a DNA in nature. In our experiments we compared the effectiveness and runtime of our GA versus a B&B algorithm and two truncated B&B algorithms that we developed on a set of 118 problem instances. The results demonstrate that the GA solved all the problems (10 runs each), and reaches optimality in 75% of the runs, had an average deviation of less than 1% from the optimal makespan, and a runtime that was much less sensitive to the size of the problem instance.     

A tabu search heuristic for the quay crane scheduling problem

This paper proposes a tabu search heuristic for the Quay Crane Scheduling Problem (QCSP), the problem of scheduling a fixed number of quay cranes in order to load and unload containers into and from a ship. The optimality criterion considered is the minimum completion time. Precedence and non-simultaneity constraints between tasks are taken into account. The former originate from the different kind of operations that each crane has to perform; the latter are needed in order to avoid interferences between the cranes. The QCSP is decomposed into a routing problem and a scheduling problem. The routing problem is solved by a tabu search heuristic, while a local search technique is used to generate the solution of the scheduling problem. This is done by minimizing the longest path length in a disjunctive graph. The effectiveness of our algorithm is assessed by comparing it to a branch-and-cut algorithm and to a Greedy Randomized Adaptive Search Procedure (GRASP).     

An iterative time‐bucket refinement algorithm for a high‐resolution resource‐constrained project scheduling problem

We consider a resource‐constrained project scheduling problem originating in particle therapy for cancer treatment, in which the scheduling has to be done in high resolution. Traditional mixed integer linear programming techniques such as time‐indexed formulations or discrete‐event formulations are known to have severe limitations in such cases, that is, growing too fast or having weak linear programming relaxations. We suggest a relaxation based on partitioning time into so‐called time‐buckets. This relaxation is iteratively solved and serves as basis for deriving feasible solutions using heuristics. Based on these primal and dual solutions and bounds, the time‐buckets are successively refined. Combining these parts, we obtain an algorithm that provides good approximate solutions soon and eventually converges to an optimal solution. Diverse strategies for performing the time‐bucket refinement are investigated. The approach shows excellent performance in comparison to the traditional formulations and a metaheuristic.     

A new heuristic algorithm for the operating room scheduling problem

Due to the great importance of operating rooms in hospitals, this paper studies an operating room scheduling problem with open scheduling strategy. According to this strategy, no time slot is reserved for a particular surgeon. The surgeons can use all available time slots. Based on Fei et al.’s model which is considered to be close to reality, we develop a heuristic algorithm to solve it. The idea of this heuristic algorithm is from dynamic programming by aggregating states to avoid the explosion of the number of states. The objective of this paper is to design an operating program to maximize the operating rooms’ use efficiency and minimize the overtime cost. Computational results show that our algorithm is efficient, especially for large size instances where our algorithm always finds feasible solutions while the algorithm of Fei et al. does not.     

考虑多类型时间依赖资源约束的敏捷卫星调度优化

随着现代空间科技的迅猛发展, 光学遥感图像数据的应用需求越来越广泛, 大力推动了光学对地观测卫星的发展. 然而, 由于高昂的发射成本的约束, 对地观测卫星的资源是有限的, 远远无法满足各类数据需求. 因此, 提高对地观测卫星的使用效率, 提高其任务执行率, 具有非常重要的应用价值. 本文聚焦于敏捷对地观测卫星的任务调度问题, 即在给定的调度周期内, 对有限的卫星资源制定合理的任务调度方案, 在满足一定星上资源约束下, 最大化观测任务收益. 该问题难点在于星上的资源是非常有限的, 例如存储图像数据的固存资源、用于采集数据和卫星姿态切换的能量资源及执行任务活动耗费的时间资源. 需要注意的是, 能量消耗量和时间消耗量依赖于任务的执行时间, 这是敏捷卫星相对传统的非敏捷卫星独有的特性. 不同任务场景对不同类型资源的需求不同, 多种资源约束互相耦合, 资源约束具有时间依赖特性, 这些难点无疑极大地增加了卫星调度的求解难度. 为高效地求解该问题,本文构建了多类型时间依赖资源约束的敏捷卫星调度整数规划模型, 并针对问题特性提出了一种基于自适应选择因子的迭代局部搜索启发式算法. 自适应选择因子综合考虑了目标收益、资源消耗量、资源约束的松弛量, 采用动态变化的资源重要度, 能快速自适应地根据当前场景下各种类型的资源数据使用量来确定最佳局部搜索方向, 从而在有限时间内找到高质量的解. 实验结果证明, 本文所提出的算法在多种情况下相比当前最好算法求解效果显著更优. 此外, 算法独有的自适应选择因子相比传统的选择因子的求解质量更高, 这是因为所设计的自适应选择因子兼顾了目标收益和资源消耗量之间权衡关系的同时, 采用动态变化的资源重要度准确捕捉了资源需求的迫切程度.     

Optimizing multiship routing and scheduling with constraints on inventory levels in a Brazilian oil company

This study addresses a real‐life multiship routing and scheduling application with inventory constraints that arises in pickup and delivery operations of different types of crude oil from various offshore oil rigs (platforms) to coastal terminals. Oil transportation largely results from the need to maintain inventories at each supply point (platform) between minimum and maximum levels, considering production rates in these operational points, and to meet demands of different oils in the terminals within the planning time horizon. Routing and scheduling of the available fleet aims to obtain solutions of minimum total costs, subject to various constraints such as the maximum volume of cargo carried on each ship, simultaneous cargo unloading in some terminals, conditions that rule ship docking in offshore platforms and terminal berths, among others. In this research, we modify and extend inventory constrained maritime routing and scheduling models to appropriately represent the problem of a case study at a Brazilian company and to solve small‐to‐moderate instances based on real data. We also present a matheuristic to deal with larger problem instances. Solution evaluation by company experts indicates that the model and this hybrid heuristic properly represent the problem and highlights the potential of their application in practice.