HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry

In this paper, we investigate a two-stage lot-sizing and scheduling problem in a spinning industry. A new hybrid method called HOPS (Hamming-Oriented Partition Search), which is a branch-and-bound based procedure that incorporates a fix-and-optimize improvement method is proposed to solve the problem. An innovative partition choice for the fix-and-optimize is developed. The computational tests with generated instances based on real data show that HOPS is a good alternative for solving mixed integer problems with recognized partitions such as the lot-sizing and scheduling problem.     

A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop

In this paper a new mixed-integer linear programming (MILP) model is proposed for the multi-processor open shop scheduling (MPOS) problems to minimize the makespan with considering independent setup time and sequence dependent removal time. A hybrid imperialist competitive algorithm (ICA) with genetic algorithm (GA) is presented to solve this problem. The parameters of the proposed algorithm are tuned by response surface methodology (RSM). The performance of the algorithm to solve small, medium and large sized instances of the problem is evaluated by introducing two performance metrics. The quality of obtained solutions is compared with that of the optimal solutions for small sized instances and with the lower bounds for medium sized instances. Also some computational results are presented for large sized instances.     

Cyclic scheduling for F.M.S.: Modelling and evolutionary solving approach

This paper concerns the domain of flexible manufacturing systems (FMS) and focuses on the scheduling problems encountered in these systems. We have chosen the cyclic behaviour to study this problem, to reduce its complexity. This cyclic scheduling problem, whose complexity is NP-hard in the general case, aims to minimise the work in process (WIP) to satisfy economic constraints. We first recall and discuss the best known cyclic scheduling heuristics. Then, we present a two-step resolution approach. In the first step, a performance analysis is carried out; it is based on the Petri net modelling of the production process. This analysis resolves some indeterminism due to the system’s flexibility and allows a lower bound of the WIP to be obtained. In the second step, after a formal model of the scheduling problem has been given, we describe a genetic algorithm approach to find a schedule which can reach the optimal production speed while minimizing the WIP. Finally, our genetic approach is validated and compared with known heuristics on a set of test problems.     

A graph coloring approach to scheduling of multiprocessor tasks on dedicated machines with availability constraints

We address a generalization of the classical 1- and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipulations we show that the problem of optimal scheduling of sparse tree-like instances can be solved in polynomial time. However, if we admit dense instances then the problem becomes NP-hard, even if there are only two machines.     

一种改进的多模式项目反应性调度问题

既有的项目反应性调度问题只关注了基准调度方案的稳定性,而忽略了项目调度目标的最优实现。本文提出了一种两阶段多模式资源受限项目反应性调度问题。第一阶段,在新的项目执行环境下,对项目进行完全重调度,得到新的最优调度目标值。第二阶段,以新的最优调度目标值为约束,以最大化调度稳定性为目标,求得新的最优调度方案。针对问题特点,基于IBM ILOG优化编程语言OPL和CPLEX V12.8.0,设计出该问题的求解程序。最后,基于标准算例,对本文提出的反应性调度方法、既有的反应性调度方法、完全重调度方法进行了充分的比较测试,结果表明本文提出的反应性调度方法在缩短项目工期、保护基准方案的稳定性方面具有明显优势。     

Fix and Relax Heuristic for a Stochastic Lot-Sizing Problem

This paper addresses a particular stochastic lot-sizing and scheduling problem. The evolution of the uncertain parameters is modelled by means of a scenario tree and the resulting model is a multistage stochastic mixed-integer program. We develop a heuristic approach that exploits the specific structure of the problem. The computational experiments carried out on a large set of instances have shown that the approach provides good quality solutions in a reasonable amount of time.     

Tabu search for discrete–continuous scheduling problems with heuristic continuous resource allocation

Problems of scheduling non-preemptable, independent jobs on parallel identical machines under an additional continuous renewable resource to minimize the makespan are considered. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation that minimize the makespan. A heuristic procedure for allocating the continuous resource is used. The tabu search metaheuristic to solve the considered problem is presented. The results produced by tabu search are compared with optimal solutions for small instances, as well as with the results generated by simple search methods – multi-start iterative improvement and random sampling for larger instances.     

Airline Crew Scheduling: State-of-the-Art

The airline industry is faced with some of the largest scheduling problems of any industry. The crew scheduling problem involves the optimal allocation of crews to flights. Over the last two decades the magnitude and complexity of crew scheduling problems have grown enormously and airlines are relying more on automated mathematical procedures as a practical necessity. In this paper we survey different approaches studied and discuss the state-of-the-art in solution methodology for the airline crew scheduling problem. We conclude with a discussion about promising areas for further work to make it possible to get very good solutions for the crew scheduling problem.     

Group-shop scheduling with sequence-dependent set-up and transportation times

This paper considers a group-shop scheduling problem (GSSP) with sequence-dependent set-up times (SDSTs) and transportation times. The GSSP provides a general formulation including the job-shop and the open-shop scheduling problems. The consideration of set-up and transportation times is among the most realistic assumptions made in the field of scheduling. In this paper, we study the GSSP with transportation and anticipatory SDSTs, where jobs are released at different times and there are several transporters to carry jobs. The objective is to find a job schedule that minimizes the makespan, that is, the time at which all jobs are completed and transported to the warehouse (or to the customer). The problem is formulated as a disjunctive programming problem and then prepared in a form of mixed integer linear programming (MILP). Due to the non-deterministic polynomial-time hardness (NP-hardness) of the GSSP, large instances cannot be optimally solved in a reasonable amount of time. Therefore, a genetic algorithm (GA) hybridized with an active schedule generator is proposed to tackle large-sized instances. Both Baldwinian and Lamarckian versions of the proposed hybrid algorithm are then implemented and evaluated through computational experiments.     

Solving the short-term electrical generation scheduling problem by an adaptive evolutionary approach

In this paper, we introduce an adaptive evolutionary approach to solve the short-term electrical generation scheduling problem (STEGS). The STEGS is a hard constraint satisfaction optimization problem. The algorithm includes various strategies proposed in the literature to tackle hard problems with constraints such as: the representation used a non-binary coding scheme that drastically reduces the search space compared with the traditional evolutionary approaches. Specialized operators are especially designed for this problem and for this kind of representation, which also includes a local search procedure. Furthermore, the algorithm is guided by an adaptive parameter control strategy. We used some very well known benchmarks for STEGS to evaluate our approach. The results are very encouraging and we have obtained new better values for all the systems tested. Our aim here is to show that evolutionary approaches can be considered as good techniques to be used to solve real-world highly constrained problems.     

Estimates of the absolute error and a scheme for an approximate solution to scheduling problems

An approach is proposed for estimating absolute errors and finding approximate solutions to classical NP-hard scheduling problems of minimizing the maximum lateness for one or many machines and makespan is minimized. The concept of a metric (distance) between instances of the problem is introduced. The idea behind the approach is, given the problem instance, to construct another instance for which an optimal or approximate solution can be found at the minimum distance from the initial instance in the metric introduced. Instead of solving the original problem (instance), a set of approximating polynomially/pseudopolynomially solvable problems (instances) are considered, an instance at the minimum distance from the given one is chosen, and the resulting schedule is then applied to the original instance.     

Modeling lotsizing and scheduling problems with sequence dependent setups

Several production environments require simultaneous planing of sizing and scheduling of sequences of production lots. Integration of sequencing decisions in lotsizing and scheduling problems has received an increased attention from the research community due to its inherent applicability to real world problems. A two-dimensional classification framework is proposed to survey and classify the main modeling approaches to integrate sequencing decisions in discrete time lotsizing and scheduling models. The Asymmetric Traveling Salesman Problem can be an important source of ideas to develop more efficient models and methods to this problem. Following this research line, we also present a new formulation for the problem using commodity flow based subtour elimination constraints. Computational experiments are conducted to assess the performance of the various models, in terms of running times and upper bounds, when solving real-word size instances.     

分支定界算法求解带有释放时间的单机双代理调度问题

本文研究了带有释放时间的单机双代理调度问题,目标函数为极小化最大完工时间和。为了便于利用优化软件求解,建立了混合整数规划模型。考虑到该问题具有NP困难性,因此采用近似与精确算法分别求解不同规模问题。针对大规模问题,提出了优势代理优先启发式算法,并证明了其渐近最优性。针对小规模问题,设计了分支定界法进行最优求解,其中基于释放时间的分支规则和基于加工中断的下界有效地减少了运算时间。最后,通过数值测试验证了分支定界算法的有效性以及启发式算法的收敛性。     

Heuristic Control of a Constraint-Based Algorithm for the Preemptive Job-Shop Scheduling Problem

In the recent years, constraint programming has been applied to a wide variety of academic and industrial non-preemptive scheduling problems, i.e., problems in which activities cannot be interrupted. In comparison, preemptive scheduling problems have received almost no attention from both the Operations Research and the Artificial Intelligence community. Motivated by the needs of a specific application, we engaged in a study of the applicability of constraint programming techniques to preemptive scheduling problems. This paper presents the algorithms we developed and the results we obtained on the preemptive variant of the famous job-shop scheduling problem. Ten heuristic search strategies, combined with two different constraint propagation techniques, are presented, and compared using two well-known series of job-shop scheduling instances from the literature. The best combination, which relies on limited discrepancy search and on edge-finding techniques, is shown to provide excellent solutions to the preemptive job-shop scheduling problem. A mean relative distance to the optimal solution of 0.32% is achieved in five minutes, on instances with 10 jobs and 10 machines (100 activities).     

重入排序问题综述

重入排序问题打破传统假设：工件在加工过程中不止一次地访问某台机器,是一种新型的排序问题. 重入的特点源于半导体生产, 并广泛存在于其他领域. 对重入排序问题已有文献中的成果进行梳理和分析,按问题所处机器环境的不同, 对内容和方法进行分类介绍和总结：包括单机问题、流水作业问题、混合流水作业问题及其他机器环境下的重入排序问题. 最后展望未来的趋势和研究方向.     

An Integer Multicommodity Flow Model Applied to the Rerostering of Nurse Schedules

The problem of rerostering service schedules is very common in organizations that work shifts around the clock every day of the year with a set number of employees. Whenever one or more workers announce that they will not be able to attend to tasks previously assigned in their schedule, those tasks must be performed at the expense of alterations in the schedules of other workers. These changes should not conflict with the rules laid down by the administration and employment contracts and should affect the previous schedules as little as possible. This is a difficult real problem calling for a computational tool to cope with it easily. In the paper the issue is described in detail in the context of nurse scheduling and formulated as an integer multicommodity flow problem with additional constraints, in a multi-level acyclical network. A heuristic was implemented as a first approach to solving the problem. Subsequently the integer linear programming formulation of the multicommodity flow model and two linear relaxations were tested using CPLEX [2] optimizers. The computational results reported regard real instances from a Lisbon state hospital. Satisfactory rosters were obtained within acceptable computational times in all instances tested, either with the integer optimizer, or with the heuristic. This being so, refinements will be undertaken to embed these methodologies in a decision support system that may assist the head nurse in her daily rerostering activities.     

Lower Bounds for Scheduling a Single Robot in a Job-Shop Environment

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the traveling salesman problem with time windows, where additionally generalized precedence constraints (minimal time-lags) have to be respected. The objective is to determine a sequence of all nodes and corresponding starting times in the given time windows in such a way that all generalized precedence relations are respected and the sum of all traveling and waiting times is minimized.We calculate lower bounds for this problem using constraint propagation techniques and a linear programming formulation which is solved by a column generation procedure. Computational results are presented for test data arising from job-shop instances with a single transport robot and some modified traveling salesman instances.     

A decomposition approach for the integrated vehicle-crew-roster problem with days-off pattern

The integrated vehicle-crew-roster problem with days-off pattern aims to simultaneously determine minimum cost vehicle and daily crew schedules that cover all timetabled trips and a minimum cost roster covering all daily crew duties according to a pre-defined days-off pattern. This problem is formulated as a new integer linear programming model and is solved by a heuristic approach based on Benders decomposition that iterates between the solution of an integrated vehicle-crew scheduling problem and the solution of a rostering problem. Computational experience with data from two bus companies in Portugal and data from benchmark vehicle scheduling instances shows the ability of the approach for producing a variety of solutions within reasonable computing times as well as the advantages of integrating the three problems.     

Isomorphic scheduling problems

We consider general properties of isomorphic scheduling problems that constitute a new class of pairs of mutually related scheduling problems. Any such a pair is composed of a scheduling problem with fixed job processing times and its time-dependent counterpart with processing times that are proportional-linear functions of the job starting times. In order to introduce the class formally, first we formulate a generic scheduling problem with fixed job processing times and define isomorphic problems by a one-to-one transformation of instances of the generic problem into instances of time-dependent scheduling problems with proportional-linear job processing times. Next, we prove basic properties of isomorphic scheduling problems and show how to convert polynomial algorithms for scheduling problems with fixed job processing times into polynomial algorithms for proportional-linear counterparts of the original problems. Finally, we show how are related approximation algorithms for isomorphic problems. Applying the results, we establish new worst-case results for time-dependent parallel-machine scheduling problems and prove that many single- and dedicated-machine time-dependent scheduling problems with proportional-linear job processing times are polynomially solvable.