Cyclic hoist scheduling in large real-life electroplating lines

This paper addresses cyclic scheduling of a single hoist in large real-life electroplating lines, where a part visits some processing tanks more than once and multiple duplicate tanks are used at some production stages having long processing times. We present a formal analysis of the problem and propose an efficient branch-and-bound algorithm. The developed analytical properties allow us to considerably eliminate dominated or infeasible solutions in the branch-and-bound procedure. Computational results on benchmark and real-life instances show that the algorithm is very efficient in scheduling large electroplating lines.     

Solution algorithms for the number of tardy jobs minimisation scheduling with a time-dependent learning effect

This paper deals with a single-machine scheduling problem with a time-dependent learning effect. The goal is to determine the job sequence that minimise the number of tardy jobs. Two dominance properties, two heuristic algorithms and a lower bound to speed up the search process of the branch-and-bound algorithm are proposed. Computational experiments show that the branch-and-bound algorithm can solve instances up to 18 jobs in a reasonable amount of time, and the proposed heuristic algorithm MFLA performs effectively and efficiently     

Single-track multi-hoist scheduling problem: a collision-free resolution based on a branch-and-bound approach

An analytical mathematical model and a branch-and-bound algorithm for single-track cyclic multi-hoist scheduling problems are proposed. The objective is to minimize the cycle time for a given number of hoists. The collision-free single-track constraints are first formulated as disjunctive inequalities. It is then shown that this formulation is a very strict and necessary condition. To be a sufficient and necessary one, two additional properties, like collision-checking rules, must hold in optimal solutions. It is proved that a solution violating these two properties due to their relaxation is always dominated by a collision-free one. Therefore, these two properties are relaxed in the branch-and-bound algorithm. The computation of lower bounds in the branch-and-bound algorithm requires the solution of a specific linear programming problem, which can be solved by using a graph-based polynomial algorithm. Computational results with both benchmark and randomly generated test instances are presented.     

Mixed-integer linear programming method for multi-degree and multi-hoist cyclic scheduling with time windows

Multi-degree cyclic hoist scheduling and multi-hoist cyclic scheduling are both capable of improving the throughput in an automatic electroplating line. However, previous research on integrated multi-degree and multi-hoist cyclic scheduling is rather limited. This article develops an optimal mixed-integer linear programming model for the integrated multi-degree and multi-hoist cyclic scheduling with time window constraints. This model permits overlap on hoist coverage ranges, and it proposes new formulations to avoid hoist collisions, by which time window constraints and tank capacity constraints are also formulated. A set of available benchmark instances and newly generated instances are solved using the CPLEX solver to test the performance of the proposed method. Computational results demonstrate that the proposed method outperforms the zone partition heuristic without overlapping, and the throughputs are improved by a significant margin using the proposed method, especially for large-size instances.     

Sequencing minimum product sets on mixed-model U-lines to minimise work overload

In a mixed-model assembly line (MMAL), varying models of the same basic product are produced in a facultative sequence. This gives rise to the short-term model sequencing problem, which has to decide on the production sequence of a given number of model copies so that work overload is minimised. Recently, many MMALs have been arranged in ‘U-lines’, where one operator supervises both the entrance and the exit. This paper addresses the model sequencing problem on a paced mixed-model U-line in a cyclic production environment. Some useful properties of the problem are characterised, and the problem is formulated to minimise the steady-state work overload. A branch-and-bound algorithm is proposed to solve small-sized problems, and a heuristic is proposed for practical-sized problems. Numerical experiments on 540 randomly generated instances show that the proposed heuristic can find near-optimal solutions efficiently.     

Single machine scheduling with preventive maintenances

We consider the single machine total flow time problem in which the jobs are non-resumable and the machine is subject to preventive maintenance activities of known starting times and durations. We propose a branch-and-bound algorithm that employs powerful optimality properties and bounding procedures. Our extensive computational studies show that our algorithm can solve large-sized problem instances with up to 80 jobs in reasonable times. We also study a two-alternative maintenance planning problem with minor and major maintenances. We give a polynomial-time algorithm to find the optimal maintenance times when the job sequence is fixed.     

一个改进的单抓钩周期性排序模型及其在自动化学处理线中的应用

计算机控制的抓钩广泛用于自动化学处理线的工件的运送。抓钩的排序直接影响系统的生产率，抓钩排序的目标是对运送进行排序以极大化生产率。当某工序处理时间非常长时，该工序成为瓶颈。为了去除该瓶颈，系统可以为该工序设计多个处理槽，这称为“多重处理槽”问题。本文提出一个改进的混合整数规划模型以求解有“多重处理槽”的单抓钩周期性排序问题的最优解。实例表明所提出的方法是有效的。     

Exact algorithms for the job sequencing and tool switching problem

The job Sequencing and tool Switching Problem (SSP) involves optimally sequencing jobs and assigning tools to a capacitated magazine in order to minimize the number of tool switches. This article analyzes two integer linear programming formulations for the SSP. A branch-and-cut algorithm and a branch-and-bound algorithm are proposed and compared. Computational results indicate that instances involving up to 25 jobs can be solved optimally using the branch-and-bound approach.     

A branch-and-bound algorithm for minimizing the sum of maximum earliness and tardiness with unequal release times

This article addresses the problem of minimizing the sum of maximum earliness and tardiness on a single machine with unequal release times. It is proven that this problem is NP-hard in the strong sense and a branch-and-bound algorithm is developed as an exact method. In the proposed algorithm, modified dispatching rules based on different release times are proposed as the upper bound, while a procedure considering preemption assumption is used to obtain a good lower bound. Also, dominance rules based on no unforced idle time, adjacent pairwise interchanges in the base problem, and job blocks are used to fathom the nodes. In order to evaluate the efficiency of the proposed algorithm, 4,860 instances were randomly generated, varying from 7 to 1,000 jobs. It is shown that the branch-and-bound algorithm was capable of optimally solving 94.1% of the instances, showing its efficiency in solving all problem sizes.     

Working time constraints in operational fixed job scheduling

In this study we consider the operational fixed job scheduling problem under working time limitations. The problem has several practical implications in both production and service operations; however the relevant research is scarce. We analyse pre-emptive and non pre-emptive versions of the problem and its special cases. We provide polynomial-time algorithms for some special cases. We show that the non pre-emptive jobs problem is strongly NP-hard, and propose a branch-and-bound algorithm that employs efficient bounding procedures and dominance properties. We conduct a numerical experiment to observe the effects of parameters on the quality of the solution. The results of our computational tests for the branch-and-bound algorithm reveal that our algorithm can solve the instances with up to 100 jobs in reasonable times. To the best of our knowledge our branch-and-bound algorithm is the first optimisation attempt to solve the problem.     

Cyclic scheduling of a single hoist in extended electroplating lines: a comprehensive integer programming solution

This paper studies the single-hoist cyclic scheduling problem in electroplating systems with two extended features. One extension is that the products must visit some processing tanks more than once (multi-function tanks). Another is that more than one identical tank is used at some stages. These extensions are common in practical electroplating lines and can increase the lines' processing capacity. However, they make the hoist scheduling problem more complicated and little research has been done to optimize the hoist moves in such extended practical systems. In this paper, we develop a comprehensive mixed integer linear programming model to find optimal solutions to the single-hoist cyclic scheduling problem for electroplating lines with these extensions. Examples are given to demonstrate the effectiveness of the model in different types of problems.     

Solution algorithms for single-machine group scheduling with ready times and deteriorating jobs

This article considers the single-machine group scheduling problem with deterioration effect and ready times. The objective of this problem is to determine the sequence of groups and the sequence of jobs to minimize the makespan. To solve the problem, an algorithm based on enumeration, an heuristic algorithm and a branch-and-bound algorithm are developed and exhaustively tested. The computational results show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions and the branch-and-bound algorithm is very effective in obtaining optimal solutions.     

A mixed integer linear programming solution for single hoist multi-degree cyclic scheduling with reentrance

This article considers single hoist multi-degree cyclic scheduling problems with reentrance. Time window constraints are also considered. Firstly, a mixed integer programming model is formulated for multi-degree cyclic hoist scheduling without reentrance, referred to as basic lines in this article. Two valid inequalities corresponding to this problem are also presented. Based on the model for basic lines, an extended mixed integer programming model is proposed for more complicated scheduling problems with reentrance. Phillips and Unger's benchmark instance and randomly generated instances are applied to test the model without reentrance, solved using the commercial software CPLEX. The efficiency of the model is analysed based on computational time. Moreover, an example is given to demonstrate the effectiveness of the model with reentrance.     

Flow shop-sequencing problem with synchronous transfers and makespan minimization

This study considers a permutation flow shop-sequencing problem with synchronous transfers between stations. The objective is to minimize the makespan. It is shown that the problem is strongly NP-hard. A branch-and-bound algorithm together with several lower and upper bounding procedures are developed. The algorithm returns optimal solutions to moderate-sized problem instances in reasonable solution times.     

Hoist Scheduling For A PCB Electroplating Facility

This paper describes a model and associated algorithm for generating maximum throughput cyclic schedules for the movements of a hoist in a PCB electroplating facility. The algorithm is enumerative in nature and involves the solution of linear programming subproblems. Computational experience with schedules for real systems is presented.     

A tabu search algorithm with solution space partition and repairing procedure for cyclic robotic cell scheduling problem

This paper proposes a tabu search (TS) algorithm to solve an NP-hard cyclic robotic scheduling problem. The objective is to find a cyclic robot schedule that maximises the throughput. We first formulate the problem as a linear program, provided that the robot move sequence is given, and reduce the problem to searching for an optimal robot move sequence. We find that the solution space can be divided into some specific subspaces by the maximal number of works-in-process. Then, we propose a TS algorithm to synchronously perform local searches in each subspace. To speed up our algorithm, dominated subspaces are eliminated by lower and upper bounds of the cycle time during the iterations. In the TS, a constructive heuristic is developed to generate initial solutions for each subspace and a repairing procedure is proposed to maintain the feasibility of the solutions generated in the initialisation stage and the neighbours search process. Computational comparison both on benchmark instances and randomly generated instances indicates that our algorithm is efficient for the cyclic robotic scheduling problem.     

DETERMINING OPTIMAL CYCLIC HOIST SCHEDULES IN A SINGLE-HOIST ELECTROPLATING LINE

We consider the problem of determining a maximum throughput cyclic schedule for the operations of a material handling hoist in an automated electroplating line. The proposed algorithm applies a set of simple algebraic inequalities to derive candidate schedules and uses a branch-and-bound-based search process to identify the optimal one. Computational results with both benchmark and random test problems are presented.     

A branch-and-bound algorithm for the single-row equidistant facility layout problem

In this paper, we deal with the single-row equidistant facility layout problem (SREFLP), which asks to find a one-to-one assignment of n facilities to n locations equally spaced along a straight line so as to minimize the sum of the products of the flows and distances between facilities. We develop a branch-and-bound algorithm for solving this problem. The lower bound is computed first by performing transformation of the flow matrix and then applying the well-known Gilmore–Lawler bounding technique. The algorithm also incorporates a dominance test which allows to drastically reduce redundancy in the search process. The test is based on the use of a tabu search procedure designed to solve the SREFLP. We provide computational results for problem instances of size up to 35 facilities. For a number of instances, the optimal value of the objective function appeared to be smaller than the best value reported in the literature.     

双机无等待流水作业调度算法研究

考虑双机无等待流水作业调度问题,此问题中每台机器都受一个非可用时间的约束,工件都有不同的释放时间。机器的非可用性时间间隔是部分重叠并且已知。目标使Makespan(最大流程时间)最小。通过不同的方式计算上限和下限,完善分支定界法。计算机实验结果显示了所述方法的有效性。     

No-wait scheduling of a two-machine flow-shop to minimise the makespan under non-availability constraints and different release dates

In this paper, we consider the two-machine no-wait flow-shop scheduling problem, when every machine is subject to one non-availability constraint and jobs have different release dates. The non-availability intervals of the machines overlap and they are known in advance. We aim to find a non-resumable schedule that minimises the makespan. We propose several lower bounds and upper bounds. These bounding procedures are used in a branch-and-bound algorithm. Computational experiments are carried out on a large set of instances and the obtained results show the effectiveness of our method.