Cyclic Hoist Scheduling Research Articles

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

ABSTRACTMulti-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.

Simultaneous 2D hoist scheduling and production line design for multi-recipe and multi-stage material handling processes

Multi-recipe and Multi-stage Material Handling (M3H) processes are broadly employed in various industries, where hoists are used for job transfer among different processing units. The hoist movement should be optimally scheduled to maximize the production efficiency. In previous studies, the hoist scheduling is based on a given one dimensional (1D) M3H production line, where spatial locations of processing units are already fixed. Such an arrangement totally separates the hoist scheduling from the optimal design of M3H processes and wastes lots of hoist traveling time on job transfer, so that the production efficiency is inherently restricted. In this paper, a novel cyclic hoist scheduling (CHS) method coupling the optimal design of two-dimensional (2D) production line has been developed for the maximum production efficiency of general M3H processes. It can maximize the production efficiency by simultaneously and optimally determining: (i) the hoist movement schedule for handling different types of jobs with different processing recipes; (ii) the allocation of different processing units in optimal 2D spatial locations; and (iii) the assignment of multi-processing capacity to most needed processing units. The developed method also considers tough processing constraints such as the customized production ratio and various processing time limits for every job in each processing units. The efficacy of the developed method has been demonstrated by case studies.

Modeling and optimization of cyclic hoist schedules in an electroplating line

This paper deals with the modeling, analysis and optimization of a specific kind of real industrial problems. This class of problems is known in the literature as Cyclic Hoist Scheduling Problem (CHSP). In such class of problems, several jobs have to flow through a production line according to an ordered bath sequence. The CHSPs appear in the manufacturing facilities to achieve a mass production and to search a repetitive sequence of moves for the hoist. In this paper, we develop P-Temporal Petri Net models to represent the behavior and validate certain qualitative properties of the basic production line. Afterward, complex configurations of the production line are modeled and their properties such as reachability of desired functioning (cyclic operation), deadlock-free, resource sharing and management are checked and validated. A mathematical analysis and a simulation study of all proposed Petri net models are carried out using mathematical fundaments of Petri nets and a Visual Object Net ++ tool. The second part of the paper deals with the development of a mixed integer linear programming models to optimize processing of each line configuration. Optimal manufacturing plans of the studied system with cyclic processing sequences are defined and the feasibility of optimal cyclic scheduling of each configuration is proved.

Hybrid discrete differential evolution algorithm for biobjective cyclic hoist scheduling with reentrance

Cyclic hoist scheduling problems in automated electroplating lines and surface processing shops attract many attentions and interests both from practitioners and researchers. In such systems, parts are transported from a workstation to another by a material handling hoist. The existing literature mainly addressed how to find an optimal cyclic schedule to minimize the cycle time that measures the productivity of the lines. The material handling cost is an important factor that needs to be considered in practice but seldom addressed in the literature. This study focuses on a biobjective cyclic hoist scheduling problem to minimize the cycle time and the material handling cost simultaneously. We consider the reentrant workstations that are usually encountered in real-life lines but inevitably make the part-flow more complicated. The problem is formulated as a biobjective linear programming model with a given hoist move sequence and transformed into finding a set of Pareto optimal hoist move sequences with respect to the bicriteria. To obtain the Pareto optimal or near-optimal front, a hybrid discrete differential evolution (DDE) algorithm is proposed. In this hybrid evolutional algorithm, the population is divided into several subpopulations according to the maximal work-in-process (WIP) level of the system and the sizes of subpopulations are dynamically adjusted to balance the exploration and exploitation of the search. We propose a constructive heuristic to generate initial subpopulations with different WIP levels, hybrid mutation and crossover operators, an evaluation method that can tackle infeasible individuals and a one-to-one greedy tabu selection method. Computational results on both benchmark instances and randomly generated instances show that our proposed hybrid DDE algorithm outperforms the basic DDE algorithm and can solve larger-size instances than the existing ε-constraint method.

A new method of cyclic hoist scheduling for multi-recipe and multi-stage material handling processes

Multi-recipe and multi-stage material handling (M3H) processes are widely employed by various industries where complex multi-product manufacturing and assembly tasks are required. Cyclic hoist scheduling (CHS) could significantly improve the productivity of an M3H process. In this paper, a novel CHS methodology has been developed, which considers employing multiple sub-cycles to efficiently deal with job duality issues associated with multi-capacity processing units. The methodology contains three modeling and solving stages. In Stage I, a mixed-integer linear programing (MILP) model is developed to obtain the optimal solution of a sub-cycle CHS problem with the tolerance of job duality. In Stage II, the obtained solution will be examined to see if the job duality exists. Once a job duality issue is identified, another MILP model in Stage III will be performed to schedule an additional sub-cycle CHS problem, which targets the minimum slot usage discrepancy caused by the identified job duality. After that, the combined CHS solutions from the previous and additional sub-cycles will be fed back to Stage II for the job duality examination again. Iteratively checking and rescheduling between Stages II and III, job duality issues will be eventually eliminated and a full scheduling cycle coupling multiple sub-cycles will be accomplished. The methodology can significantly increase the CHS optimality for M3H processes, which are demonstrated by two case studies.

Robust optimization for the cyclic hoist scheduling problem

This paper deals with the robust optimization for the cyclic hoist scheduling problem with processing time window constraints. The robustness of a cyclic hoist schedule is defined as its ability to remain stable in the presence of perturbations or variations of certain degree in the hoist transportation times. With such a definition, we propose a method to measure the robustness of a cyclic hoist schedule. A bi-objective mixed integer linear programming (MILP) model, which aims to optimize cycle time and robustness, is developed for the robust cyclic hoist scheduling problem. We prove that the optimal cycle time is a strictly increasing function of the robustness and the problem has infinite Pareto optimal solutions. Furthermore, we derive the so-called ideal point and nadir point that define the lower and upper bounds for the objective values of Pareto front. A Pareto optimal solution can be obtained by solving a single-objective MILP model to minimize the cycle time for a given value of robustness or maximize the robustness for a specific cycle time. The single-objective MILP models are solved using commercial optimization software CPLEX. Computational results on several benchmark instances and randomly generated instances indicate that the proposed approach can solve large-scale problems within a reasonable amount of time.

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.

Production-ratio oriented optimization for multi-recipe material handling via simultaneous hoist scheduling and production line arrangement

In multi-recipe and multi-stage material handling (M3H) processes, such as electroplating and polymeric coating, the productivity maximization under a customized production ratio of different types of jobs is an ultimate goal. Cyclic hoist scheduling (CHS) is certainly the most concerned aspect to improve the productivity. However, the production-ratio oriented productivity not only depends on the hoist scheduling, but also substantially relies on the production line arrangement (PLA), i.e., the spatial allocation of various processing units. This is because PLA determines the traveling time for the hoist to perform loaded and free moves among different processing units, which in turn inevitably affects the cyclic scheduling time and thus the total productivity. Therefore, CHS and PLA should be simultaneously optimized for the production-ratio oriented productivity maximization for M3H processes.In this paper, an integrated modeling methodology for productivity maximization of M3H processes has been developed with simultaneous consideration of CHS, PLA, and the customized production ratio. It introduces an MILP model that can successfully address all the major concerned issues for M3H processes, such as multiple recipes, multiple jobs, multi-capacity processing units, diverse processing time requirements, production line arrangement, and the customized production ratio in each cycle production. The efficacy of the proposed methodology is demonstrated by various case studies with in-depth analysis.

Simultaneous mixed-integer dynamic optimization for environmentally benign electroplating

Hoist scheduling, especially cyclic hoist scheduling (CHS), is used to maximize the manufacturing productivity of electroplating processes. Water-reuse network design (WRND) for the electroplating rinsing system targets the optimal water allocation, such that fresh water consumption and wastewater generation are minimized. Currently, there is still a lack of studies on integrating CHS and WRND technologies for electroplating manufacturing. In this paper, a multi-objective mixed-integer dynamic optimization (MIDO) model has been developed to integrate CHS and WRND technologies for simultaneous consideration of productivity and water use efficiency for environmentally benign electroplating. The orthogonal collocation method on finite elements is employed to convert the MIDO problem into a mixed-integer nonlinear programming (MINLP) problem. The efficacy of the methodology is demonstrated by solving a real electroplating example. It demonstrates that the computational methods of production scheduling, process design, and dynamic optimization can be effectively integrated to create economic and environmental win–win situations for the electroplating industry.

Optimal cyclic scheduling of a hoist and multi-type parts with fixed processing times

This paper proposes an exact algorithm to solve a cyclic hoist scheduling problem in a printed circuit board (PCB) electroplating facility, where multi-type parts with fixed processing times are processed in the same time and the parts are not allowed to wait in the tanks or on the hoist. Finding an optimal schedule in such a production line is equivalent to finding two types of related sequences: part input sequence and hoist move sequence. We show that the entering times of the parts are the decision variables of the problem. We formulate our problem using the notion of prohibited intervals and solve it by enumerating the non-prohibited intervals of the decision variables. This enumeration is accomplished more efficiently with a dynamic branch and bound procedure, which utilises relaxed solutions to eliminate redundant non-prohibited intervals in the search process. The proposed algorithm is polynomial in the number of tanks if the number of part types is fixed, but exponential if it is arbitrary. Computational results on randomly generated test instances indicate that the algorithm is effective.

An Evolutionary Approach for the Design and Scheduling of Electroplating Facilities

This paper tackles the Cyclic Hoists Scheduling Problem. This problem is often encountered in electroplating facilities when mass production is required. Then a repetitive sequence of moves is searched for the hoists. We more precisely deal with a global optimization problem that simultaneously considers the design and the scheduling of such production lines. It consists in studying systems integrating several transportation resources, called hoists, by minimizing the cycle time, while minimizing the number of hoists used. To achieve these goals, we use an evolutionary approach. The encoding of one solution is based on the representation of the empty moves of the hoists. To evaluate each individual, we propose a linear programming model. This one both verifies the satisfaction of constraints and provides the best cycle time for the considered number of hoists. This contribution describes a promising approach to solving a simple version of this problem, namely cyclic hoist scheduling, based on Evolutionary Algorithms (EAs), which is an optimization method inspired by biological evolution models. The issues of solution encoding and specialised genetic operators with a repair procedure of the infeasible solutions are discussed. Some results are presented with benchmark examples.

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.

Graph-Assisted Cyclic Hoist Scheduling for Environmentally Benign Electroplating

Hoist scheduling is a class of production scheduling of batch systems in the manufacturing industries. Cyclic hoist scheduling (CHS) is a type of hoist scheduling that deals with the scheduling that involves one hoist and produces some type of product in a multistage production line. The only “resource” in the production is the hoist for which various operations compete with each other in every production cycle. Currently available CHS approaches, regardless of whether they are algorithmic or heuristic based, are almost all designed to maximize the production rate by optimizing hoist movements; environmental issues are not a concern during development of the hoist schedule. This paper introduces a methodology for solving a general CHS problem where the production rate and waste reduction are simultaneously taken into account. Using this methodology, all feasible hoist schedules for a given CHS problem can be rapidly identified using a graph-assisted search algorithm. The schedules are then evaluated in terms of waste minimization capability, using the corresponding operational strategies. In evaluation, the system dynamics associated with each selected feasible hoist schedule is examined. A final hoist schedule is the best for maximum production rate and minimum waste generation. The efficacy of the methodology is demonstrated by solving an industrial electroplating example.

A polynomial algorithm for no-wait cyclic hoist scheduling in an extended electroplating line

This paper addresses cyclic hoist scheduling in a no-wait electroplating line where a part visits some processing tanks more than once and multiple duplicate tanks are used at some production stages. We prove that such an extended problem can be solved in polynomial time.

The Minimum Common-Cycle Algorithm for Cyclic Scheduling of Two Material Handling Hoists with Time Window Constraints

The problem of cyclic scheduling of two hoists is defined as follows. There are N + 1 workstations, S0, S1, …, SN, and two identical hoists that move jobs between stations. Jobs are identical and each job has to visit all stations in the order that stations are numbered. It is assumed that the hoist traveling times between stations are given constants. Each station can hold one job at a time, and each job must remain at station Si, for a period of at least ai and at most bi time units. Both ai and bi, i = 2, …, N, are given constants. Define mi, 0 ≤ i ≤ N, to be a move of a job from Si to Si+1. A cyclic schedule determines the order of N + 1 moves, mi, i = 0, 1, …, N, an assignment of these moves to hoists, and the start time of the moves in a cycle. The problem is to find a cyclic schedule that minimizes the total time (the cycle time) to complete all the N + 1 moves. Previous approaches toward solving cyclic hoist scheduling problems have been limited to single-hoist cases. In this paper, we propose a heuristic algorithm that finds schedules for systems with two hoists, and discuss an extension to the problem with more than two hoists. The algorithm uses a partitioning approach by which a system is partitioned into two sets of contiguous workstations and each hoist is assigned to a set. A sequence of alternative partitions is evaluated. For each partition, two single-hoist subproblems are formed and the optimal (minimal) cycle time for each subproblem is independently computed. The two optimal single-hoist schedules are then coupled and refined into a feasible two-hoist schedule with a common-cycle time for both hoists. The best of the generated schedules, that results in the minimum common-cycle time among the different partitions, is given as the final solution. Computational experience with both randomly generated problems and a benchmark problem arising from a real system is discussed.