Leading the lean enterprise transformation,by G. Koenigsaecker

This paper first formulates a binary integer programming (BIP) model that minimises C _max for a multi-stage flexible job shop floor with machine compatibility. Due to a computational limitation, the exact optimal model is then relaxed as a linear programming model. The output from the relaxation model then turns into the objective of the BIP-based real-time scheduling (RTS) heuristic model. The RTS heuristic requires an iteration to calculate the final C _max. At each iteration, the RTS heuristic assigns just one job to the earliest available machines. Since the set of jobs and machines included in the RTS model is relatively small, RTS can be solved in a very short computational time. We evaluate an overall effectiveness (in terms of solution quality and run time) of the RTS heuristic by way of computer experiments.     

A loading and dispatching problem in a random flexible manufacturing system

A scheduling problem in a flexible manufacturing system (FMS) is considered to be a composite of two interdependent tasks: loading and sequencing. Formulations are presented for the loading problem with two objectives:

(i) minimization of the system workload unbalance, and

(ii) minimization of system unbalance and the number of late jobs;

including constraints such as the number of tools slots with duplications, unique job routing, nonsplitting of jobs and machine capacity. For both the objectives, heuristic methods are developed and performance is compared with the exact mixed integer programming solutions. A simulation model is developed for investigating the system performance for the problem of minimizing the system unbalance using heuristic and sequential loading methods in conjunction with four—FIFO, SPT, LPT and MOPR—dispatching rules.     

Dry kiln scheduling in furniture production

In this paper, a dry kiln scheduling problem from the furniture manufacturing industry is considered. Factory-specified due dates for orders, kiln availability, kiln capacity, and travel time from the kilns to the factories are all incorporated in a model which is formulated as an integer linear program. The objective of the formulation is to minimize the maximum tardiness of orders arriving at the plants by solving a special case of scheduling n independent jobs on m non-identical parallel ciachines. Because of the computational complexity, and the fact that standard integer programming packages appear to perform very poorly on the problem, a heuristic approach is developed. Computational experience is provided which indicates that the heuristic gives very high quality solutions to problems in near real-time.     

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.     

A constraint-based perspective in resource constrained project scheduling

In this study, a new heuristic approach to the resource constrained project scheduling problem is introduced. This approach, which is called local constraint based analysis (LCBA), is more robust than the dispatching rules found in the literature, since it does not depend on an a priori insight as do the dispatching rules. LCBA consists of the application of local essential conditions which respect the current temporal and resource constraints to generate a necessary sequence of activities at a scheduling decision time point in a single-pass parallel scheduling algorithm. LCBA is a time efficient procedure due to the localized aspect with which the activities are handled. Only the activities which are schedulable at the current scheduling time are considered for the application of the essential conditions. LCBA is tested against well-known rules from the literature and some recently developed rules. This testing is done using a set of problems of a special design and also a set of optimally solved problems from a recent benchmark in the literature. It is observed that near optimal time efficient solutions are obtained by LCBA and the procedure's performance is considerably better than that of the dispatching rules.     

Optimization Models for Scheduling of Jobs

This work is motivated by a particular scheduling problem that is faced by logistics centers that perform aircraft maintenance and modification. Here we concentrate on a single facility (hangar) which is equipped with several work stations (bays). Specifically, a number of jobs have already been scheduled for processing at the facility; the starting times, durations, and work station assignments for these jobs are assumed to be known. We are interested in how best to schedule a number of new jobs that the facility will be processing in the near future. We first develop a mixed integer quadratic programming model (MIQP) for this problem. Since the exact solution of this MIQP formulation is time consuming, we develop a heuristic procedure, based on existing bin packing techniques. This heuristic is further enhanced by application of certain local optimality conditions.     

Job shop scheduling with the option of jobs outsourcing

Incorporating outsourcing in scheduling is addressed by several researchers recently. However, this scope is not investigated thoroughly, particularly in the job shop environment. In this paper, a new job shop scheduling problem is studied with the option of jobs outsourcing. The problem objective is to minimise a weighted sum of makespan and total outsourcing cost. With the aim of solving this problem optimally, two solution approaches of combinatorial optimisation problems, i.e. mathematical programming and constraint programming are examined. Furthermore, two problem relaxation approaches are developed to obtain strong lower bounds for some large scale problems for which the optimality is not proven by the applied solution techniques. Using extensive numerical experiments, the performance of the solution approaches is evaluated. Moreover, the effect the objectives's weights in the objective function on the performance of the solution approaches is also investigated. It is concluded that constraint programming outperforms mathematical programming significantly in proving solution optimality, as it can solve small and medium size problems optimally. Moreover, by solving the relaxed problems, one can obtain good lower bounds for optimal solutions even in some large scale problems.     

Optimal versus heuristic scheduling of surface mount technology lines

This paper presents and compares an exact and a heuristic approach for scheduling of printed wiring board assembly in surface mount technology (SMT) lines. A typical SMT line consists of several assembly stations in series and/or in parallel, separated by finite intermediate buffers. The objective of the scheduling problem is to determine the detailed sequencing and timing of all assembly tasks for each individual board, so as to maximize the line's productivity, which is defined in terms of makespan for a mix of board types. The limited intermediate buffers between stations result in a scheduling problem with machine blocking, where a completed board may remain on a machine and block it until a downstream machine becomes available. In addition, limited machine availability due to scheduled downtimes is considered. The exact approach is based on a mixed integer programming formulation that can be used for optimization of assembly schedules by using commercially available software for integer programming, whereas the heuristic approach is designed as a combination of tabu search and a set of dispatching rules. Numerical examples modelled after real-world SMT lines and some computational results are provided to illustrate and compare the two approaches.     

Towards robustness of response times: minimising the maximum inter-completion time on parallel machines

Motivated by scheduling practices that require a response to unplanned high-priority jobs as soon as possible without preempting any in-processing jobs, this paper considers a deterministic identical parallel machine scheduling problem to achieve robustness with regard to a worst-case response time. To the best of our knowledge, this paper is the first to study the objective of minimising the maximum inter-completion time, i.e. the maximum time difference between any two consecutive completion times of jobs. For this novel scheduling problem, we first show its NP-hardness, and then propose an integer linear programming formulation and three heuristic approaches. Numerical experiments demonstrate the efficiency of our solution methods.     

Mathematical modelling and heuristic approaches to operation scheduling problems in an FMS environment

This paper addresses an operation scheduling problem with the objective of minimizing total tardiness in a flexible manufacturing system with setup time consideration. The addressed problem is first described as a 0?1 integer programming model, and is then solved optimally. Subsequently, a heuristic is proposed to solve the problem in an acceptable running time. The heuristic begins on a schedule generator called ESCH to obtain an initial solution; then two procedures are designed to improve the solution quality. One is a sequence-improving procedure (SIP) for determining a better performance schedule from a certain routing plan; the other is a routing-exchanging procedure (REP) for selecting a good routing plan. Both procedures are achieved by simulated annealing. Computational experiments show that the proposed simulated annealing based heuristic performs well with respect to solution accuracy and efficiency.     

Single machine scheduling problem with batch setups involving positional deterioration effects and multiple rate-modifying activities

This article considers a single machine scheduling problem with batch setups, positional deterioration effects, and multiple optional rate-modifying activities to minimize the total completion time. This problem is formulated as an integer quadratic programming problem. In view of the complexity of optimally solving this problem, a two-phase heuristic algorithm is proposed where an optimal but non-integer solution is obtained in the first phase by solving a continuous relaxed version of the problem. This solution serves as a lower bound for the optimal value of the total completion time. The second phase of the algorithm generates an integer solution using a simple rounding scheme that is optimum or very close to optimum for this problem. Empirical evaluation and comparison with an existing heuristic algorithm show that the proposed heuristic algorithm is substantially more effective in solving large-size problem instances.     

Crane scheduling with time windows in circuit board production lines

This paper studies a crane scheduling problem with time windows in a flow-shop type production system. Feasibility of a state of the system is first discussed. Then, based on the insight derived from the mathematical programming formulation of feasibility, an optimization-based heuristic algorithm for real-time scheduling of the system is developed. Computer simulation on randomly generated problems shows that this algorithm has an excellent performance in maximizing throughput without defective jobs.     

面向订单的生产计划与调度的综合优化

研究了一个多订单环境下的生产计划与调度集成优化问题,以实现准时生产为目标,综合考虑产品装配结构约束的订单任务计划与订单产品零部件的加工调度,采用直接面向客户订单的工序调度模式建立了计划和调度的综合优化整数规划模型.设计了带精英策略的蚁群算法作为该数学模型的求解方法,并通过对比试验为该算法选取最佳的搜索参数.实例仿真结果表明,所建模型的正确性以及蚁群算法求解该问题的可行性和有效性.     

Exact and approximate methods for parallel multiple-area spatial scheduling with release times

Spatial scheduling problems involve scheduling jobs that each require certain amounts of two-dimensional space within a processing area of limited width and length. Thus, this requires not only assigning time slots to each job but also locations and orientations within the limited physical processing space as well. Such problems, often encountered in shipbuilding and aircraft manufacturing, are generally difficult to solve, and there is a relatively small amount of literature addressing these problems compared to other types of scheduling. In this paper, we consider a particularly complex class of spatial scheduling problems that involve scheduling each job into one of several possible processing areas in parallel to minimize the total amount of tardy time. In addition, each job has a release time before which it may not be processed. We introduce two methods for solving this type of problem: an integer programming (IP) model and a heuristic algorithm. We perform computational tests and comparisons of each method over a large number of generated benchmark problems with varying characteristics, and also compare these to a more naïve heuristic. Solving the IP model was effective for small problems but required excessive amounts of time for larger ones. The heuristic was effective and produced solutions of comparable quality to the IP model for many problems while requiring very little computational time.     

Scheduling on a two-machine permutation flow shop under time-of-use electricity tariffs

We consider a two-machine permutation flow shop scheduling problem to minimise the total electricity cost of processing jobs under time-of-use electricity tariffs. We formulate the problem as a mixed integer linear programming, then we design two heuristic algorithms based on Johnson’s rule and dynamic programming method, respectively. In particular, we show how to find an optimal schedule using dynamic programming when the processing sequence is fixed. In addition, we propose an iterated local search algorithm to solve the problem with problem-tailored procedures and move operators, and test the computational performance of these methods on randomly generated instances.     

Minimising interference for scheduling two parallel machines with a single server

In this paper, we consider the problem of scheduling a set of jobs on two parallel machines with set-up times. The set-up has to be performed by a single server. The objective is to minimise the forced idle time. The problem of minimising the forced idle time (interference problem) is known to be unary NP-hard for the case of two machines and equal set-up and arbitrary processing times. We propose a mixed integer linear programming model, which describes a special class of schedules where the jobs from a list are scheduled alternatively on the machines, and a heuristic algorithm is tested on instances with up to 100,000 jobs. The computational results indicate that the algorithm has an excellent performance even for very large instances, where mostly an optimal solution is obtained within a very small computational time.     

Modelling and symmetry breaking in scheduling problems on batch processing machines

Problems of scheduling batch-processing machines to minimise the makespan are widely exploited in the literature, mainly motivated by real-world applications, such as burn-in tests in the semiconductor industry. These problems consist of grouping jobs in batches and scheduling them on machines. We consider problems where jobs have non-identical sizes and processing times, and the total size of each batch cannot exceed the machine capacity. The processing time of a batch is defined as the longest processing time among all jobs assigned to it. Jobs can also have non-identical release times, and in this case, a batch can only be processed when all jobs assigned to it are available. This paper discusses four different versions of batch scheduling problems, considering a single processing machine or parallel processing machines and considering jobs with or without release times. New mixed integer linear programming formulations are proposed as enhancements of formulations proposed in the literature, and symmetry breaking constraints are investigated to reduce the size of the feasible sets. Computational results show that the proposed formulations have a better performance than other models in the literature, being able to solve to optimality instances only considered before to be solved by heuristic procedures.     

Solving Sequencing Problems Through Reordering Operations

An heuristic method is presented for determining low-cost solutions of one-machine scheduling problems with delay costs. The algorithm involves starting with a logically determined initial sequence and then successively improving the sequence by reordering, using insertion, exchange, and displacement operations. Computational results on a set of 197 problems, with up to 40 jobs, are compared to branch and bound, and integer programming computational experience. The reordering algorithm produced optimal solutions for all problems in this set.     

面向节能无关联平行机调度模型及分支定界法

工业企业,特别是高耗能行业,不仅要满足交货期和缩小生产周期的要求,而且不断优化能源配置,降低能耗。研究一类新的以延迟和能源消耗的加权最小为目标的生产调度问题。首先,描述问题并分析问题的复杂性。其次,建立混合整数线性规划模型。进一步,我们提出求解该问题的分支定界算法。最后,通过数值实验和数值试验,验证算法的有效性和高效性。     

Job shop scheduling with a combination of four buffering constraints

In this paper, a new scheduling problem is investigated in order to optimise a more generalised Job Shop Scheduling system with a Combination of four Buffering constraints (i.e. no-wait, no-buffer, limited-buffer and infinite-buffer) called CBJSS. In practice, the CBJSS is significant in modelling and analysing many real-world scheduling systems in chemical, food, manufacturing, railway, health care and aviation industries. Critical problem properties are thoroughly analysed in terms of the Gantt charts. Based on these properties, an applicable mixed integer programming model is formulated and an efficient heuristic algorithm is developed. Computational experiments show that the proposed heuristic algorithm is satisfactory for solving the CBJSS in real time.