Job sequencing with uncertain and controllable processing times

In this paper, a single machine scheduling problem is considered. The jobs' processing times are controllable (i.e., they may take any value within a certain range) and non-precisely defined. They are treated as linguistic variables, whose values are expressed by means of fuzzy numbers. The objective function to be minimised is: (a) the mean flow time cost plus the mean processing cost, and (b) the maximum flow time cost plus the total processing cost. The problem is modelled as an assignment problem and is solved optimally with respect to the defuzzification strategy used.     

A genetic algorithm with tabu search procedure for flexible job shop scheduling with transportation constraints and bounded processing times

In this paper, we propose a model for Flexible Job Shop Scheduling Problem (FJSSP) with transportation constraints and bounded processing times. This is a NP hard problem. Objectives are to minimize the makespan and the storage of solutions. A genetic algorithm with tabu search procedure is proposed to solve both assignment of resources and sequencing problems on each resource. In order to evaluate the proposed algorithm's efficiency, five types of instances are tested. Three of them consider sequencing problems with or without assignment of processing or/and transport resources. The fourth and fifth ones introduce bounded processing times which mainly characterize Surface Treatment Facilities (STFs). Computational results show that our model and method are efficient for solving both assignment and scheduling problems in various kinds of systems.     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.     

Minimizing total tardiness on a single machine with controllable processing times

The concept of time-cost trade-off is commonly considered in PERT/CPM, but it is seldom considered in the scheduling area. Such concept implies that the processing times of jobs are controllable by increasing or decreasing the available resources, such as manpower and equipment. In this paper, we focus on the single machine total tardiness problem with controllable processing times. First, a mixed-integer programming (MIP) model is formulated to find the optimal solution. Then, we propose both a linear programming model and a net benefit of compression (NBC) algorithm to obtain a set of optimal amounts of compression for a given sequence. To solve medium- to large-size problem instances, we develop a heuristic based on the NBC algorithm. To verify the proposed heuristic, the MIP model is used as a comparison for small-size problem instances, whereas for medium- to large-size instances the variable neighborhood search, a useful local search method, is employed. Computational results show that the proposed heuristic has a good performance.     

Single-machine makespan minimization scheduling with nonlinear shortening processing times

In this paper, we consider the single-machine makespan minimization scheduling problem with nonlinear shortening processing times. By the nonlinear shortening processing times, we mean that the processing times of jobs are non-increasing nonlinear functions of their starting times. The computational complexity of the general problem remains an open problem, but we show that even with the introduction of nonlinear shortening processing times to job processing times, some special cases remain polynomially solvable. We also show that an optimal schedule of the general makespan minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm which utilize the V-shaped property is proposed, and computational experiments show that it is effective and efficient in obtaining near-optimal solutions.     

Two-machine flowshop scheduling with intermediate transportation under job physical space consideration

In this paper, we study a coordinated production–transportation scheduling problem in a two-machine flowshop environment where a single transporter may carry several jobs simultaneously as a batch between the machines. Each job has its own physical-space requirement while being loaded into the transporter. The goal is to minimize the makespan. For the jobs with the same size of physical space during transportation, we present a heuristic algorithm with an absolute worst-case ratio of 2 and a polynomial-time optimal algorithm for a special case with given job sequence. For the jobs having different size of physical storage space, a heuristic algorithm is constructed with an absolute worst-case ratio of 7/3 and asymptotic worst-case ratio of 20/9. Computational experiments demonstrate that the two heuristic algorithms developed are capable of generating near-optimal solutions quickly.     

Single CNC machine scheduling with controllable processing times to minimize total weighted tardiness

Advanced manufacturing technologies, such as CNC machines, require significant investments, but also offer new capabilities to the manufacturers. One of the important capabilities of a CNC machine is the controllable processing times. By using this capability, the due date requirements of customers can be satisfied much more effectively. Processing times of the jobs on a CNC machine can be easily controlled via machining conditions such that they can be increased or decreased at the expense of tooling cost. Since scheduling decisions are very sensitive to the processing times, we solve the process planning and scheduling problems simultaneously. In this study, we consider the problem of scheduling a set of jobs on a single CNC machine to minimize the sum of total weighted tardiness, tooling and machining costs. We formulated the joint problem, which is NP-hard since the total weighted tardiness problem (with fixed processing times) is strongly NP-hard alone, as a nonlinear mixed integer program. We proposed a DP-based heuristic to solve the problem for a given sequence and designed a local search algorithm that uses it as a base heuristic.     

Single-machine and flowshop scheduling with a general learning effect model

Learning effects in scheduling problems have received growing attention recently. Biskup [Biskup, D. (2008). A state-of-the-art review on scheduling with learning effect. European Journal of Operational Research, 188, 315–329] classified the learning effect scheduling models into two diverse approaches. The position-based learning model seems to be a realistic assumption for the case that the actual processing of the job is mainly machine driven, while the sum-of-processing-time-based learning model takes into account the experience the workers gain from producing the jobs. In this paper, we propose a learning model which considers both the machine and human learning effects simultaneously. We first show that the position-based learning and the sum-of-processing-time-based learning models in the literature are special cases of the proposed model. Moreover, we present the solution procedures for some single-machine and some flowshop problems.     

Some single-machine and flowshop scheduling problems with a non-linear deterioration function

The deteriorating job scheduling problems have received increasing attention recently. However, most researchers assume that the actual job processing time is a linear function of its starting time. In fact, in some situations, the deterioration rate might increase or decrease as time passes. For example, the temperature of the ingot in the rolling machine might drop at a slower pace as the surface cools down. Thus, the drop of the ingot temperature might have a decreasing rate. On the other hand, the time to control a fire might go dramatically as time passes, and the time to cease a fire might have an increasing rate. In this paper, we propose a new deteriorating model where the deterioration rate might be increasing or decreasing as time passes. Under the proposed model, we provide the optimal solutions for some single-machine problems and some flowshop problems.     

Complexity and algorithms for two-stage flexible flowshop scheduling with availability constraints

This paper considers the two-stage flexible flowshop scheduling problem with availability constraints. We discuss the complexity and the approximability of the problem, and provide some approximation algorithms with finite and tight worst case performance bounds for some special cases of the problem.     

Some single-machine and m-machine flowshop scheduling problems with learning considerations

Scheduling with learning effect has drawn many researchers’ attention since Biskup [D. Biskup, Single-machine scheduling with learning considerations, European Journal of Opterational Research 115 (1999) 173-178] introduced the concept of learning into the scheduling field. Biskup [D. Biskup, A state-of-the-art review on scheduling with learning effect, European Journal of Opterational Research 188 (2008) 315-329] classified the learning approaches in the literature into two main streams. He claimed that the position-based learning seems to be a realistic model for machine learning, while the sum-of-processing-time-based learning is a model for human learning. In some realistic situations, both the machine and human learning might exist simultaneously. For example, robots with neural networks are used in computers, motor vehicles, and many assembly lines. The actions of a robot are constantly modified through self-learning in processing the jobs. On the other hand, the operators in the control center learn how to give the commands efficiently through working experience. In this paper, we propose a new learning model that unifies the two main approaches. We show that some single-machine problems and some specified flowshop problems are polynomially solvable.     

Two-machine flowshop scheduling problem with bounded processing times to minimize total completion time

We consider the two-machine flowshop scheduling problem where jobs have random processing times which are bounded within certain intervals. The objective is to minimize total completion time of all jobs. The decision of finding a solution for the problem has to be made based on the lower and upper bounds on job processing times since this is the only information available. The problem is NP-hard since the special case when the lower and upper bounds are equal, i.e., the deterministic case, is known to be NP-hard. Therefore, a reasonable approach is to come up with well performing heuristics. We propose eleven heuristics which utilize the lower and upper bounds on job processing times based on the Shortest Processing Time (SPT) rule. The proposed heuristics are compared through randomly generated data. The computational analysis has shown that the heuristics using the information on the bounds of job processing times on both machines perform much better than those using the information on one of the two machines. It has also shown that one of the proposed heuristics performs as the best for different distributions with an overall average percentage error of less than one.     

Note on “Single-machine and flowshop scheduling with a general learning effect model” and “Some single-machine and m-machine flowshop scheduling problems with learning considerations”

In this note, we show that the main results in the two papers [C.C. Wu, W.C. Lee, Single-machine and flowshop scheduling with a general learning effect model, Computers and Industrial Engineering 56 (2009) 1553-1558, W.C. Lee, C.C. Wu, Some single-machine and m-machine flowshop scheduling problems with learning considerations, Information Sciences 179 (2009) 3885-3892] are incorrect.     

Resource-constrained flowshop scheduling with separate resource recycling operations

This paper considers the relocation problem arising from public re-development projects cast as a two-machine flowshop scheduling problem. In such a project, some buildings need to be torn down and re-constructed. The two processes of tearing down and re-constructing each building are often viewed as a single operation. However, under certain circumstances, the re-construction process, i.e., the resource recycling process, can be viewed as a separate operation. In this paper we regard these two processes as separate on the assumption that they are handled by different working crews. We formulate the problem as a resource-constrained two-machine flowshop scheduling problem with the objective of finding a feasible re-development sequence that minimizes the makespan. We provide problem formulations, discuss the complexity results, and present polynomial algorithms for various special cases of the problem.     

Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management fields, is no different. The flowshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the flowshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multi-objective permutation flowshop problem. This algorithm is characterised by an effective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and flowtime. Lastly, we use a novel graphical tool to compare the performances of stochastic Pareto fronts based on Empirical Attainment Functions.     

Minimizing the number of tardy jobs on a proportionate flowshop with general position-dependent processing times

In various real life scheduling systems job processing times vary according to the number of jobs previously processed. The vast majority of studies assume a restrictive functional form to describe job processing times. In this note, we address a scheduling problem with the most general job processing time functions. The machine setting assumed is an m-machine proportionate flowshop, and the objective function is minimum number of tardy jobs. We show that the problem can be formulated as a bottleneck assignment problem with a maximum cardinality constraint. An efficient polynomial time (O(n⁴ log n)) solution is introduced.     

Bicriterion scheduling with equal processing times on a batch processing machine

In this paper we consider the problem of scheduling jobs with equal processing times on a single batch processing machine so as to minimize a primary and a secondary criteria. We provide optimal polynomial time algorithms for various combinations of the primary and secondary criteria.     

两台流水机器协调分解调度问题

研究钢管加工流程中一类新型两台机器流水车间调度问题,工件在第一台机器上加工后被分解成多个子工件.对于最小化最大完成时间的情况,给出一个多项式时间的最优算法;对于最小化最大完成时间与惩罚费用之和的情况,给出一个拟多项式时间的动态规划算法;对于考虑生产前运输的最小化最大完成时间的情况,分析了问题的复杂性.证明了第一种情况的最优算法可作为后两种情况的2-近似算法.数值实验表明了算法的有效性.     

Simulation modeling and analysis of tool sharing and part scheduling decisions in single-stage multimachine flexible manufacturing systems

This paper focuses on a simulation-based study of tool sharing problem in single-stage multimachine Flexible Manufacturing Systems. Three different scenarios are considered for investigation. A simulation model has been developed for each of these scenarios. A number of scheduling rules are incorporated in the simulation models for the decisions such as tool request selection and part launching in the context of tool sharing environment. The performance measures evaluated are mean tardiness, conditional mean tardiness and mean flow time. Based on the analysis of the simulation results, the best possible scheduling rule combinations for part launching and tool request selection have been identified for the three scenarios.