Job scheduling with forbidden setups and two objectives using genetic algorithms and penalties

One of the most important tasks in service and manufacturing systems is how to schedule arriving jobs such that some criteria will be satisfied. Up to now there have been defined a great variety of scheduling problems as well as corresponding models and solution approaches. Most models suffer from such more or less restrictive assumptions like single machine, unique processing times, zero set-up times or a single criterion. On the other hand some classical approaches like linear or dynamic programming are practicable for small-size problems only. Therefore over the past years we can observe an increasing application of heuristic search methods. But scheduling problems with multiple machines, forbidden setups and multiple objectives are scarcely considered. In our paper we apply a Genetic Algorithm to such a problem which was found at a continuous casting plant. Because of the forbidden setups the probability for a random generated schedule to be feasible is nearly zero. To resolve this problem we use three kinds of penalties, a global, a local and a combined approach. For performance investigations of these penalty types we applied our approaches to a real world test instance with 96 jobs, three machines and two objectives. We tested five different penalty levels with 51 independent runs to evaluate the impact of the penalties.     

A partial enumeration heuristic for multi-objective flowshop scheduling problems

This paper addresses the flowshop scheduling problem with multiple performance objectives in such a way as to provide the decision maker with approximate Pareto optimal solutions. It is well known that the partial enumeration constructive heuristic NEH and its adaptations perform well for single objectives such as makespan, total tardiness and flowtime. In this paper, we develop a similar heuristic using the concept of Pareto dominance when comparing partial and complete schedules. The heuristic is tested on problems involving combinations of the above criteria. For the two-machine case, and the pairs of objectives: (i) makespan and maximum tardiness, (ii) makespan and total tardiness, the heuristic is compared with branch-and-bound algorithms proposed in the literature. For two and more than two machines, and the criteria combinations considered in this article, the heuristic performance is tested against constructive heuristics reported in the literature. By means of an illustrative example, it is shown that a genetic algorithm from the literature performs better when starting from heuristic solutions rather than random solutions.     

Minimizing makespan in a two-machine flowshop scheduling with batching and release time

This paper studies two-machine flowshop scheduling with batching and release time, whose objective is to minimize the makespan. We formulate the scheduling problem as a mixed integer programming model and show that it is a strongly NP-hard problem. We derive a lower bound and develop dynamic programming-based heuristic algorithms to solve the scheduling problem. Computational experiments are carried out to evaluate the performance of the heuristic algorithms. The numerical results show that some of the heuristic algorithms can indeed find effective solutions for the scheduling problem.     

Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system

This paper addresses lot sizing and scheduling problem of a flow shop system with capacity constraints, sequence-dependent setups, uncertain processing times and uncertain multi-product and multi-period demand. The evolution of the uncertain parameters is modeled by means of probability distributions and chance-constrained programming (CCP) theory. A new mixed-integer programming (MIP) model with big bucket time approach is proposed to formulate the problem. Due to the complexity of problem, two MIP-based heuristics with rolling horizon framework named non-permutation heuristic (NPH) and permutation heuristic (PH) have been performed to solve this model. Also, a hybrid meta-heuristic based on a combination of simulated annealing, firefly algorithm and proposed heuristic for scheduling is developed to solve the problem. Additionally, Taguchi method is conducted to calibrate the parameters of the meta-heuristic and select the optimal levels of the algorithm’s performance influential factors. Computational results on a set of randomly generated instances show the efficiency of the hybrid meta-heuristic against exact solution algorithm and heuristics.     

Crane scheduling in container yards with inter-crane interference

This paper examines the problem of scheduling multiple yard cranes to perform a given set of jobs with different ready times in a yard zone with only one bi-directional travelling lane. Due to sharing of the travelling lane among two or more yard cranes, inter-crane interference, a planned move of a yard crane blocked by the other yard cranes, may happen. The scheduling problem is formulated as an integer program. It is noted that the scheduling problem is NP-complete. This research develops a dynamic programming-based heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. Computational experiments are carried out to evaluate the performance of the heuristic and the results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 7.3% above their lower bounds.     

Scheduling in network flow shops

We consider the general problem of static scheduling of a set of jobs in a network flow shop. In network flow shops, the scheduler not only has to sequence and schedule but also must concurrently determine the process routing of the jobs through the shop. In this paper, we establish the computational complexity of this new class of scheduling problem and propose a general purpose heuristic procedure. The performance of the heuristic is analyzed when makespan, cycle time and average flow time are the desired objectives.This research has been supported by the UCLA Academic Senate Grant #95.     

A variable neighbourhood search for hybrid flow-shop scheduling problem with rework and set-up times

This paper deals with hybrid flow-shop scheduling problem with rework. In this problem, jobs are inspected at the last stage, and poorly processed jobs were returned and processed again. Thus, a job may visit a stage more than once, and we have a hybrid flow-shop with re-entrant flow. This kind of a shop may occur in many industries, such as final inspection system in automotive manufacturing. The criterion is to minimize the makespan of the system. We developed a 0–1 mixed-integer program of the problem. Since the hybrid flow-shop scheduling problem is NP-hard, an algorithm for finding an optimal solution in polynomial time does not exist. So we generalized some heuristic methods based on several basic dispatching rules and proposed a variable neighbourhood search (VNS) for the problem with sequence-dependent set-up times and unrelated parallel machines. The computational experiments show that VNS provides better solutions than heuristic methods.     

Two-stage open shop scheduling with a bottleneck machine

It is known that for the open shop scheduling problem to minimize the makespan there exists no polynomial-time heuristic algorithm that guarantees a worst-case performance ratio better than 5/4, unless P≠NP. However, this result holds only if the instance of the problem contains jobs consisting of at least three operations. This paper considers the open shop scheduling problem, provided that each job consists of at most two operations, one of which is to be processed on one of the m⩾2 machines, while the other operation must be performed on the bottleneck machine, the same for all jobs. For this NP-hard problem we present a heuristic algorithm and show that its worst-case performance ratio is 5/4.     

Two-machine flowshop scheduling problems involving a batching machine with transportation or deterioration consideration

This paper considers two scheduling problems for a two-machine flowshop where a single machine is followed by a batching machine. The first problem is that there is a transporter to carry the jobs between machines. The second problem is that there are deteriorating jobs to be processed on the single machine. For the first problem with minimizing the makespan, we formulate it as a mixed integer programming model and then prove that it is strongly NP-hard. A heuristic algorithm is proposed for solving this problem and its worst case performance is analyzed. The computational experiments are carried out and the numerical results show that the heuristic algorithm is effective. For the second problem, we derive the optimal algorithms with polynomial time for minimizing the makespan, the total completion time and the maximum lateness, respectively.     

A heuristic approach to a single stage assembly problem with transportation allocation

Determining assembly scheduling and transportation allocation are two practical problems that industries face, such as the electronics and health products industries. Problems associated with assembly scheduling mainly focus on how to determine the orders’ processing sequence on the assembly line in order to minimize the waiting times before they are flown to their destinations. Problems associated with transportation allocation arise in the system of assigning processed orders to transport modes with the purpose of minimizing penalties from earliness and tardiness. To minimize overall delivery costs, businesses should decide on assembly scheduling and transportation allocation decision simultaneously. However, since simultaneously making these two decisions is not an easy task, most of the works done on them usually deal with these two problems separately. Apart from previous works, this paper establishes a mixed integer programming model that deals with these problems simultaneously. Due to the computational complexity of the problem, this paper develops a hybrid heuristic algorithm to solve this problem, and we evaluate the performance of the presented heuristic algorithm with the well-known GAMS/BARON and Lingo commercial software, which tests the heuristic algorithm on randomly-generated problems. The presented heuristic algorithm is shown to perform well compared with well-known commercial software.     

Real-world flexible resource profile scheduling with multiple criteria: learning scalarization functions for MIP and heuristic approaches

This article addresses a scheduling problem for a chemical research laboratory. Activities with potentially variable, non-rectangular resource allocation profiles must be scheduled on discrete renewable resources. A mixed-integer programming (MIP) formulation for the problem includes maximum time lags, custom resource allocation constraints, and multiple nonstandard objectives. We present a list scheduling heuristic that mimics the human decision maker and thus provides reference solutions. These solutions are the basis for an automated learning-based determination of coefficients for the convex combination of objectives used by the MIP and a dedicated variable neighborhood search (VNS) approach. The development of the VNS also involves the design of new neighborhood structures that prove particularly effective for the custom objectives under consideration. Relative improvements of up to 60% are achievable for isolated objectives, as demonstrated by the final computational study based on a broad spectrum of randomly generated instances of different sizes and real-world data from the company’s live system.     

Admission policies for the customized stochastic lot scheduling problem with strict due-dates

This papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times.We model the joint admission control/scheduling problem as a Markov decision process (MDP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward.     

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.     

Learning heuristics for basic block instruction scheduling

Instruction scheduling is an important step for improving the performance of object code produced by a compiler. A fundamental problem that arises in instruction scheduling is to find a minimum length schedule for a basic block—a straight-line sequence of code with a single entry point and a single exit point—subject to precedence, latency, and resource constraints. Solving the problem exactly is known to be difficult, and most compilers use a greedy list scheduling algorithm coupled with a heuristic. The heuristic is usually hand-crafted, a potentially time-consuming process. In contrast, we present a study on automatically learning good heuristics using techniques from machine learning. In our study, a recently proposed optimal basic block scheduler was used to generate the machine learning training data. A decision tree learning algorithm was then used to induce a simple heuristic from the training data. The automatically constructed decision tree heuristic was compared against a popular critical-path heuristic on the SPEC 2000 benchmarks. On this benchmark suite, the decision tree heuristic reduced the number of basic blocks that were not optimally scheduled by up to 55% compared to the critical-path heuristic, and gave improved performance guarantees in terms of the worst-case factor from optimality.     

A self-adaptive differential evolution heuristic for two-stage assembly scheduling problem to minimize maximum lateness with setup times

The two-stage assembly flowshop scheduling problem has been addressed with respect to different criteria in the literature where setup times are ignored. For some applications, setup times are essential to be explicitly considered since they may take considerable amount of time. We address the two-stage assembly flowshop scheduling problem with respect to maximum lateness criterion where setup times are treated as separate from processing times. We formulate the problem and obtain a dominance relation. Moreover, we propose a self-adaptive differential evolution heuristic. To the best of our knowledge, this is the first attempt to use a self-adaptive differential evolution heuristic to a scheduling problem. We conduct extensive computational experiments to compare the performance of the proposed heuristic with those of particle swarm optimization (PSO), tabu search, and EDD heuristics. The computational analysis indicates that PSO performs much better than tabu and EDD. Moreover, the analysis indicates that the proposed self-adaptive differential evolution heuristic performs as good as PSO in terms of the average error while only taking one-third of CPU time of PSO.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.