Polynomial time approximation schemes for general multiprocessor job shop scheduling

The importance of job shop scheduling as a practical problem has attracted the attention of many researchers. However, most research has focused on special cases such as single machine, parallel machine, and flowshop environments due to the “hardness” of general job shop problems. In this paper, a hybrid algorithm based on an integration of a genetic algorithm and heuristic rules is proposed for a general job shop scheduling problem with sequence-dependent setups (Jm|sjk|Cmax ). An embedded simulator is employed to implement the heuristic rules, which greatly enhances the flexibility of the algorithm. Knowledge relevant to the problem is inherent in the heuristic rules making the genetic algorithm more efficient, while the optimization procedure provided by the genetic algorithm makes the heuristic rules more effective. Extensive numerical experiments have been conducted and the results have shown that the hybrid approach is superior when compared to recently published existing methods for the same problem.

This paper investigates a more general flexible job shop scheduling problem with multiple process plans which is common in the modern manufacturing system. As an extension of the traditional flexible job shop scheduling problem, various realistic flexibility such as processing flexibility, machine flexibility and sequencing flexibility are considered in this problem. Due to the high complexity and the real-time requirement of this problem, a genetic programming-based evolutionary approach is proposed to automatically generate effective dispatching rules for this problem, and an evaluation method is developed to evaluate the generated dispatching rules. Three experiments are conducted to evaluate the performance of the proposed approach for real cases with large-scale test problems. Numerical results show that the proposed approach outperforms the classical dispatching rules and the state-of-theart algorithms, and is able to provide higher-quality solutions with less computational time.

This paper deals with the so-called general machine scheduling problems. In the general machine scheduling problems, job shop type jobs and open shop type jobs are scheduled together and the imposition of precedence constraints is allowed between operations belonging to either the same job or different jobs. This paper proposes a genetic algorithm to solve such general machine scheduling problems. Some experimental results are presented to show the applicability of the proposed method. The method can be used to solve traditional job shop scheduling, flow shop scheduling, and open shop scheduling as well as general machine scheduling problems.

Dehydration plants are broadly characterized by a multi-product nature chiefly attributed to the utilization of different raw materials to be processed sequentially so that demand constraints are met. Processing of raw materials is implemented through a series of preprocessing operations that together with drying constitute the production procedure of a pre-specified programme. The core of the manufacturing system that a typical dehydration plant involves, is scheduling of operations so that demand is fulfilled within a pre-determined time horizon imposed by production planning. The typical scheduling operation that dehydration plants involve can be formulated as a general job shop scheduling problem. The aim of this study is to describe a new metaheuristic method for solving the job shop scheduling problem of dehydration plants, termed as the Backtracking Adaptive Threshold Accepting (BATA) method. Our effort focuses on developing an innovative method, which produces reliable and high quality solutions, requiring reasonable computing effort. The main innovation of this method, towards a typical threshold accepting algorithm, is that during the optimization process the value of the threshold is not only lowered, but also raised or backtracked according to how effective a local search is. BATA is described in detail while a characteristic job shop scheduling case study for dehydration plant operations is presented.

A unidirectional mutation-selection approach for the general job shop scheduling problem is presented. The underlying algorithm uses threshold accepting as an iterative search technique and incorporates a special non-monotonic threshold function (threshold waving). Search is performed in the space of operation sequences and, for the purpose of evaluation, is combined with a simple heuristic transforming operation sequences into schedules. Mutation of solution candidates is based on a critical path analysis and, additionally, on a probabilistically employed local hill-climbing operator. Effectiveness of the approach is demonstrated within a comparison with some well-known heuristic and exact algorithms.

A genetic algorithm enhanced with neighborhood structure for general flexible job shop scheduling with parallel batch processing machine

In a paper published in 1987, an exchange heuristic for developing efficient makespans for resource constrained scheduling problems was presented. It has since been successfully applied to other types of scheduling problems including generalized job shop scheduling and project scheduling with limited resources. The increased flexibility of the heuristic is becoming reaped. As such, several modifications of the exchange heuristic to increase the performance of developing efficient makespans are now presented. Empirical results of implementing these extended heuristics to problems in general job shop scheduling and their comparison to the original heuristic are also presented. Results show that the extended heuristics produce better makespan schedules on average than the original heuristic though there is a price of increased computational time

Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines

SUMMARY The authors compare two well-known methods for setting manufacturing lead times (flow allowances) in a general job shop when early shipment of completed jobs is forbidden. One of the methods for setting a job's allowance is to make it proportional to the total processing time for the job. This method, referred to as TWK., is compared to a second method PPW. With the PPW method, a job's allowance is obtained by adding to the total job-processing time an allowance for waiting that is proportional to the number of operations that the job requires. The two allowance methods are compared using a computer simulation of an 8-machine job shop. The model is unique in that jobs are not permitted to leave the shop early. This feature of forbidding early shipment (FES) complicates the comparison between allowance methods because it draws the issue of finished-order inventory management into the analysis. Results of computer simulations over a wide range of average due-date difficulty suggest that TWK is the d...

An exchange heuristic imbedded with simulated annealing for due-dates job-shop scheduling

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the sizes of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. Here, the processing time of job j on machine i is governed by random variable P_{ij} , and its realization becomes known only upon job completion. With w_j being the given weight of job j, we study the objective to minimize the expected total weighted completion time E[Sum w_j.C_j] , where C_j is the completion time of job j. By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee (3+D)/2+e. Here, e>0 is arbitrarily small, and D is an upper bound on the squared coefficient of variation of the processing times. When jobs also have individual release dates r_{ij}, our bound is (2+D)+e. We also show that the dependence of the performance guarantees on D is tight. Via D=0, currently best known bounds for deterministic scheduling on unrelated machines are contained as special case.

Hybrid flow shop (HFS) systems represent the typical flow shop production system with parallel machines on at least one stage of operation. This paper considers unrelated machines and anticipatory sequence-dependent setup times where job families can be formed based on similar setup characteristics. This results in the opportunity to save setups if two jobs of the same family are scheduled consecutively. Three constructive heuristic approaches, aiming at minimization of makespan, total completion time and the total number of setup procedures, are implemented based on the algorithm of Nawaz, Enscore and Ham (NEH).

We present polylogarithmic approximations for the R|prec|C max and R|prec|∑ j w j C j problems, when the precedence constraints are “treelike”—i.e., when the undirected graph underlying the precedences is a forest. These are the first non-trivial generalizations of the job shop scheduling problem to scheduling with precedence constraints that are not just chains. These are also the first non-trivial results for the weighted completion time objective on unrelated machines with precedence constraints of any kind. We obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment—this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion + dilation”, as in other job shop scheduling approaches (e.g. Shmoys, Stein and Wein, SIAM J. Comput. 23, 617–632, 1994). The first step in our algorithm for the R|prec|C max problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random-delays technique of Leighton, Maggs and Rao to the case of trees. For the special case of chains, we show a dependent rounding technique which leads to a bicriteria approximation algorithm for minimizing the flow time, a notoriously hard objective function.

In this paper, three metaheuristics are proposed for solving a class of job shop, open shop, and mixed shop scheduling problems. We evaluate the performance of the proposed algorithms by means of a set of Lawrence's benchmark instances for the job shop problem, a set of randomly generated instances for the open shop problem, and a combined job shop and open shop test data for the mixed shop problem. The computational results show that the proposed algorithms perform extremely well on all these three types of shop scheduling problems. The results also reveal that the mixed shop problem is relatively easier to solve than the job shop problem due to the fact that the scheduling procedure becomes more flexible by the inclusion of more open shop jobs in the mixed shop.

This chapter concentrates on compact and cyclic compact open shop scheduling. Compact scheduling is motivated by timetabling and cyclic compact scheduling by just-in-time systems. A compact schedule requires each job to be processed in a no-wait fashion and each machine to process operations without idle time. Compact schedules do not always exist. The chapter presents smallest instances for which compact schedules do not exist and tests to determine whether compact schedules exist for a given degree Δ. Such tests run in polynomial time for open shop instances with Δ ≤ 4 but become NP-complete for Δ = 5. The minimization of makespan over all compact schedules has polynomial-time solution only for Δ ≤ 3, and it is open even for (3, 4)-biregular open shops where every job has length equal 3 and each machine workload equal 4. Deficiency has been proposed as a measure of deviation from compactness. However, the problem of minimizing deficiency is not only NP-hard in the strong sense but also the existing integer programming (IP) and constraint programming (CP) models can hardly solve problems of size n + m = 10 in reasonable time.