Machine scheduling with job class setup and delivery considerations

We study machine scheduling problems in which the jobs belong to different job classes and they need to be delivered to customers after processing. A setup time is required for a job if it is the first job to be processed on a machine or its processing on a machine follows a job that belongs to another class. Processed jobs are delivered in batches to their respective customers. The batch size is limited by the capacity of the delivery vehicles and each shipment incurs a transport cost and takes a fixed amount of time. The objective is to minimize the weighted sum of the last arrival time of jobs to customers and the delivery (transportation) cost. For the problem of processing jobs on a single machine and delivering them to multiple customers, we develop a dynamic programming algorithm to solve the problem optimally. For the problem of processing jobs on parallel machines and delivering them to a single customer, we propose a heuristic and analyze its performance bound.     

A hybrid local search algorithm for scheduling real-world job shops with batch-wise pending due dates

This paper aims at solving a real-world job shop scheduling problem with two characteristics, i.e., the existence of pending due dates and job batches. Due date quotation is an important decision process for contemporary companies that adopt the MTO (make to order) strategy. Although the assignment of due dates is usually performed separately with production scheduling, there exist strong interactions between the two tasks. Therefore, we integrate these two decisions into one optimization model. Meanwhile, each order placed by the customer defines a batch of jobs, for which the same due date should be set. Thus, the completion times of these jobs should be close to one another in order to reduce waiting time and cost. For this purpose, we propose a dispatching rule to synchronize their manufacturing progresses. A two-stage local search algorithm based on the PMBGA (probabilistic model-building genetic algorithm) and parameter perturbation is proposed to solve the integrated scheduling problem and its superiority is revealed by the applications to a real-world mechanical factory.     

Common due date assignment and scheduling with a rate-modifying activity to minimize the due date,earliness, tardiness,holding, and batch delivery cost

e consider a single-machine batch delivery scheduling and common due date assignment problem. In addition to making decisions on sequencing the jobs, determining the common due date, and scheduling job delivery, we consider the option of performing a rate-modifying activity on the machine. The processing time of a job scheduled after the rate-modifying activity decreases depending on a job-dependent factor. Finished jobs are delivered in batches. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find a common due date for all the jobs, a location of the rate-modifying activity, and a delivery date for each job to minimize the sum of earliness, tardiness, holding, due date, and delivery cost. We provide some properties of the optimal schedule for the problem and present polynomial algorithms for some special cases.     

Approximation algorithms for minimizing the total weighted number of late jobs with late deliveries in two-level supply chains

We study a supply chain scheduling problem in which n jobs have to be scheduled on a single machine and delivered to m customers in batches. Each job has a due date, a processing time and a lateness penalty (weight). To save batch-delivery costs, several jobs for the same customer can be delivered together in a batch, including late jobs. The completion time of each job in the same batch coincides with the batch completion time. A batch setup time has to be added before processing the first job in each batch. The objective is to find a schedule which minimizes the sum of the weighted number of late jobs and the delivery costs. We present a pseudo-polynomial algorithm for a restricted case, where late jobs are delivered separately, and show that it becomes polynomial for the special cases when jobs have equal weights and equal delivery costs or equal processing times and equal setup times. We convert the algorithm into an FPTAS and prove that the solution produced by it is near-optimal for the original general problem by performing a parametric analysis of its performance ratio.     

Integrated production and outbound distribution scheduling problems with job release dates and deadlines

In this paper, we study an integrated production and outbound distribution scheduling model with one manufacturer and one customer. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to the customer. Each job has a release date and a delivery deadline. The objective of the problem is to issue a feasible integrated production and distribution schedule minimizing the transportation cost subject to the production release dates and delivery deadline constraints. We consider three problems with different ways how a job can be produced and delivered: non-splittable production and delivery (NSP–NSD) problem, splittable production and non-splittable delivery problem and splittable production and delivery problem. We provide polynomial-time algorithms that solve special cases of the problem. One of these algorithms allows us to compute a lower bound for the NP-hard problem NSP–NSD, which we use in a branch-and-bound (B&B) algorithm to solve problem NSP–NSD. The computational results show that the B&B algorithm outperforms a MILP formulation of the problem implemented on a commercial solver.     

An improved approximation algorithm for single machine scheduling with job delivery

In single machine scheduling with release times and job delivery, jobs are processed on a single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs in a shipment. The delivery completion time of a job is defined as the time in which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. We provide an approximation algorithm for this problem which is better than that given in the literature, improving the performance ratio from 5/3 to 3/2.     

Tabu search and lower bounds for a combined production–transportation problem

In this paper we consider a combined production–transportation problem, where n jobs have to be processed on a single machine at a production site before they are delivered to a customer. At the production stage, for each job a release date is given; at the transportation stage, job delivery should be completed not later than a given due date. The transportation is done by m identical vehicles with limited capacity. It takes a constant time to deliver a batch of jobs to the customer. The objective is to find a feasible schedule minimizing the maximum lateness.     

Single-machine batch delivery scheduling with job release dates,due windows and earliness,tardiness, holding and delivery costs

This paper deals with a single-machine scheduling problem in which jobs are released in different points in time but delivered to customers in batches. A due window is associated with each job. The objective is to schedule the jobs, to form them into batches and to decide the delivery date of each batch so as to minimize the sum of earliness, tardiness, holding, and delivery costs. A mathematical model of the problem is presented, and a set of dominance properties is established. To solve this NP-hard problem efficiently, a solution method is then proposed by incorporating the dominance properties with an imperialist competitive algorithm. Unforced idleness and forming discontinuous batches are allowed in the proposed algorithm. Moreover, the delivery date of a batch may be decided to be later than the completion time of the last job in the batch. Finally, computational experiments are conducted to evaluate the proposed model and solution procedure, and results are discussed.     

Single-machine batch delivery scheduling with an assignable common due date and controllable processing times

We consider single-machine batch delivery scheduling with an assignable common due date and controllable processing times, which vary as a convex function of the amounts of a continuously divisible common resource allocated to individual jobs. Finished jobs are delivered in batches and there is no capacity limit on each delivery batch. We first provide an O(n⁵) dynamic programming algorithm to find the optimal job sequence, the partition of the job sequence into batches, the assigned common due date, and the resource allocation that minimize a cost function based on earliness, tardiness, job holding, due date assignment, batch delivery, and resource consumption. We show that a special case of the problem can be solved by a lower-order polynomial algorithm. We then study the problem of finding the optimal solution to minimize the total cost of earliness, tardiness, job holding, and due date assignment, subject to limited resource availability, and develop an O(nlog n) algorithm to solve it.     

Single machine scheduling with job delivery to multiple customers

We investigate a single machine scheduling problem with job delivery to multiple customers. In this problem, each job needs to be processed on the single machine, and then delivered by a single vehicle to its customer, where the job has a physical size representing the fraction of space it occupies on the vehicle. The vehicle delivers a shipment from the machine to a customer and has to return back to the machine for delivering the next shipment. It takes different constant time for the round trips between the machine and the different customers. The goal is to minimize the makespan, by that time all the jobs are processed and delivered to their respective customers, and the vehicle returns back to the machine. We propose a 2-approximation algorithm for the general case; when there are only two customers, we present an improved 5/3-approximation algorithm. The design and performance analysis of these two algorithms integrate several known results and techniques for the single machine scheduling problem, the bin-packing problem, and the knapsack problem.     

Unbounded parallel-batch scheduling with family jobs and delivery coordination

We study a scheduling problem that integrates parallel-batch production with family jobs and job delivery at the same time. The jobs are first processed on an unbounded parallel-batch machine and then delivered in batches to their specified customers by a transportation vehicle. We assume that jobs from different families (customers) cannot be processed together by the batch machine and also transported together by the vehicle. The objective is to minimize the time when the vehicle finishes delivering the last delivery batch to its customer and returns to the machine. We first show that the problem is NP-hard, and then propose for it a heuristic algorithm with a worst-case performance ratio of 3/2.     

A heuristic approach for single-machine scheduling with due dates and class setups

The single-machine sequence-independent class setup scheduling problem is examined in this paper. It is assumed that jobs are classified into classes and a setup is required between jobs of different classes, but not of the same class. Furthermore, this setup time is fixed and depends only on the current job. Since the problem is NP-hard, a heuristic algorithm is proposed to find an approximate schedule that minimizes the maximum lateness on a set of jobs. The algorithm can easily be modified to solve the maximum tardiness problems as well. The accuracy of the heuristic algorithm in generating near optimal solutions is empirically evaluated.Scope and purposeFor batch manufacturing, it maybe desirable to produce many items of the same type, or class, at the same run in order to save the setup cost. However, committing facilities to long production runs for one product may inevitably make others tardy. Small batch size may conform urgent jobs to their delivery date, but one of the consequences would be the loss of productive efficiency due to numerous setups. Therefore, scheduling is basically a trade-off between the inherently conflicting efficiency measure and due-date compliance. This paper considers a single-machine scheduling problem in which jobs are classified into classes and a setup is required between jobs of different classes. The setup time is fixed and depends only on the current job. This problem is called a sequence-independent class setup problem and is NP-complete.     

A GA methodology for the scheduling of yarn-dyed textile production

This paper presents a scheduling approach for yarn-dyed textile manufacturing. The scheduling problem is distinct in having four characteristics: multi-stage production, sequence-dependent setup times, hierarchical product structure, and group-delivery (a group of jobs pertaining to a particular customer order must be delivered together), which are seldom addressed as a whole in literature. The scheduling objective is to minimize the total tardiness of customer orders. The problem is formulated as a mixed integer programming (MIP) model, which is computationally extensive. To reduce the problem complexity, we decomposed the scheduling problem into a sequence of sub-problems. Each sub-problem is solved by a genetic algorithm (GA), and an iteration of solving the whole sequence of sub-problems is repeated until a satisfactory solution has been obtained. Numerical experiment results indicated that the proposed approach significantly outperforms the EDD (earliest due date) scheduling method—currently used in the yarn-dyed textile industry.     

Minimizing total earliness and tardiness through unrelated parallel machine scheduling using distributed release time control

Using unrelated parallel machine scheduling to minimize the total earliness and tardiness of jobs with distinct due dates is a nondeterministic polynomial-hard problem. Delayed customer orders may result in penalties and reduce customer satisfaction. On the other hand, early completion creates inventory storage costs, which increase the total cost. Although parallel machines can increase productivity, machine assignments also increase the complexity of production. Therefore, the challenge in parallel machine scheduling is to dynamically adjust the machine assignment to complete the job within the shortest possible time. In this paper, we address an unrelated parallel machine scheduling problem for jobs with distinct due dates and dedicated machines. The objective is to dynamically allocate jobs to unrelated parallel machines in order to minimize the total earliness and tardiness time. We formulate the problem as a mixed integer linear programming (MILP) model and develop a modified genetic algorithm (GA) with a distributed release time control (GARTC) mechanism to obtain the near-optimal solution. A preliminary computational study indicates that the developed GARTC not only provides good quality solutions within a reasonable amount of time, but also outperforms the MILP model, a classic GA and heuristic approaches described in the literature.     

Common due date assignment and scheduling with ready times

We consider the problem of scheduling a set of nonsimultaneously available jobs on one machine. Each job has a ready time only at or after which the job can be processed. All the jobs have a common due date, which needs to be determined. The problem is to determine a due date and a schedule so as to minimize a total penalty depending on the earliness, tardiness and due date. We show that this problem is strongly NP-hard and give an efficient algorithm that finds an optimal due date and schedule when either the job sequence is predetermined or all jobs have the same processing time. We also propose three approximation algorithms for the general and special cases together with their experimental analysis.

Scope and purpose

We consider the single machine due date assignment problem for scheduling jobs which are ready for processing at different times. The problem under consideration arises in production planning and scheduling concerning the setting of appropriate due dates for a number of customer orders arriving over time. Most of the earlier publications on this subject assumed that the jobs are ready for processing simultaneously. This assumption is too restrictive for real-life production systems where jobs arrive at different times. We show that the problem with unequal ready times is NP-hard and develop fast heuristic algorithms for it, and exact algorithms for two special cases.     

考虑工件移动时间的柔性作业车间调度问题研究

分析生产车间的实际生产状况,建立了考虑工件移动时间的柔性作业车间调度问题模型,该模型考虑了以往柔性作业车间调度问题模型所没有考虑的工件在加工机器间的移动时间,使柔性作业车间调度问题更贴近实际生产,让调度理论更具现实性。通过对已有的改进遗传算法的遗传操作进行重构,设计出有效求解考虑工件移动时间的柔性作业车间调度问题的改进遗传算法。最后对实际案例进行求解,得到调度甘特图和析取图,通过对甘特图和析取图的分析验证了所建考虑工件移动时间的柔性作业车间调度问题模型的可行性和有效性。     

Earliness–tardiness minimization on scheduling a batch processing machine with non-identical job sizes

This paper considers the scheduling problem of minimizing earliness–tardiness (E/T) on a single batch processing machine with a common due date. The problem is extended to the environment of non-identical job sizes. First, a mathematical model is formulated, which is tested effectively under IBM ILOG CPLEX using the constraint programming solver. Then several optimal properties are given to schedule batches effectively, and by introducing the concept of ARB (Attribute Ratio of Batch), it is proven that the ARB of each batch should be made as small as possible in order to minimize the objective, designed as the heuristic information for assigning jobs into batches. Based on these properties, a heuristic algorithm MARB (Minimum Attribute Ratio of Batch) for batch forming is proposed, and a hybrid genetic algorithm is developed for the problem under study by combining GA (genetic algorithm) with MARB. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in the literature, both for small and large problem instances.     

Decomposition heuristics for minimizing earliness–tardiness on parallel burn-in ovens with a common due date

This paper considers a scheduling problem for parallel burn-in ovens in the semiconductor manufacturing industry. An oven is a batch processing machine with restricted capacity. The batch processing time is set by the longest processing time among those of all the jobs contained in the batch. All jobs are assumed to have the same due date. The objective is to minimize the sum of the absolute deviations of completion times from the due date (earliness–tardiness) of all jobs. We suggest three decomposition heuristics. The first heuristic applies the exact algorithm due to Emmons and Hall (for the nonbatching problem) in order to assign the jobs to separate early and tardy job sets for each of the parallel burn-in ovens. Then, we use job sequencing rules and dynamic programming in order to form batches for the early and tardy job sets and sequence them optimally. The second proposed heuristic is based on genetic algorithms. We use a genetic algorithm in order to assign jobs to each single burn-in oven. Then, after forming early and tardy job sets for each oven we apply again sequencing rules and dynamic programming techniques to the early and tardy jobs sets on each single machine in order to form batches. The third heuristic assigns jobs to the m early job sets and m tardy jobs sets in case of m burn-in ovens in parallel via a genetic algorithm and applies again dynamic programming and sequencing rules. We report on computational experiments based on generated test data and compare the results of the heuristics with known exact solution for small size test instances obtained from a branch and bound scheme.     

Scheduling with compressible and stochastic release dates

In this work we study a one-machine scheduling problem which is featured by: (a) the release date of each job is compressible and stochastic, (b) each job has to be delivered before its due date (deadline) and (c) the manufacturer can expedite the production through overtime at an extra cost. The objective function of the scheduling problem is to minimize the total cost which includes the compressing cost and the overtime production cost. We propose a heuristic algorithm in which the stochastic problem is converted to the deterministic problem by a release-time “converting policy”. We coin a concept of a job's late-release-impact factor (LRIF) and we propose a LRIF based converting policy. We compare the LRIF based converting policy with the ones used in practice, and the numerical test shows that the LRIF based converting policy can obtain the schedule with the lowest actual total cost.     

解决并行多机提前/拖后调度问题的混合遗传算法方法

研究了带有公共交货期的并行多机提前/拖后调度问题.提出了一种混合遗传算法 方法,以便于确定公共交货期和每台机器上加工的任务代号及其加工顺序,即找到一个最优 公共交货期和最优调度,使加工完所有任务后交货期安排的成本、提前交货成本和拖后交货 成本的总和最小.数值计算结果表明了该混合遗传算法优于启发式算法,并能适用于较大规 模并行多机提前/拖后调度问题.算法计算量小,鲁棒性强.