Common due date assignment and scheduling with ready times

The multi-stage wafer probing scheduling problem (M-WPSP) with reentry is a practical variation of the parallel-machine scheduling problem. Since the M-WPSP involves multiple product families, to be processed on multiple stages, with various job due dates, ready times, reentry, serial and batch operations, sequential-dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problems. In this paper, we consider two strategies to solve the M-WPSP with reentry, where the total machine workload must be minimized. These two strategies incorporate a global planning mechanism, in advance, to determine the required stage due date of job at each process stage to prevent the due date problems occurring at the final stage. The sequential strategy schedules the jobs at the required stages according to the sequence of manufacturing process. The parallel strategy is designed specifically for the reentrant characteristic. To evaluate the efficiency of the proposed strategies, a set of test problems involving four critical factors, the product family ratio, the temperature-change consideration, the tightness of due dates, and the ready time, are designed to test the quality of solutions under two levels of workload.

We consider the problem of scheduling n jobs on a single machine. Each job i has a processing time p/sub i/, a weight w/sub i/, and a due date D/sub i/, which is a fuzzy number with a triangular membership function. The problem is to determine: (i) a job sequence, and (ii) a set of idle times each before one job, so as to minimize the total weighted earliness and tardiness cost under the fuzzy due dates. We first introduce a fuzzy distance function to measure the deviation of the completion time of a job from its fuzzy due date. We show that, given a job sequence, the problem of determining the optimal idle times is a continuous and convex optimization problem with a differentiable objective function, although the objective function after applying the fuzzy distance measure becomes nonlinear. We devise a genetic algorithm (GA) to tackle the problem, using a pigeon-hole coding scheme to represent a sequence and a nonlinear optimizer to determine the idle times. We evaluate the solutions obtained by such a GA as compared to the solutions obtained by treating the due dates as crispy numbers equal to the mean values of its fuzzy partners.

This paper studies a multiple common due date assignment problem on a single machine. The job-dependent due dates are obtained based on common flow allowance criteria. We assume that the processing time of a job is controllable by the resource amount assigned to it. The objective is to find the optimal multiple common dues, the set of jobs assigned to each due date, the sequence of jobs and resource allocation scheme to minimize a total cost based on earliness and tardiness of jobs, the common dues and resource cost. We propose an optimal algorithm to solve the problem.

This study addresses the problem of minimizing the makespan for scheduling parallel batch machines, where jobs are processed in batches and each machine has the same capacity. The processing time for each batch includes setup, preheating, and heat preservation stages, introducing both serial and parallel batching characteristics. Jobs differ in size, weight, and ready time. A mixed-integer linear programming model is formulated and its correctness is verified using small-scale instances. As the problem is NP-hard, a novel heuristic algorithm is proposed, which utilizes a dynamic scheduling strategy to effectively reduce machine idle waiting time between batches. The time complexities of the algorithm are analyzed, and the worst-case performance of the new constructive heuristic is also evaluated. For small-scale problems, the performance of the heuristics is compared with the optimal solutions obtained from the MILP model, while for large-scale problems, comparisons are made with lower bounds. Three heuristic algorithms and two improved genetic algorithms are used as benchmark algorithms. The experimental results demonstrate that the new constructive heuristic outperforms these five algorithms in terms of scheduling performance.

In supply chain management manufacturing flow lines consist of two or more work areas, arranged in series and/or in parallel, with intermediate storage areas. The first work area processes raw items and the last work area produces end items or products, which are stored in a storage area in anticipation of future demand. Firstly managers should analyze and organize the long term production optimizing the production planning of the supply chain. Secondly, they have to optimize the short term production analyzing and organizing the production scheduling of the supply chain and finally taking under consideration the stochasticity of the real world, managers have to analyze and organize the performance of the supply chain adopting the best control policy. In supply chain management production planning is the process of determining a tentative plan for how much production will occur in the next several time periods, during an interval of time called the planning horizon. Production planning also determines expected inventory levels, as well as the workforce and other resources necessary to implement the production plans. Production planning is done using an aggregate view of the production facility, the demand for products and even of time (ex. using monthly time periods). Production planning is commonly defined as the cross-functional process of devising an aggregate production plan for groups of products over a month or quarter, based on management targets for production, sales and inventory levels. This plan should meet operating requirements for fulfilling basic business profitability and market goals and provide the overall desired framework in developing the master production schedule and in evaluating capacity and resource requirements. In supply chain management production scheduling defines which products should be produced and which products should be consumed in each time instant over a given small time horizon; hence, it defines which run-mode to use and when to perform changeovers in order to meet the market needs and satisfy the demand. Large-scale scheduling problems arise frequently in supply chain management where the main objective is to assign sequence of tasks to processing units within certain time frame such that demand of each product is satisfied before its due date. For supply chain systems the aim of control is to optimize some performance measure, which typically comprises revenue from sales less the costs of inventory and those

This paper addresses one-machine scheduling with maintenance restrictions. A maintenance operation is position dependent in a sequence of normal jobs if the maintenance has to be performed after at most some defined number of job changes on the machine. We show that several problems with objective functions Cmax and Lmax are still solvable in polynomial time if position-dependent maintenance is considered. We then consider the problem of preemptive scheduling with ready times and due dates on one machine with the Lmax criterion. We show that this problem is computationally hard and present the characteristics of this problem—for example, the fact that optimum schedules may be nonactive. After determining a set of dominance properties, branch-and-bound and local search algorithms are proposed. The performance of the algorithms is evaluated using a series of computational experiments.

Based on several existing literatures that use mixed integer programming (MIP) to solve parallel machine scheduling problems, this study tests and compares three MIP models. Each order has its own ready date, due date and processing time. The completion time of the order cannot over the its due date. If not, penalties for tardiness will occur. Formulation 1 used in immediate-precedence variables [1]. Formulation 2 is an improved version of immediate-precedence variables original proposed by [2]. Formulation 3 used linear ordering variables[1]. The results reveal that Formulation 2 has better computational performance than other does.

In this paper we consider a single machine preemptive scheduling problem to minimize the weighted number of late jobs. There are given n jobs and for each job we have a release date, a processing time and a due date. It is assumed that certain specified jobs have to be completed on time. The due dates for these jobs are considered as deadlines. while for the other jobs due dates may be violated. For the case of similarly ordered release and due dates (when there is no advantage to preemption) as well as for the case of embedded release and due date intervals and preemption allowed, we transform the initial problem into a reduced problem, where all jobs with deadlines are eliminated. It gives an opportunity to propose O(n log n) algorithms for some special cases of the considered problems.

Optimal restricted due date assignment in scheduling

This paper develops some useful concepts and properties for the problem of sequencing n jobs on one machine so as to minimize the maximum lateness when the jobs may have unequal ready times, processing times, and due dates, and pre-emption is not permitted. The properties established include the equivalence among three versions of the problem, the symmetrical nature of the problem and the additive and multiplicative characteristics of the job set parameters. These properties are applied to forward and backward sequencing. A strong sufficient optimality condition is developed and used to obtain tight lower bounds on the optimal solution. The paper demonstrates the applicability of the concepts and properties to the development of efficient optimal and heuristic procedures and to the design of experiments for evaluating the relative performance of solution procedures. Optimal single-pass solutions for special cases of the problem are given.

We study a set of single-machine two-agent scheduling problems where the performance measure of the first agent, , is the weighted number of jobs completed exactly at the due date, i.e. completed in a just-in-time mode. The performance measure of the second agent, , is either the makespan, the total completion times or the weighted number of jobs completed exactly at the due date. For each combination of performance measures of the two agents, we study four different variations of the problem. We show that all four-problem variations are strongly -hard for when the performance measure of the second agent is either the makespan or the total completion time, even if all of the first agent’s weights are equal. We also study the special case of these problems where the job processing times of the second agent are all equal. For this special case, we prove that three variations of this problem are ordinary -hard with respect to the instance size, while all four problem variations are polynomial solvable with respect to the number of jobs. For the problem where the performance measure of both agents is the weighted number of jobs completed at the due date, we show that one problem variation is solvable in polynomial time, while all other three variations are ordinary -hard.

An Optimal Static Priority Rule for Stochastic Scheduling with Impatience

This paper considers the problem of scheduling n jobs on a single machine to minimize the number of tardy (or late) jobs. Each job has a release date, a processing time and a due date. The general case with non-equal release dates and different due dates is considered. Using new and efficient lower bounds and several dominance rules, a branch and bound scheme is proposed based on the definition of a master sequence, i.e. a sequence containing at least one optimal sequence. With this procedure, 95% of 140-job instances are optimally solved in a maximum of one-hour CPU time.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work