Setting due dates in a stochastic single machine environment

A set of n   jobs with statistically independent random processing times has to be processed on a single machine without idling between jobs and without preemption. It is required to set due dates and promise them to customers. During the production stage, earliness and tardiness against the promised due dates will be penalized. The goal is to minimize the total expected penalties. We consider two due date setting procedures with optimum customer service level, and an O(nlogn)$\mathrm{O}(n\log n)$ time complexity. We show that one is asymptotically optimal but the other is not. Both heuristics include safety time and the sequence remains the same regardless of disruptions, so the result is robust. For the normal distribution we provide sufficient optimality conditions, precedence relationships that the optimal sequence must obey, and tight bounds.     

Search heuristics for a parallel machine scheduling problem with ready times and due dates

We consider a problem of scheduling orders on identical parallel machines. An order can be released after a given ready time and must be completed before its due date. An order is split into multiple jobs (batches) and a job is processed on one of the parallel machines. The objective of the scheduling problem is to minimize the holding costs of orders including work-in-process as well as finished job inventories. We suggest two local search heuristics, simulated annealing and taboo search algorithms, for the problem. Performance of the suggested algorithms is tested through computational experiments on randomly generated test problems.     

Branch-and-bound method for minimizing the weighted completion time scheduling problem on a single machine with release dates

In this paper, we consider a single-machine scheduling problem with release dates. The aim is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose two new lower bounds that can be, respectively, computed in O(n²) and in O(nlogn) time where n is the number of jobs. We prove a sufficient and necessary condition for local optimality, which can also be considered as a priority rule. We present an efficient heuristic using such a condition. We also propose some dominance properties. A branch-and-bound algorithm incorporating the heuristic, the lower bounds and the dominance properties is proposed and tested on a large set of instances.     

Meta-heuristics for stable scheduling on a single machine

This paper presents a model for single-machine scheduling with stability objective and a common deadline. Job durations are uncertain, and our goal is to ensure that there is little deviation between planned and actual job starting times. We propose two meta-heuristics for solving an approximate formulation of the model that assumes that exactly one job is disrupted during schedule execution, and we also present a meta-heuristic for the global problem with independent job durations.     

Lot scheduling on a single machine

In a practical situation, a manufacturer receives different orders from its customers. Different orders may contain different quantities of the product. Therefore, the manufacturer has to decide how to group these orders into different lots based on the capacity of the lot processing machine (such as integrated circuit tester, heated container, etc.) and then decides the sequence of these lots. In this paper, we study a lot scheduling problem with orders which can be split. The objective is to minimize the total completion time of all orders. We show that this problem can be solved in polynomial time.     

Asymptotic performance ratio of an online algorithm for the single machine scheduling with release dates

We analyze the single machine weighted completion time problem with release dates and prove that the asymptotic performance ratio of a simple online algorithm is one. This implies that this algorithm generates a solution whose relative error decreases to zero as the number of jobs increases. Our proof does not require any probabilistic assumption on the job parameters and relies heavily on properties of optimal solutions to a linear programming relaxation of the problem.     

Distributed scheduling based on due dates and buffer priorities

Several distributed scheduling policies are analyzed for a large semiconductor manufacturing facility, where jobs of wafers, each with a desired due date, follow essentially the same route through the manufacturing system, returning several times to many of the service centers for the processing of successive layers. It is shown that for a single nonacyclic flow line the first-buffer-first-serve policy, which assigns priorities to buffers in the order that they are visited, is stable, whenever the arrival rate, allowing for some burstiness, is less than the system capacity. The last-buffer-first-serve policy (LBFS), where the priority ordering is reversed, is also stable. The earliest-due-date policy, where priority is based on the due date of a part, as well as another due-date-based policy of interest called the least slack policy (LS), where priority is based on the slack of a part, defined as the due date minus an estimate of the remaining delay, are also proved to be stable     

Jackson's semi-preemptive scheduling on a single machine

We propose an effective improvement of the well-known Jackson's preemptive schedule lower bound for the single machine scheduling problem with heads and tails. The semi-preemptive scheduling concept roughly consists in reducing the preemption impact by constraining some particular job parts to be processed in reduced time intervals. The impact of semi-preemptive scheduling is twofold: it yields a lower bound which dominates the preemptive one, and enables more effective adjustments of the heads and tails. Our experimental study revealed that suitably embedding our procedure within Carlier's algorithm makes feasible to solve all of the hard instances which could not be solved by its original variant.     

Exact algorithms for inventory constrained scheduling on a single machine

This paper focuses on single machine scheduling subject to inventory constraints. Jobs add or remove items to or from the inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine where the objective is to minimize the total weighted completion time. We develop properties of optimal solutions and design a branch and bound algorithm and a dynamic programming algorithm with two extensions. We compare the approaches in our computational study and empirically derive parameter settings leading to instances which are hard to solve.     

Algorithms for some maximization scheduling problems on a single machine

In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT _j and for the problem of maximizing the number of tardy jobs 1‖maxΣU _j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT _j is polynomially solvable. For several special cases of problem 1‖maxΣT _j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.     

Single machine scheduling with delivery dates and cumulative payoffs

We address a single machine scheduling problem with a new optimization criterion and unequal release dates. This new criterion results from a practical situation in the domain of book digitization. Given a set of job-independent delivery dates, the goal is to maximize the cumulative number of jobs processed before each delivery date. We establish the complexity of the general problem. In addition, we discuss some polynomial cases and provide a pseudopolynomial time algorithm for the two-delivery-dates problem based on dynamic programming and some dominance properties. Experimental results are also reported.     

Integrated batch sizing and scheduling on a single machine

In this paper, we address the integrated batch sizing and scheduling problem. We consider a single machine which can handle at most one customer order at a time and for which the nominal production rate is the same for all the customer orders. Demand is deterministic, and all the orders are ready to be processed at time zero and must be delivered at a given due date. Each order can be satisfied from different batches. Upper and lower bounds on the size of the batches are considered. We seek a feasible schedule that minimizes the sum of the tardiness costs and the setup costs incurred by creating a new batch. We present some structural properties of the optimal schedules for both single-order and multiple-order problems and then propose dynamic programming algorithms based on these properties. Computational results that show the efficiency of the method are reported.     

Tabu search methods for a single machine scheduling problem

In this paper we discuss the use of three local search strategies within a tabu search (TS) method for the approximate solution of a single machine scheduling problem. The problem consists of minimizing the sum of the set-up costs and linear delay penalties whenN jobs, arriving at time zero, are to be scheduled for sequential processing on a continuously available machine. Following a review of a previous study of this problem, we first consider a TS method that uses the common approach of making a succession of pairwise job exchanges, or swaps, to move from one trial solution to another. Next, we consider the use of insert moves to define the local neighborhood of each trial solution. These moves consist of transferring a single job from one position to another in the schedule. Finally, we construct a TS method (TS-hybrid) that employs both swap and insert moves. Experiments with benchmark problems of up to 60 jobs illustrate that there is an advantage in using more than one strategy to move from one trial solution to another within a TS method.This work was begun during the author's summer internship at the Advanced Knowledge Systems Group of US West Advanced Technologies.     

A beam search heuristic for scheduling a single machine with release dates and sequence dependent setup times to minimize the makespan

This paper considers the problem of scheduling a set of jobs subject to arbitrary release dates and sequence-dependent setup times on a single machine with the objective of minimizing the maximum completion of all the jobs, or makespan. This problem is often found in manufacturing processes such as painting and metalworking. A new mixed integer linear program (MILP) is firstly proposed. Because the problem is known to be NP-hard, a beam search heuristic is developed. Computational experiments are carried out using a well-known set of instances from the literature. Our results show that the proposed heuristic is effective in finding high quality solutions at low computational cost.     

A note: Common due date assignment for a single machine scheduling with the rate-modifying activity

In this paper we study the single machine common due date assignment and scheduling problem with the possibility to perform a rate-modifying activity (RMA) for changing the processing times of the jobs following this activity. The objective is to minimize the total weighted sum of earliness, tardiness and due date costs. Placing the RMA to some position in the schedule can decrease the objective function value. Several properties of the problem are considered which in some cases can reduce the complexity of the solution algorithm.     

Single-machine scheduling with a common due window

We study several single-machine non-preemptive scheduling problems to minimize the sum of weighted earliness–tardiness, weighted number of early and tardy jobs, common due window location, and flowtime penalties. We allow the due window location to be either a decision variable or a given parameter. We assume that the due window location has a tolerance and the window size is a given parameter. We further make the assumption that the ratios of the job processing times to the earliness–tardiness weights are agreeable for the first problem. We propose pseudo-polynomial dynamic programming algorithms to optimally solve the problems. We also provide polynomial time algorithms for several special cases.Scope and purpose The widespread use of Just-In-Time philosophy in manufacturing to eliminate inventories leads to a new class of scheduling problems in which the earliness and/or number of early jobs are penalized as well as the tardiness and/or tardy jobs. In this type of environments, the jobs are sometimes associated with a period of time within which they incur no penalty since the customers will generally allow a time interval for the delivery of the products. This time period is called a due window. There are a variety of applications with due windows in factory automation, production maintenance, and so on. In this paper, we consider the common due window problems to minimize the weighted earliness–tardiness, weighted number of early–tardy jobs and weighted flowtime on a single machine. The main contributions of this paper are identifying the computational complexity of the problems, developing dynamic programming algorithms to optimally solve them, and providing efficient and exact polynomial algorithms for the special cases.     

Coupled-task scheduling on a single machine subject to a fixed-job-sequence

This paper investigates single-machine coupled-task scheduling where each job has two tasks separated by an exact delay. The objective of this study is to schedule the tasks to minimize the makespan subject to a given job sequence. We introduce several intriguing properties of the fixed-job-sequence problem under study. While the complexity status of the studied problem remains open, an O(n²) algorithm is proposed to construct a feasible schedule attaining the minimum makespan for a given permutation of 2n tasks abiding by the fixed-job-sequence constraint. We investigate several polynomially solvable cases of the fixed-job-sequence problem and present a complexity graph of the problem.     

Two-stage flowshop scheduling with a common second-stage machine

This article considers minimizing the makespan in a two-stage flowshop scheduling problem with a common second-stage machine. After introducing the problem, we show that it is -hard and give two special cases which are polynomially solvable. Next, we propose a heuristic algorithm and analyze its worst-case error bound. We then develop some lower bounds. Finally, we perform some computational experiments to test the average performance of the proposed heuristic.