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.     

Knowledge-based single machine scheduling

Production scheduling remains as one of the most important functions in manufacturing systems. Knowledge-based systems provide new insight to production scheduling. The increasing complexity of selecting the right procedure, understanding the procedure and solving an instant can be simplified with the help of knoweldge-based expert systems. This paper explains a prototype system developed using a rule-based expert system shell, M.1, for an application limited to single machine scheduling only.     

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.     

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.     

Dynamic non-preemptive single machine scheduling

Considering a dynamic single machine problem in which operations cannot be split, we first develop a decision theory based heuristic called DT-TD (Decision Theory-Tactically Delayed) of computational complexity O(n²). Using a simple look-ahead procedure, it produces, actically delayed (TD) schedules. We then develop a branch-and-bound (BB) algorithm (which uses DT-TD to obtain the initial upper bound) to obtain the optimum schedule. The optimum schedules are examined to identify conditions where TD schedules are necessary. Results based on 540 test problems suggest that TD schedules are important, for job shop scheduling under the range of conditions examined, when due dates are arbitrary and utilization is low. Additional test results indicate that the difference between the optimum schedule and the optimum non-delay schedule could be substantial. Finally, the performance of the DT-TD heuristic is analyzed by comparing its solution to the optimum solution obtained using the BB algorithm. The results indicate that the DT-TD heuristic is effective.     

Single machine flow-time scheduling with a single breakdown

Summary We consider the problem of scheduling tasks on a single machine to minimize the flowtime. The machine is subject to breakdowns during the processing of the tasks. The breakdowns occur at a random times and the machine is unavailable until it is repaired. The times for repair are random and independent of each other and of the breakdown process. A task that is preempted due to a breakdown must be restarted and otherwise preemptions are not allowed. We show in the case of a single breakdown that if the distribution function of the time to breakdown is concave then Shortest Processing Time (SPT) first scheduling stochastically minimizes the flowtime. For the case of multiple breakdowns we show that SPT minimizes the expected flowtime when the times to breakdown are exponentially distributed. If the time for a single breakdown is known before scheduling begins, and the processing times of the tasks are also known, then we show that the problem of deciding whether there is a schedule with flowtime less than or equal to a given value is NP-complete. Finally, we bound the performance of SPT scheduling in the deterministic case when there is a single breakdown.The work of this author was partially supported by The Lady Davis Fellowship Trust through a Lady Davis Visiting Professorship at the Technion, Haifa, Israel     

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.     

Online interval scheduling on a single machine with finite lookahead

We study an online weighted interval scheduling problem on a single machine, where all intervals have unit length and the objective is to maximize the total weight of all completed intervals. We investigate how the function of finite lookahead improves the competitivities of deterministic online heuristics, under both preemptive and non-preemptive models. The lookahead model studied in this paper is that an online heuristic is said to have a lookahead ability of LD if at any time point it is able to foresee all the intervals to be released within the next LD   units of time. We investigate both competitive online heuristics and lower bounds on the competitive ratio, with lookahead 0≤LD≤1$0\le \mathit{LD}\le 1$ under the preemptive model, and lookahead 0≤LD≤2$0\le \mathit{LD}\le 2$ under the non-preemptive model. A method to transform a preemptive lookahead online algorithm to a non-preemptive online algorithm with enhanced lookahead ability is also given. Computational tests are performed to compare the practical competitivities of the online heuristics with different lookahead abilities.     

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.     

Robust scheduling on a single machine to minimize total flow time

In a real-world manufacturing environment featuring a variety of uncertainties, production schedules for manufacturing systems often cannot be executed exactly as they are developed. In these environments, schedule robustness that guarantees the best worst-case performance is a more appropriate criterion in developing schedules, although most existing studies have developed optimal schedules with respect to a deterministic or stochastic scheduling model. This study concerns robust single machine scheduling with uncertain job processing times and sequence-dependent family setup times explicitly represented by interval data. The objective is to obtain robust sequences of job families and jobs within each family that minimize the absolute deviation of total flow time from the optimal solution under the worst-case scenario. We prove that the robust single machine scheduling problem of interest is NP-hard. This problem is reformulated as a robust constrained shortest path problem and solved by a simulated annealing-based algorithmic framework that embeds a generalized label correcting method. The results of numerical experiments demonstrate that the proposed heuristic is effective and efficient for determining robust schedules. In addition, we explore the impact of degree of uncertainty on the performance measures and examine the tradeoff between robustness and optimality.     

On scheduling a single machine with resource dependent release times

We consider a single machine scheduling problem with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. The objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. It is known that the problem is polynomially solvable in O(n⁴) with n the number of jobs.     

On the complexity of bi-criteria scheduling on a single batch processing machine

This paper considers hierarchical bi-criteria scheduling on a single batch processing machine where the primary criterion is the makespan. We show that the problem where the secondary criterion is the total completion time can be solved in polynomial time for a given machine capacity and the problem where the secondary criterion is the (weighted) number of late jobs is (strongly) NP-hard.     

On-line scheduling on a single machine: minimizing the total completion time

This note deals with the scheduling problem of minimizing the sum of job completion times in a system with n jobs and a single machine. We investigate the on-line version of the problem where every job has to be scheduled immediately and irrevocably as soon as it arrives, without any information on the later arriving jobs. We prove that for any sufficiently smooth, non-negative, non-decreasing function f(n) there exists an O(f(n))-competitive on-line algorithm for minimizing the total completion time if and only if the infinite sum converges. Received: 6 May 1997 / 3 February 1999     

Approximation results for a bicriteria job scheduling problem on a single machine without preemption

We study the problem of minimizing the average weighted completion time on a single machine under the additional constraint that the sum of completion times does not exceed a given bound B(1|∑Cj?B|∑wjCj) for which we propose a (2,1)-approximation algorithm. We also address the problem 1|∑cjCj?B|∑wjCj for which we present a (2,2)-approximation algorithm. After showing that the problem of minimizing two different sums of weighted completion times is intractable, we present an algorithm which computes a (2(1+?),1) (respectively (2(1+?),2))-approximate Pareto curve for the problem 1‖(∑Cj,∑wjCj) (respectively 1‖(∑cjCj,∑wjCj)).     

Preemption in single machine earliness/tardiness scheduling

We consider a single machine earliness/tardiness scheduling problem with general weights, ready times and due dates. Our solution approach is based on a time-indexed preemptive relaxation of the problem. For the objective function of this relaxation, we characterize cost coefficients that are the best among those with a piecewise linear structure with two segments. From the solution to the relaxation with these best objective function coefficients, we generate feasible solutions for the original non-preemptive problem. We report extensive computational results demonstrating the speed and effectiveness of this approach.     

Intelligent controllers for bi-objective dynamic scheduling on a single machine with sequence-dependent setups

This article addresses the problem of dynamic job scheduling on a single machine with Poisson arrivals, stochastic processing times and due dates, in the presence of sequence-dependent setups. The objectives of minimizing mean earliness and mean tardiness are considered. Two approaches for dynamic scheduling are proposed, a Reinforcement Learning-based and one based on Fuzzy Logic and multi-objective evolutionary optimization. The performance of the two scheduling approaches is tested against the performance of 15 dispatching rules in four simulation scenarios with different workload and due date pressure conditions. The scheduling methods are compared in terms of Pareto optimal-oriented metrics, as well as in terms of minimizing mean earliness and mean tardiness independently. The experimental results demonstrate the merits of the proposed methods.