Target-oriented robust satisficing models for the single machine scheduling problems with release time

The aim of this note is to study single machine scheduling problems with resource dependent release times. Each job starts as soon as it is released and release cost will be generated if its actual release time deviates from the initial release time. The objective is determining a sequence of jobs in addition to their release times concurrently, in order that weighted release cost, makespan and total completion times of jobs are minimized. Two cases are considered, in which the problem with restricted initial release time is NP-hard and the problem with unrestricted initial release time is polynomially solvable by efficient algorithm with the analysis of optimality properties.

A single machine scheduling problem in which both the processing times and due‐dates of the jobs awaiting servicing are random variables is analyzed. It is proved that the properties of the shortest processing time rule and the due‐date rule which are known for the deterministic situation also hold in the probabilistic environment when they are suitably, and reasonably, refined for this context.

In this chapter, we consider some practical scheduling problems under unavailability constraints (breakdown periods, maintenance durations and/or setup times). Such problems can be met in different industrial environments and be associated to numerous real-life applications. This explains why many researchers have become interested in this subject. We aim to present the recent approaches proposed to solve these problems and to discuss their performances. This family of scheduling problems, addressed in this chapter, has been intensively studied (Kacem [8], Lee [17], Schmidt [24]). The studied criteria in this chapter are related to the flowtime minimization (the weighted and unweighted cases). The chapter is organized in two main parts. The first part focuses on the single machine scheduling problem (see Section 2). The second part is devoted to the parallel machine scheduling problem (see Section 3). In each part, we present the main contributions and explain their principles (complexity results, heuristic algorithms and their worstcase performance, existing approximation schemes, exact methods, branch-and-bound algorithms, dynamic programming, integer linear models, lower bounds. . .). Finally, Section 4 concludes the paper.

Single machine scheduling problems with release time are the prototypes for other complicated scheduling systems. Genetic local search algorithms are proposed to minimize total weighted completion time. Numerical experiments to evaluate the three embedding local search techniques are done. The results indicate that the 2r i+t i rule proposed by Liu and MacCathy (1991) outperform ERT and WSPT.Key wordsGenetic Local Search AlgorithmSingle Machine SchedulingRelease Time

This paper studies a new single machine scheduling problem with sequence-dependent setup time, release time, due time and group technology assumption originated from a wire rod and bar rolling process in steel plants. The objective is to find an optimal batch sequence and job sequences of all batches to minimize the number of late jobs. A two-stage mixed integer program is created to describe and solve this problem. The first stage can be solved in a short time by CPLEX while the second one is time-consuming when dealing with large-scale cases. Thus, an iterated greedy algorithm able to solve the second stage fast is developed. The experimental results demonstrate that the proposed two-stage mixed integer program can be solved optimally by CPLEX for small-scale cases and the proposed algorithm can effectively solve the second stage for large-scale cases.

This paper considers the single-machine scheduling problems in which two distinct agents are concerned. Each agent has a set of jobs with different release times, and both of them expect to complete their respective jobs as early as possible. We take the makespan of each agent as its own criterion and take the linear combination of the two makespans as our objective function. In this paper, both off-line and online models are considered. When preemption is allowed, we present an exact algorithm for the off-line model and an optimal algorithm for the on-line model. When preemption is not allowed we point out that the problem is NP-hard for the off-line model and give a (2+1/θ)-competitive algorithm for the on-line model. We also prove that a lower bound of the competitive ratio for the later model is 1 + θ/(1 + θ), where θ is a given factor not less than 1.

The research on the theory and method of single machine scheduling is a difficult subject, but it is very important for the companies to improve the production efficiency and effectiveness. The study on single machine scheduling problem has the history of 50 years, but there is still a gap between the classical scheduling theories and practical scheduling problems. According to this characteristic, the problems in practical scheduling area and the various factors need to be concerned are mentioned, and the main methods to solving the single machine scheduling problem and their applications are presented in details. Finally, the directions and suggestions of future work in single machine scheduling problem are summarized.

This paper considers the single machine scheduling problem with cost constraints based on customer driven using noncooperative game theory. The single machine scheduling problem with cost constraints based on customer driven is introduced, and customers bidding strategy is analyzed using noncooperative game method. Then noncooperative game model of single machine scheduling with cost constraints is defined using noncooperative game theory, in which the customer is mapped to the player, customer quotation corresponds to player strategy, and a payoff function of players is defined on condition of two main customer objectives. The satisfactory result of scheduling problem can be achieved by seeking Nash equilibrium solution, and the steps of seeking Nash equilibrium solution for the proposed scheduling game model are given. A single scheduling case is analyzed and solved, and the result verifies the validity of the proposed game model and the solving method.

Linear decision rules is a method for solving multistage stochastic linear programming problems. In this article we consider the feasibility of applying it to the hydropower scheduling problem. In our case, the price-taking producer determines a long-term reservoir management strategy that maximizes the market value of revenues from selling the electricity output in a well-functioning market. Uncertainty is present both in market prices and in reservoir inflows. Traditional methods for this problem suffer from a computing effort that grows exponentially with the number of stages and the number of state variables. The Linear Decision Rules (LDR) approximation is effective at reducing computational complexity, and is well-suited to multistage problems. By restricting the decision variables to be affine functions of the realisations of the uncertain parameters, the original intractable problem is transformed into a tractable one with short computational time. The approach is demonstrated on four Norwegian hydropower plants.

This paper establishes a robust optimization model and proposes constraint generation algorithm to solve a robust single machine scheduling problem with random release times. The performance criterion of interest is the maximum waiting time (MWT) over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our robust optimization model needs only the information of release time intervals. We formulate this uncertain optimization problem as a 0–1 linear programming model with a large number of constraints. To solve the model efficiently, a constraint generation algorithm (CGA) is proposed which generate constraint iteratively to obtain the optimal solution. The robustness of the optimal sequence under various probability distributions of release times is verified by simulation. Extensive computational experiments are implemented to demonstrate the effectiveness and efficiency of the proposed solution method.

Evolutionary algorithm for stochastic job shop scheduling with random processing time

ONE OF TIlE MOST interesting characteristics of recent aggregative ino(dels of economic growth is perhaps the specification of optimal growth paths under varying assumptions and conditions defining optiinality. Assuming that an optimal growth path for a fixed horizon can be specified for a developed or an underdeveloped economy, difficult decision problems of macro-dyniamic policy-making arise, when appropriate governmental actions are needed to secure the convergence of the observed growth path to the optimal one. The solutions of these decision problems by simple mathematical models are considered here with special emphasis on their uncertainty and dynamic aspects. The implications of alternative preference functions are analyzed here to show how optimal decision rules can be derived under various orders of truncation2, where truncation refers to the (degree of incomplete sp)ecification of the probability distribution of the random elements of the problem, i.e., the risk preference function (or disutility function) of the problem. Our approach would be to analyze the concept of 'a linear decision rule' developed by Theil [71 and emphasized recently by Holt [6] who used a quadratic risk function in a simple aggregative Keynesian model based on the multiplicr, the income identity and private investment as the only random variable. For illustrative purposes, we would use the principle of optimality of Pontryagin [9] as a generalization of the extremum conditions of variational calculus to derive the optimal time

Fast solution of single-machine scheduling problem with embedded jobs

Energy-efficient bi-objective single-machine scheduling with power-down mechanism

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.