Scheduling jobs with values dependent on their completion times

The paper concerns two scheduling problems with job values and losses of job values (costs) dependent on job completion times. In the first problem, we consider scheduling jobs with stepwise values in parallel processor environment. In the stepwise value, there is given a number of moments at which the job value decreases and between them the job value is constant (thus, the value deteriorates over time). The maximized criterion is the total job value. We prove strong NP-hardness of a single processor case of the problem and construct a pseudo-polynomial time algorithm for a special case with fixed number of unrelated parallel processors and fixed number of common moments of job value changes. Additionally, for uniform and unrelated parallel processors we construct and experimentally test several heuristic algorithms based on the list strategy. The second problem is a single processor one with piecewise linear losses of job values (the loss increases over time). The minimized criterion is the total loss of job value. We prove strong NP-hardness of the problem and existence of a pseudo-polynomial time exact algorithm for its special case. We also construct some heuristic algorithms for this problem and verify experimentally their efficiency.     

Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in a multi-layer ceramic capacitor production line, we study a scheduling problem of batch processing machine in which a number of jobs are processed simultaneously as a batch. The performance measures considered include makespan, total completion time, and total weighted completion time. We first present a new simple integer programming formulation for the problem, and using this formulation, one can easily find optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is very large, we propose a number of heuristic algorithms and design a hybrid genetic algorithm to solve practical big-size problems in a reasonable computational time. To verify performance of the algorithms, we compare them with lower bounds for the problems. From the results of these computational experiments the heuristic algorithms including the genetic algorithm show different performances for the three problems.     

Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine

This paper considers the problem of scheduling deteriorating jobs and due date assignment on a single machine. The actual processing time of a job is a linear increasing function of its starting time. The problem is to determine the optimal due dates and the processing sequence simultaneously to minimize costs for earliness, due date assignment and weighted number of tardy jobs. We present polynomial-time algorithms to solve the problem in the case of two popular due date assignment methods: CON and SLK.     

Heuristics for operational fixed job scheduling problems with working and spread time constraints

Operational fixed job scheduling problems select a set of jobs having fixed ready and processing times and schedule the selected jobs on parallel machines so as to maximize the total weight. In this study, we consider working time and spread time constrained versions of the operational fixed job scheduling problems. The working time constraints limit the total processing load on each machine. The spread time constraints limit the time between the start of the first job and the finish of the last job on each machine. For the working time constrained problem, we present a filtered beam search algorithm that evaluates the promising nodes of the branch and bound tree. For the spread time constrained problem we propose a two phase algorithm that defines the promising sets for the first jobs and finds a solution for each promising set. The results of our computational tests reveal that our heuristic algorithms perform very well in terms of both solution quality and time.     

A note on “minimizing a weighted quadratic function of job lateness in the single machine system”

A set of jobs is to be scheduled on a single machine where an idle time is allowed to be inserted before the processing of the first job begins. The objective is to find an optimal sequence that minimizes the weighted sum of a quadratic function of job lateness. Sen et al. [Sen, T., Dileepan, P., Lind, M.R., 1995. Minimizing a weighted quadratic function of job lateness in the single machine system. International Journal of Production Economics 42(3), 237–243] presented a branch-and-bound algorithm for the problem; however, as shown in this note, their algorithm does not work because the branching rule for adjacent jobs is not applicable to non-adjacent jobs.     

Minimizing mean absolute deviation of completion time about a common due window subject to maximum tardiness for a single machine

This study deals with the problem of scheduling jobs on a single machine to minimize the mean absolute deviation of the job completion time about a large common due window subject to the maximum tardiness constraint. Using the well-known three-field notation, the problem is identified as MAD/large DueWindow/T_max. The common due window is set to be large enough to allow idle time prior to the beginning of a schedule to investigate the effect of the T_max constraint. Penalties arise if a job is completed outside the due window. A branch and bound algorithm and a heuristic are proposed. Many properties of the solutions and precedence relationships are identified. Our computational results reveal that the branch and bound algorithm is capable of solving problems of up to 50 jobs and the heuristic algorithm yields approximate solutions that are very close to the exact solution.     

Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective

This paper addresses the problem of scheduling a set of independent jobs on unrelated parallel machines with job sequence dependent setup times so as to minimize a weighted mean completion time. The study of the problem stemmed from a real service industry problem. This problem is at least NP-hard in the ordinary sense, even when there are only two identical machines with no setups. Seven heuristic algorithms are proposed and tested by simulation. The results and analysis of quite extensive computational experiments are reported and discussed. The findings through the computational results are presented. Whether this problem is strongly NP-hard is left as an open question.     

Robust and stable flexible job shop scheduling with random machine breakdowns using a hybrid genetic algorithm

This paper addresses the problem of finding robust and stable solutions for the flexible job shop scheduling problem with random machine breakdowns. A number of bi-objective measures combining the robustness and stability of the predicted schedule are defined and compared while using the same rescheduling method. Consequently, a two-stage Hybrid Genetic Algorithm (HGA) is proposed to generate the predictive schedule. The first stage optimizes the primary objective, minimizing makespan in this work, where all the data is considered to be deterministic with no expected disruptions. The second stage optimizes the bi-objective function and integrates machines assignments and operations sequencing with the expected machine breakdown in the decoding space. An experimental study and Analysis of Variance (ANOVA) is conducted to study the effect of different proposed measures on the performance of the obtained results. Results indicate that different measures have different significant effects on the relative performance of the proposed method. Furthermore, the effectiveness of the current proposed method is compared against three other methods; two are taken from literature and the third is a combination of the former two methods.