Daniel Oron

Due-date assignment and maintenance activity scheduling problem

In the scheduling problem addressed in this note we have to determine: (i) the job sequence, (ii) the (common) due-date, and (iii) the location of a rate modifying (maintenance) activity. Jobs scheduled before (after) the due-date are penalized according to their earliness (tardiness) value. The processing time of a job scheduled after the maintenance activity decreases by a job-dependent factor. The objective is minimum total earliness, tardiness and due-date cost. We introduce a polynomial (O(n^4)) solution for the problem.

Open-shop batch scheduling with identical jobs

Abstract This paper addresses batch scheduling problems on an m -machine open-shop. The objectives are minimum makespan and minimum flowtime. We assume identical processing time jobs, machine- and sequence-independent setup times and batch availability. The minimum makespan problem is shown to be solved in constant time . Specifically, we show that the optimal number of batches is either m or n ⌊ n / m ⌋ (where m and n are the number of machines and the number of jobs, respectively). The complexity of the minimum flowtime problem is unknown. We propose an O ( n ) time algorithm which extends the solution of the single-machine case, and produces close-to-optimal solutions.

Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning

Job deterioration and machine learning co-exist in various real life scheduling settings. This paper studies several single machine scheduling problems under the joint effect of nonlinear job deterioration and time-dependent learning. We assume that the processing time of a job increases when its processing is delayed. In addition, it is assumed that the machine undergoes a learning process, decreasing the time required to process a given job. The following objectives are considered: the makespan, the sum of completion times (square) and the maximum lateness. We derive polynomial-time optimal solutions for all the objectives.

Minimizing flow-time on a single machine with integer batch sizes

We address a classical minimum flow-time, single-machine, batch-scheduling problem. Processing times and setups are assumed to be identical for all jobs and batches, respectively. Santos and Magazine (Oper. Res. Lett. 4(1985) 99) introduced an efficient solution for the relaxed (non-integer) problem. We introduce a simple rounding procedure for Santos and Magazines solution, which guarantees optimal integer batches.

Optimal due date assignment and resource allocation in a group technology scheduling environment

We study a single machine scheduling problem in which the scheduler determines due dates for different jobs in a group technology environment. In group technology (GT) environment, a partition of the jobs into groups (families) is given and jobs of the same family are required to be processed consecutively. The partition of the jobs into families is done in order to achieve efficiency of high-volume production by exploiting similarities of different products and activities in their production. Since customers of similar jobs may expect that all jobs within the same group will be assigned with the same due date, we suggest an original due date assignment method in which all jobs within a family are restricted to be assigned the same due date, while each family can be assigned a due date without any restriction. The proposed method provides an extension of two earlier methods that appear in the literature, one which includes a single family and the other in which the number of families is identical to the number of jobs. Our objective is to find the job schedule and the due date for each group that minimizes an objective function which includes earliness, tardiness and due date assignment penalties. We also extend the analysis to address the case in which the job processing times are resource dependent. For this case we include the total weighted resource consumption and the makespan penalties to the objective function.

A single machine batch scheduling problem with bounded batch size

We address a single-machine batch scheduling problem to minimize total flow time. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. As in many practical situations, batch sizes may be bounded. In the first setting studied in this paper, all batch sizes cannot exceed a common upper bound. In the second setting, all batch sizes share a common lower bound. An optimal solution consists of the number of batches and their (integer) size. We introduce an efficient solution for both problems.

Scheduling Controllable Processing Time Jobs in a Deteriorating Environment

The author regrets two errors in the published paper: 1. On Page 52, Lemma 3: ‘non-increasing order’ should be ‘non-decreasing order’. 2. On Page 55, Lemma 6: ‘non-increasing order’ should be ‘non-decreasing order’. The proofs are correct and consistent with the amended statements. The author apologises for any inconvenience caused and would like to express his gratitude to Professor Lu Liu for pointing out these errors. Journal of the Operational Research Society (2016) 67, 535

Single machine scheduling with two competing agents and equal job processing times

We study various two-agent scheduling problems on a single machine with equal job processing times. The equal processing time assumption enables us to design new polynomial-time or faster-than-known optimization algorithms for many problems. We prove, however, that there exists a subset of problems for which the computational complexity remains NP-hard. The set of hard problems includes different variations where the objective functions of the two agents are either minimizing the weighted sum of completion times or the weighted number of tardy jobs. For these problems, we present pseudo-polynomial time algorithms.

A note on flow-shop and job-shop batch scheduling with identical processing-time jobs

We address a batch scheduling problem of n identical processing time jobs on an m-machine flow-shop and a 2-machine job-shop. The objective is makespan minimization. Both problems are shown to be solved in O(n).

A note on the SPT heuristic for solving scheduling problems with generalized due dates

Two NP-hard scheduling problems on parallel identical machines with generalized due dates are studied. We focus on two objectives: (i) minimizing maximum tardiness and (ii) minimizing total tardiness. In both cases, we introduce a shortest processing time first (SPT)-based heuristic and simple lower bounds on the optimal cost. Our numerical study indicates that the SPT heuristic performs extremely well in all settings.