Liron Yedidsion

A bicriteria approach to scheduling a single machine with job rejection and positional penalties

Single machine scheduling problems have been extensively studied in the literature under the assumption that all jobs have to be processed. However, in many practical cases, one may wish to reject the processing of some jobs in the shop, which results in a rejection cost. A solution for a scheduling problem with rejection is given by partitioning the jobs into a set of accepted and a set of rejected jobs, and by scheduling the set of accepted jobs among the machines. The quality of a solution is measured by two criteria: a scheduling criterion, F1, which is dependent on the completion times of the accepted jobs, and the total rejection cost, F2. Problems of scheduling with rejection have been previously studied, but usually within a narrow framework—focusing on one scheduling criterion at a time. This paper provides a robust unified bicriteria analysis of a large set of single machine problems sharing a common property, namely, all problems can be represented by or reduced to a scheduling problem with a scheduling criterion which includes positional penalties. Among these problems are the minimization of the makespan, the sum of completion times, the sum and variation of completion times, and the total earliness plus tardiness costs where the due dates are assignable. Four different problem variations for dealing with the two criteria are studied. The variation of minimizing F1+F2 is shown to be solvable in polynomial time, while all other three variations are shown to be

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

\mathcal{NP}

Just-in-time scheduling with controllable processing times on parallel machines

-hard. For those hard problems we provide a pseudo polynomial time algorithm. An FPTAS for obtaining an approximate efficient schedule is provided as well. In addition, we present some interesting special cases which are solvable in polynomial time.

A bicriteria approach to minimize maximal lateness and resource consumption for scheduling a single machine

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.

Operations scheduling under electricity time-varying prices

AbstractWe study scheduling problems with controllable processing times on parallel machines. Our objectives are to maximize the weighted number of jobs that are completed exactly at their due date and to minimize the total resource allocation cost. We consider four different models for treating the two criteria. We prove that three of these problems are

Microgels for Efficient Protein Purification

\mathcal{NP}

Bicriteria problems to minimize maximum tardiness and due date assignment cost in various scheduling environments

-hard even on a single machine, but somewhat surprisingly, the problem of maximizing an integrated objective function can be solved in polynomial time even for the general case of a fixed number of unrelated parallel machines. For the three

Conformance checking and performance improvement in scheduled processes

\mathcal{NP}

Setting defect charts control limits to balance cycle time and yield for a tandem production line

-hard versions of the problem, with a fixed number of machines and a discrete resource type, we provide a pseudo-polynomial time optimization algorithm, which is converted to a fully polynomial time approximation scheme.

Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling

Abstract We extend the classical single-machine maximal lateness scheduling problem to the case where the job processing times are controllable by allocating a continuous and nonrenewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between maximal lateness and total resource consumption using a bicriteria approach. We present a polynomial time algorithm that constructs this trade-off curve assuming a specified general type of convex decreasing resource consumption function. We illustrate the algorithm with a numerical example.