In this research, a bi-objective scheduling problem with controllable processing times on identical parallel machines is investigated. The direction of this paper is mainly motivated by the adoption of the just-in-time (JIT) philosophy on identical parallel machines in terms of bi-objective approach, where the job processing times are controllable. The aim of this study is to simultaneously min...

We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizin...

We present a unified analysis for single-machine scheduling problems in which the actual job processing times are controlled by either a linear or a convex resource allocation function and also vary concurrently depending on either the job’s position in the sequence and/or on the total processing time of the already processed jobs. We show that the problem is solvable in Oðn log nÞ time by usin...

We study scheduling problems with controllable processing times on parallel machines, in which the decision-maker selects an actual processing time for each job from a given interval. The chosen values of the processing times must be such that each job can be preemptively scheduled within a given time interval, and it is required to minimize a certain cost function that depends on the chosen ti...

We study the earliness-tardiness scheduling problem on a single machine with due date assignment and controllable processing times. We analyze the problem with three different due date assignment methods and two different processing time functions. For each combination of these, we provide a polynomialtime algorithm to find the optimal job sequence, due date values and resource allocation minim...

This paper considers a genetic algorithm (GA) for a machine-job assignment with controllable processing times (MJACPT). Integer representation with standard genetic operators is used. In an objective function, a job assignment is obtained from genetic code and for this, fixed assignment processing times are calculated by solving a constrained nonlinear convex optimization problem. Additionally,...

In this paper, we present a general methodology for designing polynomial-time algorithms for bicriteria scheduling problems on parallel machines with controllable processing times. For each considered problem, the two criteria are the makespan and the total compression cost, and the solution is delivered in the form of the break points of the efficient frontier. We reformulate the scheduling pr...