An Interpolation-Based Polynomial Method of Estimating the Objective Function Value in Scheduling Problems of Minimizing the Maximum Lateness

An approach to estimating the objective function value of minimization maximum lateness problem is proposed. It is shown how to use transformed instances to define a new continuous objective function. After that, using this new objective function, the approach itself is formulated. We calculate the objective function value for some polynomially solvable transformed instances and use them as interpolation nodes to estimate the objective function of the initial instance. What is more, two new polynomial cases, that are easy to use in the approach, are proposed. In the end of the paper numeric experiments are described and their results are provided.

Polynomial Algorithm for Constructing Pareto-Optimal Schedules for Problem 1∣rj∣Lmax,Cmax

In this chapter, we consider the single machine scheduling problem with given release dates, processing times, and due dates with two objective functions. The first one is to minimize the maximum lateness, that is, maximum difference between each job due date and its actual completion time. The second one is to minimize the maximum completion time, that is, to complete all the jobs as soon as possible. The problem is NP-hard in the strong sense. We provide a polynomial time algorithm for constructing a Pareto-optimal set of schedules on criteria of maximum lateness and maximum completion time, that is, problem 1 ∣ r j ∣ L max , C max , for the subcase of the problem: d 1 ≤ d 2 ≤ … ≤ d n ; d 1 − r 1 − p 1 ≥ d 2 − r 2 − p 2 ≥ … ≥ d n − r n − p n .

Scheduling job shop problems with operators with respect to the maximum lateness

This paper deals with the problem of assigning operators to jobs, within a free assignment-changing mode, in a job-shop environment subject to a fixed processing sequence of the jobs. We seek an assignment of operators that minimizes the maximum lateness. Within this model, a job needs an operator during the entire duration of its processing. We show that the problem is 𝒩𝒫-hard when the number of operators is arbitrary and exhibit polynomial time algorithms for the cases involving one and two operators, respectively.