In one-machine scheduling, MIP time-indexed formulations are often used to provide very good lower bounds through Lagrangian relaxations. In order to get an improved lower bound, we add valid cuts to a time-indexed formulation and show we still have a Lagrangian relaxation that can be solved as a shortest path in a graph. Two branch-and-bound algorithms are then presented for the earliness-tard...

This paper considers Just-In-Time Job-Shop Scheduling, in which each activity has an earliness and a tardiness cost with respect to a due date. It proposes a constraint programming approach, which includes a novel filtering algorithm and dedicated heuristics. The filtering algorithm uses a machine relaxation to produce a lower bound that can be obtained by solving a Just-In-Time Pert problem. I...

The problem of scheduling groups of jobs on a single machine under the group technology assumption is studied. Jobs of the same group are processed contiguously and a sequence independent setup time precedes the processing of each group. All jobs have a common fixed due date, which can be either unrestrictively large or restrictively small. The objective is to minimize the total weighted earlin...

The problem of determining a schedule of jobs with unit time lengths on a single machine that minimizes the total weighted earliness and tardiness penalties with respect to arbitrary rational due dates is formulated as an integer programming problem We show that if the penalties meet a certain criterion called the Dominance Condition then there exists an extremal optimal solution to the LP rela...

The just-in-time production philosophy has led to a growing interest in scheduling problems considering both earliness and tardiness penalties. Most publications considering these so-called non-regular objective functions are devoted to single machine problems. In the case of multi-machine problems, there are some papers dealing with parallel machine problems. However, for multi-operation sched...

appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. one type of scheduling problems is just-in-time (jit) scheduling and in this area, motivated by jit manufacturing, this study investigates a mathematical model for...

The just-in-time concept in manufacturing has aroused interest in machine scheduling problems with earliness-tardiness penalties. In particular, common due date problems, which are structurally less complicated than problems with general due dates, have emerged as an interesting and proliic eld of research. We prove that so-called almost common due date problems, in which the due date d j and p...