A constraint propagation (filtering) turned out to be an efficient method how to reduce search space for backtrack-based algorithms. This paper brings several improvements of filtering methods for batch processing with sequence dependent setup times. The first one is domain filtering based on a precedence graph—such filtering can be useful even when no precedences are given at the start. I desc...

Finding a hard real-time feasible schedule is not trivial since this problem is NP-hard in its general form. There are two general approaches for scheduling tasks: runtime and pre-runtime scheduling. For many cases, runtime methods do not find a feasible schedule even if such a schedule exists. Such situations often occurs when the design model imposes intertask relations, such as precedence an...

Constraint-based scheduling is a powerful tool for solving real-life scheduling problems thanks to a natural integration of special solving algorithms encoded in global constraints. The filtering algorithms behind these constraints are based on propagation rules modelling some aspects of the problems, for example a unary resource. This paper describes new incremental propagation rules integrati...

Process planning that is based on environmental consciousness and energy-efficient scheduling currently plays a critical role in sustainable manufacturing processes. Despite their interrelationship, these two topics have often been considered to be independent of each other. It therefore would be beneficial to integrate process planning and scheduling for an integrated energy-efficient optimisa...

Work-flow scheduling is for finding the allocation method to achieve optimal resource utilization. In process, constraints, such as time, cost and quality, need be considered. How balance these parameters a NP-hard problem, nonlinear manufacturing process increases difficulty of scheduling, so it necessary provide an effective heuristic algorithm. Aiming at problems, multi-objective virtual wor...

Consider the problem of scheduling n tasks with precedence constraint ≺ on m parallel processors so as to minimize the makespan. Let ω and ω′ be the makespans of the optimal nonpreemptive and optimal preemptive schedules, respectively. Liu’s conjecture states that ω ω′ ≤ 2m m+1 . In this paper, we present a simple proof of the conjecture for ≺= ∅, and give an improved bound closer to that in th...

The simple assembly line balancing (SALB) problem is a significant challenge faced by industries across various sectors aiming to optimise production efficiency and resource allocation. One important issue when the decision-maker balances how keep cycle time under given all cells, even though there variability in some parameters. When are stochastic elements, approaches use constraint relaxatio...

This thesis studies the approximability of scheduling problems in different contexts. Chapter 2 gives a short introduction to the field of scheduling theory and presents a simple single machine scheduling problem that will form the base for all variants considered in the remainder of this thesis. We point out that this scheduling problem, though long known to be efficiently solvable in its orig...

Traditionally, simulation has been applied as an off-line tool for mid or long-term planning and for operational design whereas optimisation has been applied on-line on a daily basis for scheduling. The impact of variability and randomness on the real system greatly increases the difficulty of scheduling and control of manufacturing systems. Therefore, the is a great interest for using on-line ...