This paper proposes various lower bounds to the makespan of the flexible job shop scheduling problem (FJSP). The FJSP is known in the literature as one of the most difficult combinatorial optimisation problems (NP-hard). We will use genetic algorithms for the optimisation of this type of problems. The list of the demands is divided in two sets: the actual demand, which is considered as certain ...

Temporal networks play a crucial role in modeling temporal relations in planning and scheduling applications. Temporal Networks with Alternatives (TNAs) were proposed to model alternative and parallel processes in production scheduling, however the problem of deciding which nodes can be consistently included in such networks is NP-complete. A tractable subclass, called Nested TNAs, can still co...

We present in this paper an iterative algorithm to solve constraint forces for haptic interactive simulation. The haptic forces are induced by interaction with guidance virtual fixtures having forbidden regions. In general, a haptic rendering based on an explicit formulation of the constraint forces (with virtual springs) can lead to severe numerical stability problems in case of hard constrain...

The paper considers a three-machine shop scheduling problem to minimize the makespan, in which the route of a job should be feasible with respect to a machine precedence digraph with three nodes and one arc. For this NP-hard problem that is related to the classical flow shop and open shop models, we present a simple 1.5approximation algorithm and an improved 1.4-approximation algorithm.

One of the most critical concerns cloud service providers is balancing renewable and fossil energy consumption. On other hand, policy organizations governments to reduce consumption greenhouse gas emissions in data centers. Recently, a lot research has been conducted optimize virtual machine placement on physical machines minimize Many previous studies have not considered deadline scheduling In...

An unrelated parallel machine scheduling problem motivated by the of a printed circuit board assembly (PCBA) under surface mount technology (SMT) is discussed in this paper. This involved eligibility restrictions, sequence-dependent setup times, precedence constraints, unequal job release and constraints shared resources with objectives minimizing makespan total tardiness. Since NP-hard, mathem...

In this paper the multiple projects resourceconstrained project scheduling problem is considered. Several projects are to be scheduled simultaneously with sharing several kinds of limited resources in this problem. Each project contains non-preemptive and deterministic duration activities which compete limited resources under resources and precedence constraints. Moreover, there are the due dat...

A cyclic scheduling problem is specified by a set of activities that are executed an infinite number of times subject to precedence and resource constraints. The cyclic scheduling problem has many applications in manufacturing, production systems, embedded systems, compiler design and chemical systems. This paper proposes a Constraint Programming approach based on Modular Arithmetic, taking int...

In this paper, we study an assembly job shop scheduling problem with tree-structured precedence constraints and jobs characterized by specific bills of materials. We propose a fast and efficient constructive heuristic that is able to easily deal with real-world sized instances. The production schedule takes into account the actual availability of materials in stock as well as the supply times a...

The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint problems are a generalisation of the CSP which allow the user to model optimisation problems. Considerable effort has been made in identifying properties wh...