Medium-term production planning and short-term scheduling match future production load and capacities over various horizons and on different levels of detail. Although these two levels of the decision hierarchy are strongly interdependent, traditional systems handle them separately. In the Proterv-II prototype system that was developed for manufacturing industries, the two levels are linked by ...

Abstract We consider a variant of the NP-hard problem assigning jobs to machines minimize completion time last job. Usually, precedence constraints are given by partial order on set jobs, and each job requires all its predecessors be completed before it can start. In this paper, we different type relation that has not been discussed as extensively is called OR-precedence. for start, require at ...

Many real-world constraint satisfaction problems (CSPs) can be over-constrained or too large to solve using a standard constructive/backtracking approach. Instead, faster heuristic techniques have been proposed that perform a partial search of all possible solutions using an iterative repair or hill-climbing approach. The main problem with such approaches is that they can become stuck in local ...

Abstract—Resource –constrained project scheduling problem (RCPSP) is a well known NP hard problem. This paper proposes a hybrid approach of constraint programming (CP) and integer programming (IP) which could solve RCPSP with ideal efficiency and quality. Constraint propagation is key element of constraint programming and is widely used in cumulative resource problem (CRP). CRP can be taken as ...

This paper introduces a global constraint encapsulating a regular constraint together with several cumulative costs. It is motivated in the context of personnel scheduling problems, where a schedule meets patterns and occurrence requirements which are intricately bound. The optimization problem underlying the multicost-regular constraint is NP-hard but it admits an efficient Lagrangian relaxati...

In heavy traffic nodes of rail networks, as in main stations, conflicts and subsequent train delays greatly propagate during operations. A disturbance which is at origin only a few seconds long can quickly lead to other delays of over five minutes. To limit this phenomenon, newmethods andmodels are necessary to optimise the use of scarce resources like platforms and track sections. The operator...

This paper investigates the multistage hybrid flow shop (HFS) scheduling problems using the new bat algorithm. A HFS is the generalisation of flowshop with multiple machines. HFS is one of the important scheduling problems that represent many industries like iron and steel, chemical, textile and ceramic industries. The HFS scheduling problems have been proved to be NP-hard. A recently developed...

Constraint Programming is a methodology for problem solving which allows the user to describe data and constraints of the problem without explicitly solving in the declarative phase. Constraint Satisfaction Problems (CSP) can simply be defined as a set of variables and a set of constraints among the values of the variables. Typical method of solving CSP models is building the solution by backtr...

The Resource Constrained Project Scheduling Problem (rcpsp) is a general scheduling problem. It consists of a set of activities and a set of renewable resources. Each resource is available in a given constant amount. Each activity has a duration and requires a constant amount of resource to be processed. Preemption is not allowed. Activities are related by two sets of constraints: temporal cons...