Improvement of Lagrangian relaxation performance for open pit mines constrained long-term production scheduling problem

Constrained long-term production scheduling problem(CLTPSP) of open pit mines has been extensively studied in the past few decades due to its wide application in mining projects and the computational challenges it poses become an NP-hard problem.This problem has major practical significance because the effectiveness of the schedules obtained has strong economical impact for any mining project.Despite of the rapid theoretical and technical advances in this field,heuristics is still the only viable approach for large scale industrial applications.This work presents an approach combining genetic algorithms(GAs) and Lagrangian relaxation(LR) to optimally determine the CLTPSP of open pit mines.GAs are stochastic,parallel search algorithms based on the natural selection and the process of evolution.LR method is known for handling large-scale separable problems; however,the convergence to the optimal solution can be slow.The proposed Lagrangian relaxation and genetic algorithms(LR-GAs) combines genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers.This approach leads to improve the performance of Lagrangian relaxation method in solving CLTPSP.Numerical results demonstrate that the LR method using GAs to improve its performance speeding up the convergence.Subsequently,highly near-optimal solution to the CLTPSP can be achieved by the LR-GAs.

Scheduling Multi-Mode Resource-Constrained Projects Using Heuristic Rules Under Uncertainty Environment

Project scheduling is a key objective of many models and is the proposed method for project planning and management.Project scheduling problems depend on precedence relationships and resource constraints,in addition to some other limitations for achieving a subset of goals.Project scheduling problems are dependent on many limitations,including limitations of precedence relationships,resource constraints,and some other limitations for achieving a subset of goals.Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required,which are known and stable during the implementation process.The concept of deterministic project scheduling conflicts with real situations,in which in many cases,some data on the activity’s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations.Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us.We use the multi-mode resource allocation and schedulingmodel that takes into account the dynamicity features of all parameters,that is,the scheduling process must be flexible to dynamic environment features.In this paper,we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations,in which we apply the proposed heuristic rules(PHR)for scheduling multi-mode resource-constrained projects.Five projects are considered test problems for the PHR.The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems.The results in many cases of the proposed priority rules are very promising,where they achieve better scheduling dates in many test case problems and the same results for the others.The proposed model is based on the dynamic features for project topography.

Multi-Mode Resource Constrained Project Scheduling Models for Progress and Equal Time Interval Payments

This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progress payment （PP） and the payment at an equal time interval （ETI）. The objective of each model is to maximize the net present value （NPV） for all cash flows in the project, subject to the related operational constraints. The models are characterized as NP-hard. A heuristic algorithm, coupled with two upper bound solutions, is proposed to efficiently solve the models and evaluate the heuristic algorithm performance which was not performed in past studies. The results show that the performance of proposed models and heuristic algorithm is good.

A New Algorithm for Resource Constraint Project Scheduling Problem Based on Multi-Agent Systems

The resource constrained project scheduling problem (RCPSP) and a decision-making model based on multi-agent systems (MAS) and general equilibrium marketing are proposed. An algorithm leading to the resource allocation decision involved in RCPSP has also been developed. And this algorithm can be used in the multi-project scheduling field as well.Finally, an illustration is given.