The preemptive resource-constrained project scheduling problem subject to due dates and preemption penalties: An integer programming approach

Extensive research has been devoted to resource constrained project scheduling problem. However, little attention has been paid to problems where a certain time penalty must be incurred if activity preemption is allowed. In this paper, we consider the project scheduling problem of minimizing the total cost subject to resource constraints, earliness-tardiness penalties and preemption penalties, where each time an activity is started after being preempted; a constant setup penalty is incurred. We propose a solution method based on a pure integer formulation for the problem. Finally, some test problems are solved with LINGO version 8 and computational results are reported

A Multi Objective Fibonacci Search Based Algorithm for Resource Allocation in PERT Networks

The problem we investigate deals with the optimal assignment of resources to the activities of a stochastic project network. We seek to minimize the expected cost of the project include sum of resource utilization costs and lateness costs. We assume that the work content required by the activities follows an exponential distribution. The decision variables of the model are the allocated resource quantities. We construct a continuous time Markov chain model for the activity network and use the PhaseType distribution to evaluate the project completion time. Then we use Fibonacci search over the interval of permissible allocations to the activity to seek the minimum expected cost

A Comparison of NSGA II and MOSA for Solving Multi-depots Time-dependent Vehicle Routing Problem with Heterogeneous Fleet

Time-dependent Vehicle Routing Problem is one of the most applicable but least-studied variants of routing and scheduling problems. In this paper, a novel mathematical formulation of time-dependent vehicle routing problems with heterogeneous fleet, hard time widows and multiple depots, is proposed. To deal with the traffic congestions, we also considered that the vehicles are not forced to come back to the depots, from which they were departed. In order to solve our bi-objective formulation, we presented two well-known Meta-heuristic algorithms, namely NSGA II and MOSA and compared their performance based on a set of randomly generated test problems. The results confirm that our MILP model is valid and both NSGA II and MOSA work properly. While NSGA II finds closer solutions to the true Pareto front, MOSA finds evenly- distributed solutions which allows the algorithm to search the space more diversely

An Exact Algorithm for the Mode Identity Project Scheduling Problem

In this paper we consider the non-preemptive variant of a multi-mode resource constrained project scheduling problem (MRCPSP) with mode identity, in which a set of project activities is partitioned into disjoint subsets while all activities forming one subset have to be processed in the same mode. We present a depth-first branch and bound algorithm for the resource constrained project scheduling problem with mode identity. The proposed algorithm is extended with some bounding rules to reduce the size of branch and bound tree. Finally, some test problems are solved and their computational results are reported

Robust optimization of train scheduling with consideration of response actions to primary and secondary risks

Nowadays, with the rapid development of rail transportation systems, passenger demand and the possibility of the risks occurring in this industry have increased. These conditions cause uncertainty in passenger demand and the development of adverse impacts as a result of risks, which put the assurance of precise planning in jeopardy. To deal with uncertainty and lessen negative impacts, robust optimization of the train scheduling problem in the presence of risks is crucial. A two-stage mixed integer programming model is suggested in this study. In the first stage, the objective of the nominal train scheduling problem is to minimize the total travel time function and optimally determine the decision variables of the train timetables and the number of train stops. A robust optimization model is developed in the second stage with the aim of minimizing unsatisfied demand and reducing passenger dissatisfaction. Additionally, programming is carried out and the set of optimal risk response actions is identified in the proposed approach for the presence of primary and secondary risks in the train scheduling problem. A real-world example is provided to demonstrate the model's effectiveness and to compare the developed models. The results demonstrate that secondary risk plays a significant role in the process of optimal response actions selection. Furthermore, in the face of uncertainty, robust solutions can significantly and effectively minimize unsatisfied demand by a slightly rise in the travel time and the number of stops obtained from the nominal problem

A Bi-Objective Robust Model for Location-Routing and Capacity Sharing in Districting Regions under Uncertainty

One of the most important approaches that can lead to the creation of various advantagesfor enterprises is the districting regions into the service offering locations and the demandunits, which causes the increase in level of customers’ access to get the service. On theother hand, if vehicle routing is carried out in districting regions in order to deliver productsto customers, the planning of customer service can be improved. However, in none of theresearch conducted in the area of design supply chain, vehicle routing in districting regionshas been not investigated. Therefore, in the current study, a bi-objective mathematicalmodel is presented to simultaneously focus on districting regions, facility location–allocation, service sharing, intra-district service transfer and vehicle routing. The firstobjective function minimizes the total cost of designing the CLSC network, which includescosts of opening facility and vehicle routing. The second objective function minimizes themaximum volume of surplus demand from service providers in order to achieve anappropriate balance in demand volume across all regions. Moreover, a robust optimizationapproach is used to take into account uncertainty in some parameters of the proposedmodel. In addition, the validity of the proposed mathematical model and the proposedsolution has been investigated on a real case in the oil and gas industry

A constructive heuristic for time-dependent multi-depot vehicle routing problem with time-windows and heterogeneous fleet

In this paper, we consider the time-dependent multi-depot vehicle routing problem. The objective is to minimize the total heterogeneous fleet cost assuming that the travel time between locations depends on the departure time. Also, hard time window constraints for the customers and limitation on maximum number of the vehicles in depots must be satisfied. The problem is formulated as a mixed integer programming model. A constructive heuristic procedure is proposed for the problem. Also, the efficiency of the proposed algorithm is evaluated on 180 test problems. The obtained computational results indicate that the procedure is capable to obtain a satisfying solution

An Iterated Local Search Algorithm for Estimating the Parameters of the Gamma/Gompertz Distribution

Extensive research has been devoted to the estimation of the parameters of frequently used distributions. However, little attention has been paid to estimation of parameters of Gamma/Gompertz distribution, which is often encountered in customer lifetime and mortality risks distribution literature. This distribution has three parameters. In this paper, we proposed an algorithm for estimating the parameters of Gamma/Gompertz distribution based on maximum likelihood estimation method. Iterated local search (ILS) is proposed to maximize likelihood function. Finally, the proposed approach is computationally tested using some numerical examples and results are analyzed

A solution procedure for preemptive multi-mode project scheduling problem with mode changeability to resumption

Extensive research has been devoted to the multi-mode resource constrained project scheduling problem (MRCPSP). However, little attention has been paid to problems where preemption is allowed. This paper involves the preemptive multi-mode resource constrained project scheduling problem (P-MRCPSP) to minimize the project makespan subject to mode changeability after preemption. This problem is a more realistic model and extended case of multi-mode resource constrained project scheduling problem. A binary integer programing formulation is proposed for the problem. The problem formed in this way is an NP-hard one forcing us to use the Simulated Annealing (SA) algorithm to obtain a global optimum solution or at least a satisfying one. The performance of the proposed algorithm is evaluated on 480 test problems by statistically comparing in term of the objective function and computational times. The obtained computational results indicate that the proposed algorithm is efficient and effective. Also, it is concluded from the results that mode change is very effective to improve the optimal makespan of the project. Keywords: Project scheduling, Mode change, Simulated Annealing, Preemption, Resumptio