Uncertainty assessments of linear timecost tradeoffs using neutrosophic set Abstract   Resource allocation via project scheduling plays an important role to balance project time and cost. In this paper, we are designing a framework to handle scheduling problems using neutrosophic activity duration times. We consider important aspects of timecost tradeoffs while taking into account the real and uncertain situation surrounded by the projects. In real situations, there are many considerable aspects which should be considered by managers, for instance, the tradeoffs between the project completion time and cost and the uncertain conditions of the environment. Since the concept of the deterministic project scheduling and timecost tradeoffs conflict with the real situation, where in many cases, some data on the activities durations of the project changes during the implementation process. Fuzzy scheduling and timecost tradeoffs models assume only truthmembership functions dealing with uncertainties surrounded by the projects and their activities duration which are unable to handle indeterminacy and inconsistency. Therefore, neutrosophic theory is a better framework that takes into account the dynamic features of all parameters. Trapezoidal neutrosophic numbers are used to estimate the activities durations in this paper. The crisp model for activities time obtained by applying score and accuracy functions. The goal here is to minimize the cost of projects under uncertain environmental conditions.

A LazyConstraints Approach to ResourceConstrained Project Scheduling We study the complex combinatorial optimization problem to schedule the activities of a single project with the objective to complete the project within the shortestpossible amount of time such that the limited resource capacities as well as the prescribed precedence relations between pairs of the activities are taken into account. In addition to various specific solution algorithms, the related literature proposes several MixedInteger Linear Programming (MILP) models, but these models remain complex to solve even for smallsized instances. We present a novel approach based on an MILP model in which the resourcecapacity constraints are formulated for all inclusionminimal sets of activities which, due to the limited capacities of the resources, cannot be processed simultaneously. We propose to remove these constraints from the model and iteratively add those constraints back which are violated in the solutions obtained. For a set of test instances from the literature, our computational results indicate that with respect to both, the deviation of the project duration obtained from the lower bound devised from the criticalpath length and the number of instances solved to optimality, the novel lazyconstraints approach outperforms ten stateoftheart MILP models.