This paper discusses the problem of allocation of constrained renewable resource to Splittable activities of a single project. If the activities of stochastic projects can be split, these projects may be completed in shorter time when the available resource is constrained. It is assumed that the resource amount required to accomplish each activity is a discrete quantity and deterministic. The activity duration time is assumed to be a discrete random variable with arbitrary experimental distribution. Solving stochastic mathematical programming model of problem is very hard. So, here some existing methods for deterministic problems have been generalized for stochastic case. Solutions of generalized methods are relatively better than random solutions. However, the authors developed the new algorithm that may improve the solutions of generalized methods and project Completion Time Distribution Function (CTDF). Comparison of solution of a method with random solutions is a common assessment method in literature research. Hence, the efficiency of the proposed algorithm represented using this method.

This study presents a multimodal hub location problem which has the capability to split commodities by limited-capacity hubs and transportation systems, based on the assumption that demands are stochastic for multi-commodity network flows. In the real world cases, demands are random over the planning horizon and those which are partially fulfilled, are lost. Thus, the present study handles demands using a discrete chance constraint programming to make the model one step closer to the reality. On the other hand, commodity splitting makes it possible for the remaining portion of commodity flow to be transported by another hub or transportation system in such a way that demands are completely fulfilled as much as possible. The problem decides on the optimum location of hubs, allocates spokes to established hubs efficiently, adopts and combines transportation systems and then makes a right decision as to whether transportation infrastructure to be built at points lacking a suitable transportation infrastructure and having the potential for infrastructure establishment. A Mixed Integer Linear Programming (MILP) model is formulated with the aim of cost minimization. Also, the proposed sensitivity analysis shows that, the discrete chance constraint programming is a good approximation of the continuous chance constraint programming when an uncertain parameter follows a normal distribution. The results indicate the higher accuracy and efficiency of the proposed model comparing with other models presented in the literature.

The Network Design Problem (NDP) is one of the important problems in combinatorial optimization. Among the network design problems, the Multicommodity Capacitated Network Design (MCND) problem has numerous applications in transportation, logistics, telecommunication, and production systems. The MCND problems with Splittable flow variables are NP-hard, which means they require exponential time to be solved in optimality. With binary flow variables or unSplittable MCND, the complexity of the problem is increased significantly. With growing complexity and scale of real world capacitated network design applications, metaheuristics must be developed to solve these problems. This paper presents a simulated annealing approach with innovative representation and neighborhood structure for unSplittable MCND problem. The parameters of the proposed algorithms are tuned using Design of Experiments (DOE) method and the Design-Expert statistical software. The performance of the proposed algorithm is evaluated by solving instances with different dimensions from OR-Library. The results of the proposed algorithm are compared with the solutions of CPLEX solver. The results show that the proposed SA can find near optimal solution in much less time than exact algorithm.