In the context of public transportation system, improving the service quality and robustness through minimizing the average passengers waiting time is a real challenge. This study provides robust stochastic programming models for train timetabling problem in urban rail transit systems. The objective is minimization of the weighted summation of the expected cost of passenger waiting time, its va...

in traditional portfolio selection model coefficients often are certain and deterministic, but in real world these coefficients are probabilistic. so decision maker cannot estimate them exactly. financial optimization is one of the most attractive areas in decision under uncertainty. in the portfolio selection problem the decision maker considers simultaneously conflicting objectives such as ra...

in the recent decade, special attention is paid to reverse logistic due to economic benefits of recovery and recycling of used products as well as environmental legislation and social concerns. on the other hand، many researches claim that separately and sequential planning of forward and reverse logistic causes sub-optimality. effective transport activities are also one of the most important c...

The multi-objective optimization for a multi-product multi-period four-echelon supply chain network consisting of manufacturing plants, distribution centers (DCs) and retailers each with uncertain services and uncertain customer nodes are aimed in this paper. The two objectives are minimization of the total supply chain cost and maximization of the average number of products dispatched to custo...

This paper deals with a realistic multi-period liner ship fleet planning problem by incorporating stochastic dependency of the random and period-dependent container shipment demand. This problem is formulated as a multi-period stochastic programming model with a sequence of interrelated two-stage stochastic programming (2SSP) problems characterized ship fleet planning in each single period. A s...

In this paper, developed a new multi-product, multi-period, and multi-level closed-loop green supply chain planning model under uncertain conditions. The formulated model consists of five objective functions, which minimize the cost of the supply chain, minimize the CO2 emission of transportation vehicles, maximize the reliability of manufacturing and distribution centers, maximize t...

The design of closed-loop logistics (forward and reverse logistics) has attracted growing attention with the stringent pressures of customer expectations, environmental concerns and economic factors. This paper considers a multi-product, multi-period and multi-objective closed-loop logistics network model with regard to facility expansion as a facility location–allocation problem, which more cl...

In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general tran...