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 dema...

nonlinear knapsack problems (nkp) are the alternative formulation for the multiple-choice knapsack problems. a powerful approach for solving nkp is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...

stochastic approach to vehicle routing problem: development and theories abstract in this article, a chance constrained (ccp) formulation of the vehicle routing problem (vrp) is proposed. the reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. knowing that reliable computer software for lar...

This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide conditional value-at-risk reformulation MPC optimization that is in expected cost and chance constraints. The constraint over-approximated as simpler, tightened reduces computational burde...

We study joint chance constrained programs (JCCPs). JCCPs are often non-convex and non-smooth, and thus are generally challenging to solve. In this paper, we propose a logarithmsum-exponential smoothing technique to approximate a joint chance constraint by the difference of two smooth convex functions and use a sequential convex approximation algorithm, coupled with a Monte Carlo method, to sol...