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In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some...
We consider a stochastic single item production‐inventory‐routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation...
We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, and then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects...
We propose the policy graph as a structured way of formulating a general class of multistage stochastic programming problems in a way that leads to a natural decomposition. We also propose an extension to the stochastic dual dynamic programming algorithm to solve a subset of problems formulated as a policy graph. This subset includes discrete‐time, convex, infinite‐horizon, multistage stochastic programming...
The transshipment location–allocation problem consists of locating transshipment facilities (e.g., intermodal hubs) of a transportation network and allocating freight flows through them, from several origins to several destinations, to satisfy demand and supply constraints. The objective is to maximize the total net transportation utility given by the total shipping utility minus the total cost to...
We consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the Monte‐Carlo sampling. For...
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