In the last decade, multi-stage stochastic programs with recourse have been broadly used to model real-world applications. This paper reviews the main optimization methods that are used to solve multi-stage stochastic programs with recourse. In particular, this paper reviews four types of optimization approaches to solve multi-stage stochastic programs with recourse: direct methods, decompositi...

This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is pre...

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective functio...

banks' major responsibility, as the largest financial intermediaries, is to provide and allocate resources. this activity has its own risks which cause banks to seek ways of preventing or transferring them to other places. islamic banks as substitutes of conventional banks in islamic countries have, in their turn, faced similar risks. in regard to new evolutions in banking industry and man...

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed – but costs here become more expensive by a fa...

We study the online maximum matching problem with recourse in a model in which the edges are associated with a known recourse parameter k. An online algorithm for this problem has to maintain a valid matching while edges of the underlying graph are presented one after the other. At any moment the algorithm can decide to include an edge into the matching or to exclude it, under the restriction t...

PURPOSE TAS-102 is a combination of the thymidine-based nucleoside analog trifluridine and the thymidine phosphorylase inhibitor tipiracil. Efficacy and safety of TAS-102 in patients with metastatic colorectal cancer (mCRC) refractory or intolerant to standard therapies were evaluated in the phase 3 RECOURSE trial. Results of RECOURSE demonstrated significant improvement in overall survival (OS...

We consider a competitive pricing problem where there are multiple firms with limited inventories of substitutable products. Each firm chooses the prices that it charges for its product over a finite selling horizon. The demand of each firm jointly depends on the prices of all firms in a deterministic fashion through a linear demand function. The goal of each firm is to choose its prices to max...