We review convex approximations for stochastic programs with simple integer recourse. Both for the case of discrete and continuous random variables such approximations are discussed, and representations as continuous simple recourse problems are given.

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic ...

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...

Uncertainty is a facet of many decision environments and might arise for various reasons, such as unpredictable information revealed in the future, or inherent fluctuations caused by noise. Stochastic optimization provides a means to handle uncertainty by modeling it by a probability distribution over possible realizations of the actual data, called scenarios. The field of stochastic optimizati...

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...