Contrary to the situation with stochastic gradient descent, we argue that when using stochastic methods with variance reduction, such as SDCA, SAG or SVRG, as well as their variants, it could be beneficial to reuse previously used samples instead of fresh samples, even when fresh samples are available. We demonstrate this empirically for SDCA, SAG and SVRG, studying the optimal sample size one ...

The problem of nding e cient maintenance and inspection schemes in the case of components with a stochastic life time is studied and a mixed integer programming solution is proposed. The problem is compared with the two simpler problems of which the studied problem is a generalisation: The opportunistic replacement problem, assuming components with a deterministic life time and The opportunisti...

We consider convex stochastic programming problems with probabilistic constraints involving integer valued random variables The concept of a p e cient point of a probability distribution is used to derive various equivalent problem for mulations Next we introduce the concept of r concave discrete probability distri butions and analyse its relevance for problems under consideration These notions...

We describe a stochastic network interdiction model for deploying radiation detectors at border checkpoints to detect smugglers of nuclear material. The model is stochastic because the smuggler’s origin-destination pair, the type of material, and the level of shielding are known only through a probability distribution when the detectors are installed. We formulate a mixed-integer program for th...

By investigating in detail discontinuities of the first kind of real-valued functions and the analysis of unordered sums, where the summands are given by values of a positive real-valued function, we develop a measure-theoretical framework which in particular allows us to describe rigorously the representation and meaning of sums of jumps of type ∑ 0<s≤t Φ ◦ |∆Xs|, where X : Ω×R+ −→ R is a stoc...

We present a brief overview of four stages of nurse planning. For the last stage, which assigns nurses to patients, a stochastic integer programming model is developed. A Benders’ decomposition approach is proposed to solve this problem, and a greedy algorithm is employed to solve the recourse subproblem. Patient-to-nurse ratio constraints are introduced to balance the workload of nurses as wel...

Today’s business has inevitably been set in the global supply chain management environment. International transportation has never played such an important role in the global supply chain network, because movement of shipments from one country to another tends to be more frequent than ever before. This paper studies international transportation problems experienced by an international transport...

We present a new technique (RIIPS) for solving rostering problems in the presence of service uncertainty. RIIPS stands for “Rostering by Iterating Integer Programming and Simulation”. RIIPS allows great complexity of the stochastic system being rostered. This modelling freedom comes at a price, as the approach can be extremely computationally intensive. Therefore any reduction in computational ...

We consider a two-type stochastic competition model on the integer lattice Z. The model describes the space evolution of two “species” competing for territory along their boundaries. Each site of the space may contain only one representative (also referred to as a particle) of either type. The spread mechanism for both species is the same: each particle produces offspring independently of other...