The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions (“dynamic programming”) or scenario trees (“stochastic programming”) to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier … Read more
We introduce the noncooperative fixed charge transportation problem (NFCTP), which is a game-theoretic extension of the fixed charge transportation problem. In the NFCTP, competing players solve coupled fixed charge transportation problems simultaneously. Three versions of the NFCTP are discussed and compared, which differ in their treatment of shared social costs. This may be used from … Read more
In this paper we provide a deterministic fully polynomial time approximation scheme (FPTAS) for counting two-rowed contingency tables that is faster than any either deterministic or randomized approximation scheme for this problem known to date. Our FPTAS is derived via a somewhat sophisticated usage of the method of K-approximation sets and functions introduced by Halman … Read more
As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry … Read more
Finite horizon periodic review backlog models are considered in this paper for an inventory system that remanufactures two types of cores: buyback cores and normal cores. Returns of used products as buyback cores are modelled to depend on past demands and past sales. We obtain an optimal inventory policy for the model in which returns … Read more
The classical Sard theorem states that the set of critical values of a $C^{k}$-map from an open set of $\R^n$ to $\R^p$ ($n\geq p$) has Lebesgue measure zero provided $k\geq n-p+1$. In the recent paper by Barbet, Dambrine, Daniilidis and Rifford, the so called “preparatory Sard theorem” for a compact countable set $I$ of $C^k$ … Read more
In this paper, a new method for determining all minimal representations of a face of a polyhedron is proposed. A main difficulty for determining prime and minimal representations of a face is that the deletion of one redundant constraint can change the redundancy of other constraints. To reduce computational efforts in finding all minimal representations … Read more
We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We consider an approach in which the decision-maker (DM) considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the … Read more
We analyze a problem of dynamic logistics planning given uncertain demands for a multi-location production-inventory system with transportable modular production capacity. In such systems, production modules provide capacity, and can be moved from one location to another to produce stock and satisfy demand. We formulate a dynamic programming model for a planning problem that considers … Read more
In real life applications optimization problems with more than one objective function are often of interest. Next to handling multiple objective functions, another challenge is to deal with uncertainties concerning the realization of the decision variables. One approach to handle these uncertainties is to consider the objectives as set-valued functions. Hence, the image of one … Read more