The probabilistic satisfiability problem is to verify the consistency of a set of probability values or intervals for logical propositions. The (tight) probabilistic entailment problem is to find best bounds on the probability of an additional proposition. The local approach to these problems applies rules on small sets of logical sentences and probabilities to tighten the given probability int...

We consider the resource allocation problem related to Virtual Private Networks (VPNs). VPN provides connections between geographically dispersed endpoints over a shared network. To realize VPN service, sufficient amount of bandwidth of network resources must be reserved for any traffic demand specified by a customer. We assume that there are many customers that want to purchase VPN services, a...

This paper studies a districting problem which arises in the context of financial product pricing. The challenge lies in partitioning a set of small geographical regions into a set of larger territories. In each territory, the customers will share a common price. These territories need to be contiguous, contain enough customers and be as homogeneous as possible in terms of customer value. To ad...

We consider the customary formulation of non-cyclic train timetabling, calling for a maximumprofit collection of compatible paths in a suitable graph. The associated ILP models look for a maximum-weight clique in a(n exponentially-large) compatibility graph. By taking a close look at the structure of this graph, we analyze the existing ILP models and propose some new stronger ones, all having t...

We provide a production planning framework for variant rich customized products (such as automobiles, computers), by calculating entirely constructible configuration sets for future customer demands in a novel manner. Most of the established approaches analyse configurations out of historical order banks for estimating the appropriate set of future demands. In the current environment of rapidly...

Column generation has become a powerful tool in solving large scale integer programs. We argue that most of the often reported compatibility issues between pricing oracle and branching rules disappear when branching decisions are based on the reduction of the variables of the oracle’s domain. This can be generalized to branching on variables of a so-called compact formulation. We constructively...

Several logics for reasoning under uncertainty distribute probabil ity mass over sets in some sense These include probabilistic logic Dempster Shafer theory other logics based on belief functions and second order probabilistic logic We show that these logics are in stances of a certain type of linear programming model typically with exponentially many variables We also show how a single linear ...

In this paper, we study algorithms for probabilistic satisfiability (PSAT), an NP-complete problem, and their empiric complexity distribution. We define a PSAT normal form, based on which we propose two logic-based algorithms: a reduction of normal form PSAT instances to SAT, and a linearalgebraic algorithm with a logic-based column generation strategy. We conclude that both algorithms present ...

Producing work schedules for airline crew normally results in individually different schedules. Some airlines do however want to give the same schedule to groups of people. The construction of such groups must respect certain rules, provide a good matching of certain factors and fit well into the normal process of producing anonymous trips starting and ending at the home base and assigning thes...

Much effort in the discrete location theory has aimed at developing insights concerning the classical models with one decision maker only. In this paper, we study a competitive model with two noncooperative decision makers: the leader and the follower. They compete to attract clients from the given market and wish to maximize their own profits. In fact, this is the noncooperative Stackelberg ga...