We introduce the logic of bunched implications, BI, in which multiplicative (or linear) and additive (or intuitionistic) implications live side-by-side. We provide a truth conditional semantics, a proof theory and a categorical semantics of proofs. We explain how BI arises as a logic of resources and sketch a development of this computational interpretation, which is quite diierent from that of...

This paper presents a fuzzy approach for solving the bi-level integer linear fractional programming problem (BILFPP). At the first phase of the solution algorithm and to avoid the complexity of non convexity of this problem, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the Charnes & Cooper transformation is used to convert th...

A summary of deterministic operations research models in linear programming, inventory theory, and dynamic programming. 1 Linear Programming A mathematical model of the problem is developed basically by applying a scientific approach as described earlier. There are a number of activities to be performed and each unit of each activity consumes some amount of each type of a resource. Resources ar...

In some countries, regional authorities may attempt to rebalance the allocation of national facilities in benefit their own region which, turn, cause disturbances central government’s decision-making proces. Regarding hierarchical nature these types decisions, classical optimization models are not effective and use multi-level programming can increase efficiency planning. Our paper aims address...