generally ordering policies are done by two methods, including fix order quantity (foq) and fix order period (fop). these methods are static and either the quantity of ordering or the procedure of ordering is fixing in throughout time horizon. in real environments, demand is varying in any period and may be considered as uncertainty. when demand is variable in any period, the traditional and st...

We investigate the dynamic variable ordering (DVO) technique commonly used in conjunction with tree-search algorithms for solving constraint satisfaction problems. We first provide an implementation methodology for adding DVO to an arbitrary tree-search algorithm. Our methodology is applicable to a wide range of algorithms including those that maintain complicated information about the search h...

The increasing popularity of SAT and BDD techniques in formal hardware verification and automated synthesis of logic circuits encourages the search for additional speedups. Since typical SAT and BDD algorithms are exponential in the worst-case, the structure of realworld instances is a natural source of improvements. While SAT and BDD techniques are often presented as mutually exclusive alterna...

Many combinatorial optimization problems can be formulated as 0/1 integer programs (0/1 IPs). The investigation of the structure of these problems raises the following tasks: count or enumerate the feasible solutions and find an optimal solution according to a given linear objective function. All these tasks can be accomplished using binary decision diagrams (BDDs), a very popular and effective...

It is well known that appropriate variable and value ordering heuristics are often crucial when solving constraint satisfaction problems. A variable ordering heuristic which is often recommended, and is often successful, is based on the `failrst' principle: choose next the variable with the smallest remaining domain. General-purpose value ordering heuristics are less common, but it has been arg...

Ordered binary decision diagrams (BDDs) yield a data structure for switching functions that has been proven to be very useful in many areas of computer science. The major problem with BDD-based calculations is the variable ordering problem which addresses the question of finding an ordering of the input variables which minimizes the size of the BDD-representation. In this paper, we discuss the ...

Modern CAD tools must represent large Boolean functions compactly in order to obtain reasonable runtimes for synthesis and veriication. The Shared Binary Decision Diagram (SBDD) with negative edge attributes can represent many functions in a compact form if a proper variable ordering is used. In this work we describe a technique for reordering the variables in an SBDD to reduce the size of the ...