Alexander A. Kolokolov

A Genetic Algorithm for the Allocation of Buffer Storage Capacities in a Production Line with Unreliable Machines

In this paper, we consider a flow-line manufacturing system organized as a series of workstations separated by finite buffers. The failure and repair times of machines are supposed to be exponentially distributed. The production rate of each machine is deterministic, and different machines may have different production rates. The buffer allocation problem consists in determining the buffer capacities with respect to a given optimality criterion, which depends on the average production rate of the line, the buffer acquisition and installation cost, and the inventory cost. For this problem we propose a genetic algorithm where the tentative solutions are evaluated with an approximate method based on the Markov-model aggregation approach.

Analysis of Decomposition Algorithms with Benders Cuts for p-Median Problem

In this paper the algorithms for solving the p-median problem based on the Benders decomposition are investigated. A family of problems hard for solving with such algorithms is constructed and then generalized to a special NP-hard case of the p-median problem. It is shown that the effectiveness of the considered algorithms depends on the choice of the optimal values of the dual variables used in Benders cuts. In particular, the depth of the cuts can be equal to one.

Concave Cost Supply Management for Single Manufacturing Unit

The considered problem consists of product delivery from a set of providers to the manufacturing units (single unit and single planning period in our case). The cost function is concave. Given the lower and upper bounds on the shipment size for each provider, the demand of the manufacturing unit has to be satisfied. In this chapter it is shown that this optimisation problem is NP-hard even to find a feasible solution to this problem. Considering the problem in integer programming formulation we propose a pseudo-polynomial algorithm, using the dynamic programming technique. Some possible approaches to solving the problem with multiple manufacturing units are discussed.

Analysis and Solving SAT and MAX-SAT Problems Using an L-partition Approach

In this paper, we study SAT and MAX-SAT using the integer linear programming models and L-partition approach. This approach can be applied to analyze and solve many discrete optimization problems including location, covering, scheduling problems. We describe examples of SAT and MAX-SAT families for which the cardinality of L-covering of the relaxation polytope grows exponentially with the number of variables. These properties are useful in analysis and development of algorithms based on the linear relaxation of the problems. Besides we present the L-class enumeration algorithm for SAT using the L-partition approach. In addition we consider an application of this algorithm to construct exact algorithm and local search algorithms for the MAX-SAT problem.

A bicriteria problem of optimal service centers location

Abstract The problem of service centers location is formulated as a bicriteria optimization problem of finding a dominating set in graph. We investigate the properties of this problem and propose the methods for its solving. The results of computer experiment for instances with random data are presented.

Complex Optimization Problems in Locational Analysis and Scheduling

This issue is composed of updated and extended versions of seven papers selected atthe IFAC Symposiums INCOM06 and INCOM09. All the papers passed through arigorous peer review process with at least 3 referees each. This was performed twice:once before the symposium, for their initial version, and again after the symposium,for the extended version.The 12th and 13th IFAC symposiums INCOM06 (www.emse.fr/incom06)andINCOM09 (incom09.org) were major scientific events on

On Average Number of Iterations of Some Algorithms for Solving the Set Packing Problem

Abstract We consider the set packing problem as a corresponding integer linear programming problem. For L -class enumeration algorithm and the first Gomory cutting plane algorithm we found the polynomial upper bounds on average iterations number. The regular partitions approach and known upper bounds on the average number of feasible solutions were used for the estimations.