Modeling the Dynamics of the Random Demand Inventory Management System

At any given time, a product stock manager is expected to carry out activities to check his or her holdings in general and to monitor the condition of the stock in particular. He should monitor the level or quantity available of a given product, of any item. On the basis of the observation made in relation to the movements of previous periods, he may decide to order or not a certain quantity of products. This paper discusses the applicability of discrete-time Markov chains in making relevant decisions for the management of a stock of COTRA-Honey products. A Markov chain model based on the transition matrix and equilibrium probabilities was developed to help managers predict the likely state of the stock in order to anticipate procurement decisions in the short, medium or long term. The objective of any manager is to ensure efficient management by limiting overstocking, minimising the risk of stock-outs as much as possible and maximising profits. The determined Markov chain model allows the manager to predict whether or not to order for the period following the current period, and if so, how much.

Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization

Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.

The Theory of Composite Characteristics Under Sampling Scheme Without Discontinuing Inspection

In this paper,we establish the model of a finite,irreducible non-periodic and ergodic Markov chain for the sampling scheme without discotinuing state,then calculate and analyse the composite characteristics of a three-level skip-lot sampling scheme.