The Optimal Control Poliecs On Markov Queueing-Inventory System

Stochastic inventory systems have their uncertainty mainly rooted in demand andreplenishment. On this topic, a rich amount of researches have been accomplished. Thereal inventory decision-making, however, also depends on the queueing behaviors of thecustomers. Indeed, queueing inventory system, as a special inventory service systemthat combines customer queueing and inventory services, widely exists in real word. Atpresent, research on the queueing inventory system is limited, and study on thequeueing inventory system is therefore of great importance both in theory and practice.This dissertation studies a class of queueing inventory systems with Markov structure,introducing such crucial factors as demand service consuming inventory in bulk into thedecision-making for controlling inventory. The purpose of this dissertation is toestablish the theoretical basis and methodology for analyzing Markov queueinginventory systems. This dissertation proposed a formal processing procedure forstudying the control polices on Markov queueing inventory systems. The procedurecomprises of model building, model analyzing and solving, the inventory cost functionbuilding, cost function analyzing and optimization algorithm designing, and numericalsimulation and management insights discovering. By the proposed procedure, thisdissertation establishes the basic research paradigm for the control polices on Markovqueueing inventory system.Firstly, a stochastic inventory system with continuous-review （s， S）replacementpolicy is considered. The steady-state probability distribution of inventory level and thesteady-state performance measures for the inventory control are derived by analysisbased on birth-death process. To minimize the inventory cost function, a constrainednon-linear inventory optimal model is formulated. Moreover, an improved geneticalgorithm (IGA) solves this optimal model for the integer type optimums. The results ofnumerical experiments validate IGA and reveal important insight for the inventorymanagement.Secondly, a priority queueing inventory system with selected service policy is studied. A priority (s， Q)queueing inventory system with selected service mechanismplaces a fixed order for units when the on-hand inventory drops below the safety level,and serves an ordinary customer at the probability p. In particular, the inventory levelstate transitions equation is set up; the steady state probability distribution, as well asthe performance indexes of the system, are obtained by a recursive algorithm. Inaddition, the inventory cost function is established and an optimization algorithm isdesigned based on the analytical properties of the cost function. Besides, numericalexperimental results demonstrate the effectiveness of the proposed optimizationalgorithm. The lesson from the experimental results is twofold: if the two types ofcustomers have dramatically different shortage costs, the inventory cost can be reducedthrough a selected service mechanism; in contrast, if the two types of customers havecomparable shortage costs, a selected service mechanism can increase inventory cost.Next, a queueing inventory system with （s， s+q） policy under batch demand isexplored. The arrival of demands follows a compound Poisson process. When theon-hand inventory decreases to level s, the manager immediately places an order to themaximum inventory level （s+q）. By formulating the model in term of state transitionequations, the steady state probability distributions of inventory and shortage areobtained. Furthermore, for the inventory cost function, a computationally efficientalgorithm for determining the optimal values for safety stock and maximum inventorycapacity is developed. Moreover, the sensitivities of the system parameters areinvestigated.After that, the dissertation considers a queueing-inventory system with servicelevel constraint. Under the policy (s， Q), the steady-state balance equations are setupbased on queueing theory, and the probability distribution for inventory levels and thesteady-state performance measures, used for inventory control, are derived. To minimizethe inventory cost function, an inventory control model with constrained service level isbuilt. Provided the optimal model is a nonlinear integer optimal model, an improvedgenetic algorithm (IGA) is used for the search of optima. The numerical results showthat, when demand service level of the market is greater than endogenic service level ofthe inventory system, exerting service level constraint can save the inventory cost. Finally, this dissertation considers the perishable queueing inventory systemserving two classes of customers. By establishing the inventory service model with twoclasses of customers and introducing the deteriorating inventory items, this dissertationproposes a control method for perishable inventory control based on the queueinganalysis technique, and discusses the problems on inventory management. The optimalinventory control policies are obtained and the management insights are disclosed.