The Study Of Online Inventory Problem In Supply Chain

Along with the development of economic, the price of the international commodities isgreat uncertainty such as oil, iron ore. It leads to disequilibrium between production andsales volume of enterprises, inventory hidden loss and proft decline, and serious damage tothe stable operation of the related industries. In addition, prices are usually supposed todetermine or obey a certain distribution and the optimal solution changes as the actual pricesdo not conform to the distribution in the classical inventory problem. Therefore, researchthe price online inventory problem is very necessary.This thesis investigates the price online inventory problem in which decisions as to whento replenish and how much to buy must be made in an online fashion without concrete knowl-edge of future prices. We consider four cases with cost function, interrelated prices withoutdemand, interrelated prices with constant demand and interrelated prices with linear relateddemand with the price. Then we set up the corresponding models, present the correspondingonline algorithms and give the corresponding competitive ratios which a performance indexof online algorithms for the cases.First of all, this thesis investigates the price online inventory problem with cost function.We present fve models for diferent information such as continuous, discrete, the upper andlower bounds of price and the fuctuations ratio of price. Then we present an online algorithm,calculate the competitive ratio of the online algorithm for the fve models, respectively, andprove that the online algorithm is optimal.Secondly, we investigate the price online inventory problem with interrelated prices andwithout demand. We present two models which are the exponential model and the loga-rithmic model with diferent price correlations. For the exponential model, we propose analgorithm SLP1by solving a linear programming and derive its competitive ratio. For thelogarithmic model, we propose an algorithm SLP2and also calculate its competitive ratioby the same method. Additionally, we show that the algorithm SLP1is optimal for the ex-ponential model and the algorithm SLP2is optimal for the logarithmic model under certainconditions, that is, local optimal.The last, we investigate the price online inventory problem with interrelated prices anddemand, in which each price is interrelated with its preceding price. We consider two caseswith the constant demand and linear related with price demand. Then we present two modelswhich are the exponential model and the logarithmic model with diferent price correlations for every case. we present the corresponding algorithm and give the competitive ratio of thealgorithm for every model by linear programming, respectively. Moreover, we extend theconclusions of every model to one general case. Finally, we give some numerical examplesfor the conclusions, then we evaluate the performance of the algorithms by comparing thevalue of competitive ratios of the algorithms and the ratios of the algorithm cost and ofineoptimal cost for corresponding input price sequence.At the end of this thesis, we summarize the full text and put forward three future researchdirections which are the price online inventory problem contains various costs and demand atthe same time, multi-parameter online inventory problem and the online inventory problemwith updated information.