Study On Some Online Inventory Problem In Supply Chain

This thesis investigates the inventory problem in which the price is online, and the retailer, should decide when and how much to replenish even without knowing the complete future price information. The general situation of price online inventory problem, the situation with cost function and the lower bound of possible prices varies with time, the situation with interrelated prices and the situation with forecast are considered. The corresponding models are established and the corresponding online algorithms are put forward. Moreover, the competitive ratios are given.First of all, this thesis investigates the optimal strategy for online inventory problem, and presents three models based on part of the future price information that the decision maker knows. Competitive ratios of the DPTB algorithm are derived using the competitive analysis respectively. This thesis has proven that the DPTB algorithm is optimal when the price is online. Moreover, the study finds that the competitive ratio grows as a function of the price fluctuation ratio and if the price fluctuation ratio is set as a constant, then the competitive ratio grows as a function of the purchasing duration. The competitive ratio of the worst case, where the competitive ratio of the DPTB algorithm and the competitive ratio of the general case in a practical situation are compared by some numerical examples, we can draw a conclusion that the DPTB algorithm guarantees the worst case, which means the competitive ratio of the DPTB algorithm is close to the tight.Secondly, the inventory problem with the cost function and the lower bound of possible prices varies with time is investigated. In the actual inventory problem, you need the order costs, purchase costs when purchasing goods, inventory costs when items ordered back to be sold, and even the transportation costs etc., so we need to consider all kinds of costs. In the cost minimization inventory problem, the online decision maker is more sensitive to the lower bound of prices, so we consider the situation of the lower bound of prices varies with time. Competitive ratio of the DPTB algorithm is derived using the competitive analysis.Then, the price online inventory problem with interrelated prices is investigated. We assume that the daily price has a certain correlation with the previous price and daily purchase price fluctuates between different ranges. The linear and logarithmic model are considered. We present the dprice-conservative algorithm DPC, obtain the upper and lower bounds of competitive ratio by adopting the competitive analysis respectively. Moreover, by using some numerical examples of competitive ratio attained, it is found that this DPC algorithm is more suitable for purchase price which fluctuates in the smooth.The last, the online model is extended to allow decision makers to anticipate and benefit from a forecast even forecasting failure, decision maker can control the risk and make the performance of the online algorithm is not too bad in terms of the optimal algorithm with respect to offline. Two typical forecast models are considered that the first model of below the forecast prices, which drop to a certain level, the second model of top predict that prices not drop to a certain level. Different algorithms are designed with different predictions, and obtained the corresponding competitive ratios by the competitive analysis method. Several times forecast scenario allowing the entire purchase process are also considered and sensibility analysis is made.