Stochastic Programming Research On Order Problem In Group Purchase With Free Shipping

With the popularization of Electronic commerce, it takes us gigantic con-venience in our life and it has changed our consumption patterns. Network providers seize this opportunity and launch a series of sales promotion scheme. Network provider will provide free shipping service if order quantity reaches a certain requirement. Retailers prefer this discount deal. They would like to or-der in the form of group buying for meeting the requirements of free shipping. But the choice of order strategy is influenced on the retailers’ demand which is always unknown. Order strategy is depended on many factors such as weather, competition. The free shipping research before is based on the situation that distribution function of random variable is known. In fact the retailers’de-mand is always unknown. Stochastic programming research of order strategy in group purchase with free shipping is necessary.According of the above, considering order strategy with free shipping and the unknown demand, the essay study the stochastic programming problem,which assumes only limited information of the distributions of the underlying uncertainties, such as known mean,support, and covariance. One basic idea of our methods is to approximate the recourse decisions via decision rules, we discussed the objective function by using cooperative game theory, which explain that each of the retailers’ strategy is optimal. The essay provides a solved method by robust optimization which is based on linear decision rule. Specifically, our approximate models are in the forms of the so-called second- order cone (SOC) programs, which could be solved efficiently both in theory and in practice.At the last part,we show an example for the method.There are details in this thesis:1) Considering the problem of order strategy with free shipping require-ments, a stochastic programming model aimed with minimizing the cost is given. Then we discussed the model based on the linear decision and deflected linear decision rule. Our approximate models are in the forms of the so-called second-order cone (SOC) programs.2) At the third part the essay provides a solved method by robust opti-mization which is based on linear decision rule and obtains the robust coun-terpart of the model, we use an example to prove the analysis above and the algorithm are computational tractable.3) Finaly, we discussed the objective function using cooperative game theory, which explain that each of the retailers’strategy is optimal.