On Solving Stochastic PERT Networks and Using RFIDs for Operations Management

Abstract

The current methods used to solve stochastic PERT networks overlook the true distribution of the maximum of two distributions and thus fail to compute an accurate estimation of the project completion time. This dissertation presents two different methods to solve stochastic PERT networks. With each method, both by using mixtures of Gaussians and also by using mixtures of truncated exponentials, the distribution of the maximum of two distributions can be approximated accurately. In the first method a PERT network is first transformed into a MoG Bayesian network and then Lauritzen-Jensen algorithm is used to make inferences in the resulting MoG Bayesian network. The transformation process involves approximating non-Gaussian distributions using MoG's, finding maximum of two distributions using MoG's. As PERT networks are transformed into MoG Bayesian networks arc reversals may also become necessary since MoG Bayesian networks does not allow discrete variables to have continuous parents. This dissertation presents arc reversals in hybrid Bayesian networks with deterministic variables between every possible pair of variables. In the second stage of the research MTE Bayesian networks are introduced as an alternative for solving stochastic PERT networks. We demonstrated the easy applicability of MTE potentials by finding the marginal probability distribution of a PERT example using MTE's. This calculation process involves the conversion of the PERT network into a PERT Bayes net, transformation of the PERT Bayes net into a MTE network and finally propagation of the MTE potentials using the Shenoy-Shafer architecture. Finding the distribution of the maximum of two distributions using MTE's is described as an operation necessary to propagate in MTE PERT networks. The second essay of this dissertation discusses a potential application of radio frequency identification (RFID) and collaborative filtering for targeted advertising in grocery stores. Every day hundreds of items in grocery stores are marked down for promotional purposes. Whether these promotions are effective or not depends primarily on whether the customers are aware of them or not and secondarily whether the products on promotion are products in which the customer will be interested. Currently, the companies are relatively incapable of influencing the customers' decision-making process while they are shopping. However, the capabilities of RFID technology enable us to transfer the recommendation systems of e-commerce to grocery stores. In our model, using RFID technology, we get real time information about the products placed in the cart during the shopping process. Based on that information we inform the customer about those promotions in which the customer is likely to be interested in. The selection of the product advertised is a dynamic decision making process since it is based on the information of the products placed inside the cart while customer is shopping. Collaborative filtering is used for the identification of the advertised product and Bayesian networks will be used for the application of collaborative filtering. We are assuming a scenario where all products have RFID tags, and grocery carts are equipped with RFID readers and screens that would display the relevant promotions. We present our model first using the data set available for the Netflix prize competition. As the second stage of the research we use grocery data set and develop a new heuristic to select the products to be used in the Bayesian network created.