In this thesis, we consider stochastic systems which arise in different real-world application contexts. The first problem we consider is based on product adoption and pricing. A monopolist selling a product has to appropriately price the product over time in order to maximize the aggregated profit. The demand for a product is uncertain and is influenced by a number of factors, some of which are price, advertising, and product technology. We study the influence of price on the demand of a product and also how demand affects future prices. Our approach involves mathematically modelling the variation in demand as a function of price and current sales. We present a simulation-based algorithm for computing the optimal price path of a product for a given period of time. The algorithm we propose uses a smoothed-functional based performance gradient descent method to find a price sequence which maximizes the total profit over a planning horizon. The second system we consider is in the domain of sensor networks. A sensor network is a collection of autonomous nodes, each of which senses the environment. Sensor nodes use energy for sensing and communication related tasks. We consider the problem of finding optimal energy sharing policies that maximize the network performance of a system comprising of multiple sensor nodes and a single energy harvesting(EH) source. Nodes periodically sense a random field and generate data, which is stored in their respective data queues. The EH source harnesses energy from ambient energy sources and the generated energy is stored in a buffer. The nodes require energy for transmission of data and and they receive the energy for this purpose from the EH source. There is a need for efficiently sharing the stored energy in the EH source among the nodes in the system, in order to minimize average delay of data transmission over the long run. We formulate this problem in the framework of average cost infinite-horizon Markov Decision Processes[3],[7]and provide algorithms for the same.

This thesis presents two classes of models of boundedly rational decision makers - one with application to finance and the other to pricing. It consists of three parts. The first part of the thesis investigates the impact of investors' boundedly rational forecasting on asset price bubbles. We present a class of models, called extrapolation-correction models, of boundedly rational investor behavior. That is, the investors in our model, quite reasonably, use data available to them, i.e. past price data, to form forecasts about future prices. We relate the model parameters to various behavioral aspects like investor memory, caution/confidence, and panic. We present the resulting dynamical system model of asset price bubbles and relate the behavior of the dynamical system to the parameters capturing investor forecasting behavior. We show that, depending on the behavioral parameters, the associated dynamical system can converge to the fundamental value, go into predictable price cycles, or go into unpredictable price cycles. In particular, we find that the greater the weight investors' forecasts put on the most recent observations, the greater the tendency for the asset prices to exhibit cycles, forming positive and negative bubbles. We also find that when forecasts are strongly affected by recent prices, the price process becomes chaotic and it becomes increasingly difficult to forecast future prices accurately. The second part of the thesis addresses the question: How do investors make their price forecasts? We present the design of an experiment where investors participate in a virtual asset market run over a computer network. During the course of the experiment, the participants report their price forecasts and enter buy and sell orders. The computer software determines the market clearing prices. Despite full disclosure of the assets' dividends and the fundamental value, the price trajectories in all three experimental sessions exhibited cycles. We calibrated various models, including rational expectations based models and the extrapolation-correction family of models presented in the first part of the thesis. The results indicate that rational expectations hypothesis does not provide an accurate model of forecast formation. Moreover, a simple one-parameter exponential smoothing model is much better at modeling forecast formation, with the extrapolation-correction models making the fit slightly better. The third part of the thesis explores a different aspect of customer rationality - that of customer impatience - and its effect on pricing of product versions. We consider a setting in which impatient customers are faced with frequent product introductions, for example, products like Apple iPhones. This raises the following questions regarding customers: Given the pricing strategy of the firm, what are the optimal buying behaviors of the customers? How does customer buying behavior change in relation to impatience? We consider two settings. In the first setting, the firm offers a trade-in price for existing customers and a higher full price for new customers. In the second setting, the firm offers the same prices to new and existing customers, however there is an introductory full price and a discounted price later in the product cycle. We model the customer's problem in these two settings and characterize their optimal actions as a function of the price parameters. We also analyze the bilevel program for the firm's pricing decisions. We see that in both settings considered there are certain well-defined regions in the price space wherein the firm's optimal decision lies. We also provide some numerical computations to study the behavior of the optimal prices as the cost per unit increases.

鑒於過去文獻可知，由於同一地區內的鄰近住宅擁有相同區位及市場特性，因而不動產價值存在高度相依性。空間相依性的產生往往是因為近鄰區域內的住宅有相似的建築結構（往往在同一個時間所興建），以及享有相同社會服務。由於建商在產品策略決策上會參考同一時間內鄰近競爭個案的產品策略，所以鄰近的新推個案會有相似的建築特徵以及相似的產品訂價。因此新推個案的訂價與鄰近的個案產生相關性，而新推個案訂價的相依性程度也會隨著時間距離遞減。 　　本文的目的在於將空間和時間的相依性最適地納入新推個案的訂價模型。採用582個台北市建商推案樣本進行實證。本研究分別以Moran’s I值和LISA值兩項指數來檢測空間自相關，並且比較傳統OLS迴歸模型、空間落遲模型，以及空間誤差模型三個模型的預測能力。此外，我們以不同的空間和時間的加權矩陣納入空間誤差模型中討論。 　　研究結果顯示，考量空間相依性之空間迴歸模型其解釋能力明顯優於一般傳統迴歸模型。而比起空間統計模型，時空迴歸模型更可以提高估計新推個案訂價的準確性。此外，研究結果亦顯示考慮時空交互影響的時空迴歸模型乃為新推個案訂價的最佳推估模式。 / It is well-known from the literature that the values of real estates are highly dependent on their locational and market characteristics of the buildings in adjacent areas. Spatial dependence mainly derives from factors that buildings at nearby properties have similar structural features (which were often developed at the same time) and often share the same social welfare. As developers in making decisions on product strategy will make reference to the strategy of nearby products of competitive cases which developed during the same time, therefore, within a certain period of time, the adjacent new construction will often have similar construction attributes as well as similar products pricing. Not only the pricing of a new construction is likely to be related to the pricing of adjacent new construction, but also the pricing of a new construction would be prone to autocorrelation decays in accordance with time distance. The aim of this paper is to analyze on how to take this temporal and spatial dependence into account in the pricing model of the new construction in the most appropriate way. We use a database of 582 asking prices of real estate developers in Taipei city. Two indices for measuring spatial autocorrelation are considered including (i) Moran’s I Index and (ii) LISA’s Index. We compared the predictive ability of three models including (i) OLS model, (ii) spatial lag model, and (iii) spatial error model. Moreover, we discussed the different temporal and spatial weight matrices in the spatial error model. According to our research results, we concluded that spatial statistical models obviously perform better than the traditional OLS model. Temporal and spatial statistical models would provide more accurate predictions on the pricing of a new construction than spatial statistical models do. The research result reveals that the best pricing model of the new construction is temporal and spatial statistical models which include temporal and spatial correlation.

Revenue Management (RM) has become one of the most successful application areas of Operation Research. What started off as an obscure practice among few airlines in U.S in early seventies, has attained the status of mainstream business practice, thanks to the major success enjoyed by companies applying RM. Over the same period, academic and industrial research on the methodology of RM has also grown rapidly. Despite the vast technical literature on the subject of revenue management, relatively few papers explicitly model the customer’s choice behavior. Such a behavior of customers could have major impact on revenue realized by an organization. Motivated by this, we focus on addressing the problem faced by a seller who serves customers exhibiting buy-down behavior. We address two important problems faced by a seller with few perishable goods. His objective is to obtain maximum revenue possible by sales of his perishable goods. The seller now potentially faces the problem of fixing the price of the products and then control the availability of products so as to maximize his revenue by minimizing the number of customers who buy-down. The first problem is the multi-product pricing problem where we consider a monop- olistic market situation in which a seller has some quantities of perishable goods under his disposal. The seller has the option of adding few additional features to the base product(perishable good) and thereby differentiating the products to cater to different market segments. Adding each additional feature involves certain cost and there are no restrictions on the availability of the features except that a feature can be added to the base product atmost once . The customers are price-sensitive and the seller is aware of the price-demand relationship of the various customer segments. A customer looking for a product buys the product if and only if the price is less than his reservation price. The sellers’ problem is to identify the price and bundling of features for the various customer segments so as to generate maximum possible revenue. We develop a Mixed integer non-linear mathematical programming model for the problem. We then split the problem into pricing problem and bundling problem and solve them sequentially. We finally provide a numeric example to illustrate the solution procedure. Once the prices are fixed, the next problem is to control the availability of products so as to prevent the buy-down behavior of the customers. We deal with the situation of a seller with two substitutable products. The price of both products are fixed over entire selling period. In a traditional control mechanism structure if the sequence of arrival of customers are known, then it becomes trivial to solve the problem of setting control limits which would prevent buy-down behavior. But in reality it never happens that the seller knows the arrival sequence. Hence in this study to isolate the effect of arrival sequence from other complexities like demand variability, we assume a deterministic demand for both the products but the arrival sequence is randomized. We initially analyze the above described problem and develop a static control mech- anism. We show that the static control mechanism is asymptotically equivalent to the traditional selling mechanism. Then we move on to make modification in the static con- trol mechanism and make it a dynamic control mechanism such that it will respond to the buy-down customers. In order to analyze the performance of dynamic control mechanism, we build a simulation model that would compare traditional selling mechanism and dynamic control mechanism. Statistical analysis is then done on the simulation results. It is shown that for all values of buy-down proportion, on an average the dynamic control mechanism outperforms the traditional control mechanism. Further there is a trend in revenues generated depending upon the buy-down proportion which is also explained. The chapter concludes with operating guidelines for better revenue realization. The organization of the thesis is as follows. In chapter 2, we present the literature survey. We start off with the history of RM and proceed to discuss the inventory control problems in RM in detail. Then we discuss literatures dealing with customer choice behavior. In chapter 3, we define and model the multi - product pricing problem. We present a mixed integer non-linear mathematical program to model the pricing problem. The solution to this problem is divided into two sub problems - the pricing problem and the bundling problem. Solution methodologies for both sub - problem are given and the chapter concludes with a numerical illustration for a 3 - product pricing problem. In chapter 4, we define and address the inventory control problem for a two product case when customers exhibit buy-down nature. We develop a static control mechanism and study its properties. Then we move on to the dynamic control mechanism which would suit real - world conditions. Finally we study the quality of developed methodology using statistical testing methods.