In this thesis, we consider contextual newsvendor problems where one seeks to determine ordering quantities of perishable products based on the observations of past demands and some features (such as seasonality, weather forecasts, economic indicators, etc.) related to the demand. We propose solving the problems via a single-step optimal decision-tree approach. Unlike the traditional two-step approach that first predicts a demand distribution based on given features and then optimizes the order quantity, our approach seeks to determine a tree-based ordering policy that directly maps given features to optimal order quantities. We show how the optimal policies can be found by solving mixed-integer programming (MIP) problems. The tree structure overcomes the black-box nature of most machine learning algorithms while reaching better performance than simple solutions such as linear regression. In addition to risk-neutral newsvendor problems, we further extend the method to address risk-averse newsvendor problems formulated based on Conditional Value-at-Risk (CVaR). Numerical experiments on synthetic and real-world data suggest that our approach outperforms existing approaches with the same objective function, such as the ERM-based convex optimization model which is referred to as Ban and Rudin's big data newsvendor model, and quantile regression decision trees.

This thesis examines decision optimization of product recalls. Product recalls in recent years have shown unprecedented impact on both immediate economic and reputational damage to the company and long-lasting impact on the brand and industry. Admittedly, imperfect product quality makes recalls inevitable. Thus, we explore from three perspectives to elicit business insights regarding better management and risk control. Chapter 1 introduces the topic of product recall management optimization and its real-world motivation. Chapter 2 views the decision making of "when to initiate a product recall" as a dynamic process and takes the feedback of customer returns to update the product defect rate. Updating is simplified by the conjugate properties of beta distribution and Bernoulli trials. We develop the optimal stopping model to find the thresholds of total product returns above which initiating recall is optimal. We implement dynamic programming to solve the model optimally. For large-size problems, we propose a simulation method to balance computation time with solution quality. Chapter 3 allows the company to control the recall risk by investing in quality. We adopt the one-stage stochastic newsvendor model and add quality-dependent recall risk. The resulting model is not concave in production quantity and quality levels. The parametric analysis reveals several interesting features such as the optimal ordering quantity and quality level have a conflicting relationship. We further extend our model from internal supply to external supply from multiple sources. Chapter 4 examines managing product recalls from the closed-loop supply chain management and disruption management perspectives. We model the location and allocation decisions of both manufacturing plants and reprocessing facilities where facilities are built after the recalls. Numerical experiments show the costs of overlooking potential recalls vary greatly, indicating the necessity of considering recalls in initial designs and the importance of accurate recall probability prediction. Chapter 5 summarizes. / Thesis / Doctor of Philosophy (PhD)

In this paper we investigate a manufacturer's sustainable sourcing strategy that includes recycled materials. To produce a short life-cycle electronic good, strategic raw materials can be bought from virgin material suppliers in advance of the season and via emergency shipments, as well as from a recycler. Hence, we take into account virgin and recycled materials from different sources simultaneously. Recycling makes it possible to integrate raw materials out of steadily increasing waste streams back into production processes. Considering stochastic prices for recycled materials, stochastic supply quantities from the recycler and stochastic demand as well as their potential dependencies, we develop a single-period inventory model to derive the order quantities for virgin and recycled raw materials to determine the related costs and to evaluate the effectiveness of the sourcing strategy. We provide managerial insights into the benefits of such a green sourcing approach with recycling and compare this strategy to standard sourcing without recycling. We conduct a full factorial design and a detailed numerical sensitivity analysis on the key input parameters to evaluate the cost savings potential. Furthermore, we consider the effects of correlations between the stochastic parameters. Green sourcing is especially beneficial in terms of cost savings for high demand variability, high prices of virgin raw material and low expected recycling prices as well as for increasing standard deviation of the recycling price. Besides these advantages it also contributes to environmental sustainability as, compared to sourcing without recycling, it reduces the total quantity ordered and, hence, emissions are reduced.

There are numerous applications of game theory in the analysis of supply chains where multiple actors interact with each other in order to reach their own objectives. In this paper we review the use of non-cooperative game theory in inventory management within the newsvendor framework describing a single period inventory control model with the focus on horizontal interactions among multiple independent newsvendors. We develop a framework for identifying these types of horizontal interactions including, for example, the models with the possibility of inventory sharing via transshipments, and situations with substitutable products sold by multiple newsvendors. Based on this framework, we discuss and relate the results of prior research and identify future research opportunities.

Uncertainty is a norm in business decisions. In this research, we focus on the inventory decisions for companies with uncertain customer demands. We first investigate forward buying strategies for single stage inventory decisions. The situation is common in commodity industry where prices often fluctuate significantly from one purchasing opportunity to the next and demands are random. We propose a combined heuristic to determine the optimal number of future periods a firm should purchase at each ordering opportunity in order to maximize total expected profit when there is uncertainty in future demand and future buying price. Second, we study the complexities of bundling of products in an Assemble-To-Order (ATO) environment. We outline a salvage manipulator mechanism that coordinates the decentralized supply chain. Third, we extend our salvage manipulator mechanism to a two stage supply chain with a long cumulative lead time. With significant lead times, the assumption that the suppliers all see the same demand distribution as the retailer cannot be used.

The thesis studies the problem well-known in literature as the newsvendor problem. After summarizing the basic model we pay attention to two extensions of this problem and their combination in single model. The first extension concerns the possibility of the vendor to choose his selling price. The second extension is creation of market with several vendors. We describe both situations in the first chapter of the thesis. In the second chapter we study the combination of both extensions, which means the market with several vendors who can choose their selling prices. We touched several models of such market and we found that the problem is very complex. However we found the optimal reaction of one vendor on the strategy of the other vendor in case of special market with two vendors. That enabled us to create a programme that examines such market, mainly the dependence of the optimal decision of one vendor on the strategy of the second vendor and presence of the Nash equilibriums. 1

An optimal ordering scheme for the capacitated, finite-horizon, multi-period, multiproduct newsvendor problem was proposed by cite {shao06} using a hedging point policy. This solution requires the calculation of a central curve that divides the different ordering regions and a vector that defines the target inventory levels. The central curve is a nonlinear curve that determines the optimal order quantities as a function of the initial inventory levels. In this paper we propose a method for calculating this curve and vector using spline functions, infinitesimal perturbation analysis (IPA), and convex optimization. Using IPA the derivatives of the cost with respect to the variables that determine the spline function are efficiently calculated. A convex optimization algorithm is used to optimize the spline function, resulting in a optimal policy. We present the mathematical derivations and simulation results validating this solution.

The presence of substitution among multiple similar products plays an important role in inventory management. It has been observed in the literature that incorporating the impact of substitution among products can substantially improve the profit and reduce the understock or overstock risk. This thesis focuses on exploring and exploiting the impact of substitution on inventory management problems by theoretically analyzing mathematical models and developing efficient solution approaches. To that end, we address four problems. In the first problem, we study different pricing strategies and the role of substitution for new and remanufactured products. Our work presents a two-stage model for an original equipment manufacturer (OEM) in this regard. A closed-form one-to-one mapping of product designs onto the optimal product strategies is developed, which provides useful information for the retailer. Our second problem is a multi-product newsvendor problem with customer-driven demand substitution. We completely characterize the optimal order policy when the demand is known and reformulate this nonconvex problem as a binary quadratic program. When the demand is stochastic, we formulate the problem as a two-stage stochastic program with mixed integer recourse, derive several necessary optimality conditions, prove the submodularity of the profit function, develop polynomial-time approximation algorithms, and show their performance guarantees. Our numerical investigation demonstrates the effectiveness of the proposed algorithms and, furthermore, reveals several useful findings and managerial insights. In the third problem, we study a robust multi-product newsvendor model with substitution (R-MNMS), where both demand and substitution rates are uncertain and are subject to cardinality-constrained uncertainty set. We show that for given order quantities, computing the worst-case total profit, in general, is NP-hard, and therefore, address three special cases for which we provide closed-form solutions. In practice, placing an order might incur a fixed cost. Motivated by this fact, our fourth problem extends the R-MNMS by incorporating fixed cost (denoted as R-MNMSF) and develop efficient approaches for its solution. In particular, we propose an exact branch-and-cut algorithm to solve small- or medium-sized problem instances of the R-MNMSF, and for large-scale problem instances, we develop an approximation algorithm. We further study the effects of the fixed cost and show how to tune the parameters of the uncertainty set. / Doctor of Philosophy / In a multi-product supply chain, the substitution of products arises if a customer's first-choice product is out-of-stock, and she/he have to turn to buy another similar product. It has been shown in the literature that the presence of product substitution reduces the assortment size, and thus, brings in more profit. %and reduce the inventory level. However, how to quantitatively study and analyze substitution effects has not been addressed in the literature. This thesis fills this gap by developing and analyzing the profit model, and therefore, providing judicious decisions for the retailer to make in order to maximize their profit. In our first problem, we consider substitution between new products and remanufactured products. We provide closed-form solutions, and a mapping that can help the retailer in choosing optimal prices and end-of-life options given a certain product design. In our second problem, we study multi-product newsvendor model with substitution. We first show that, when the probability distribution of customers' demand is known, we can tightly approximate the proposed model as a stochastic integer program under discrete support. Next, we provide effective solution approaches to solve the multi-product newsvendor model with substitution. In practice, typically, there is a limited information available on the customers' demand or substitution rates, and therefore, for our third problem, we study a robust model with a cardinality uncertainty set to account for these stochastic demand and substitution rates. We give closed-form solutions for the following three special cases: (1) there are only two products, (2) there is no substitution among different products, and (3) the budget of uncertainty is equal to the number of products. Finally, similar to many inventory management problems, we include a fixed cost in the robust model and develop efficient approaches for its solution. The numerical study demonstrates the effectiveness of the proposed methods and the robustness of our model. We further illustrate the effects of the fixed cost and how to tune the parameters of the uncertainty set.

This thesis studies the allocation of stock in a two-level inventory system with stochastic demand. The system consists of one central warehouse which supplies N non-identical retailers with one single product. Customer demand occurs solely at the retailers and follows independent Poisson processes. The purpose is to investigate the value of using a more advanced allocation policy than First Come-First Serve at the central warehouse. The focus is on evaluating how well the simple First Come-First Serve assumption works in a system where the warehouse has access to real-time point-of-sale data, and where shipments are time based and consolidated for all retailers. The considered allocation policy is a myopic policy where the solution to a minimization problem, formulated as a constrained newsvendor problem, determines how the warehouse allocates its stock to the retailers. The minimization problem is solved using (a heuristic method based on) Lagrangian relaxation, and simulation is used to evaluate the average inventory holding costs and backorder costs per time unit when using the considered policy. The simulation study shows that cost savings around 1-4 percent can be expected for most system configurations. However, there were cases where savings were as high as 5 percent, as well as cases where the policy performed worse than First Come-First Serve. The study also shows that the highest cost savings are found in systems with relatively low demand, few retailers, short transportation times and a short time interval between shipments.

In this thesis we study problems in the context of inventory control and facility location. In chapter 2 we study the competition among risk averse newsvendors. We showed that the well-known result for the single-product monopoly firm, which states higher risk aversion causes the firm to reduce its order quantity, cease to hold under the competition. We concluded that the higher risk aversion does not necessarily cause both firms to reduce their order quantity. We showed that the impact of risk aversion on equilibrium quantities is a trade-off between two effects: (a) Own risk aversion increment which causes that the firm reduces its order quantity and (b) Effect of spillover demand from competitor which causes that the firm increases its order quantity. We also show which firm raises its order quantity as both firms become more risk averse depending on their attributes: profitability ratio (overstocking to understocking ratio), initial risk aversion level and demand characteristic (distribution and substitution). In Chapter 3, we study how the operational decisions of a firm's manager depend on her own incentives, the capital structure, and financial decisions in the context of the newsvendor framework. We showed that in contrast to common practices, tying the manager's compensation to stock price (equity value) may not be optimal for shareholders. We propose to tie the managers' compensation to the firm value or include a debt-like instrument in the compensation package to mitigate the risk taking behaviour of the managers. We also show how the board of directors can modify the compensation structure based on the state of the economy and publicly available information about company's demand. In Chapter 4, we study the effect of risk attitude of decision makers on well-known location problems with uncertain demand. In addition to providing mathematical formulations for those problems, we also discussed how we can solve these problems using linearization techniques. We also shed some light on the importance of considering the volatility and correlation structure. Furthermore, we apply a Bayesian updating method, a useful tool for updating the probability distribution to incorporate the consultants' view about uncertain factors in location problems.