Quality vs. Quantity of Data in Contextual Decision-Making: Exact Analysis under Newsvendor Loss

When building datasets, one needs to invest time, money and energy to either aggregate more data or to improve their quality. The most common practice favors quantity over quality without necessarily quantifying the trade-off that emerges. In this work, we study data-driven contextual decision-making and the performance implications of quality and quantity of data. We focus on contextual decision-making with a Newsvendor loss. This loss is that of a central capacity planning problem in Operations Research, but also that associated with quantile regression. We consider a model in which outcomes observed in similar contexts have similar distributions and analyze the performance of a classical class of kernel policies which weigh data according to their similarity in a contextual space. We develop a series of results that lead to an exact characterization of the worst-case expected regret of these policies. This exact characterization applies to any sample size and any observed contexts. The model we develop is flexible, and captures the case of partially observed contexts. This exact analysis enables to unveil new structural insights on the learning behavior of uniform kernel methods: i) the specialized analysis leads to very large improvements in quantification of performance compared to state of the art general purpose bounds. ii) we show an important non-monotonicity of the performance as a function of data size not captured by previous bounds; and iii) we show that in some regimes, a little increase in the quality of the data can dramatically reduce the amount of samples required to reach a performance target. All in all, our work demonstrates that it is possible to quantify in a precise fashion the interplay of data quality and quantity, and performance in a central problem class. It also highlights the need for problem specific bounds in order to understand the trade-offs at play

Data Science and the Ice-Cream Vendor Problem

Newsvendor problems in Operations Research predict the optimal inventory levels necessary to meet uncertain demands. This thesis examines an extended version of a single period multi-product newsvendor problem known as the ice cream vendor problem. In the ice cream vendor problem, there are two products – ice cream and hot chocolate – which may be substituted for one another if the outside temperature is no too hot or not too cold. In particular, the ice cream vendor problem is a data-driven extension of the conventional newsvendor problem which does not require the assumption of a specific demand distribution, thus allowing the demand for ice cream and hot chocolate respectively to be temperature dependent. Using Discrete Event Simulation, we first simulate a real-world scenario of an ice cream vendor problem via a demand whose expected value is a function of temperature. A sample average approximation technique is subsequently used to transform the stochastic newsvendor program into a feature-driven linear program based on the exogenous factors of probability of rainfall and temperature. The resulting problem is a multi-product newsvendor linear program with L1-regularization. The solution to this problem yields the expected cost to the ice cream vendor as well as the optimal order quantities for ice cream and hot chocolate, respectively

A decision rule based on goal programming and one-stage models for uncertain multi-criteria mixed decision making and games against nature

This paper is concerned with games against nature and multi-criteria decision making under uncertainty along with scenario planning. We focus on decision problems where a deterministic evaluation of criteria is not possible. The procedure we propose is based on weighted goal programming and may be applied when seeking a mixed strategy. A mixed strategy allows the decision maker to select and perform a weighted combination of several accessible alternatives. The new method takes into consideration the decision maker’s preference structure (importance of particular goals) and nature (pessimistic, moderate or optimistic attitude towards a given problem). It is designed for one-shot decisions made under uncertainty with unknown probabilities (frequencies), i.e. for decision making under complete uncertainty or decision making under strategic uncertainty. The procedure refers to one-stage models, i.e. models considering combinations of scenarios and criteria (scenario-criterion pairs) as distinct meta-attributes, which means that the novel approach can be used in the case of totally independent payoff matrices for particular targets. The algorithm does not require any information about frequencies, which is especially desirable for new decision problems. It can be successfully applied by passive decision makers, as only criteria weights and the coefficient of optimism have to be declared

An Integrated Framework For Configurable Product Assortment Planning

A manufacturer\u27s assortment is the set of products or product configurations that the company builds and offers to its customers. While the literature on assortment planning is growing in recent years, it is primarily aimed at non-durable retail and grocery products. In this study, we develop an integrated framework for strategic assortment planning of configurable products, with a focus on the highly complex automotive industry. The facts that automobiles are highly configurable (with the number of buildable configurations running into thousands, tens of thousands, and even millions) with relatively low sales volumes and the stock-out rates at individual dealerships (even with transshipments) are extremely high, pose significant challenges to traditional assortment planning models. This is particularly the case for markets such as the U.S. that mostly operate in a make-to-stock (MTS) environment. First, we study assortment planning models that account for exogenous demand models and stock-out based substitution while considering production and manufacturing complexity costs and economies-of-scale. We build a mathematical model that maximizes the expected profit for an Original Equipment Manufacturer (OEM) and is a mixed-integer nonlinear problem. We suggest using linear lower/upper bounds that will be solved through a Modified-Branch and Bound procedure and compare the results with commercial mixed-integer nonlinear solvers and show superiority of the proposed method in terms of solution quality as well as computational speed. We then build a modeling framework that identifies the optimal assortment for a manufacturer of automotive products under environmental considerations, in particular, Corporate Average Fuel Economy (CAFE) requirements as well as life-cycle Greenhouse Gas (GHG) emission constraints. We present a numerical experiment consisting of different vehicle propulsion technologies (conventional, Diesel, and hybrid) and study the optimal shares of different technologies for maximizing profitability under different target levels of CAFE requirements. Finally, we develop assortment planning formulations that can jointly identify optimal packages and stand-alone options over different series of the product model. Our numerical experiment reveals that product option packaging has a considerable effect on managing product complexity and profitability

COOPERATION OR COMPETITION: A STUDY OF SOCIAL CAPITAL AND PRODUCTION DECISION UNDER POTENTIAL VERTICAL COMPETITION

Since the 2000s when retailers recognised the huge market potential, the growth of private labels has been unstoppable worldwide. As a result of the recession of national brands, manufacturers are in a relatively weaker position when dealing with large retailers. The relationship between manufacturers and retailers has transformed from pure cooperation to a delicate balance of cooperation and competition. Yet, how such a balance influences supply chain dynamics is an intriguing and overdue issue. This thesis explores the influence of social capital over manufacturers’ perceptions regarding their retailers’ trustworthiness in the presence of potential vertical competition, as well as the consequential performance from the perspective of cognitive abilities. Data was collected through an online scenario-based role play (SBRP) experiment, where 371 participants were recruited and put in three groups. In each group, participants were provided with a scenario depicting the product substitution level between a newly launched private label and a national brand. The data was analysed statistically to test the hypotheses. The results identify relational capital as the most influential dimension of social capital in suppressing manufacturer’s perception of opportunistic information sharing behaviour from retailers, and suggest that such suppression is moderated by the level of product substitution between private labels and national brands. This thesis has reference value to academia by looking into the overlapping issues of supply chain management and marketing and providing empirical evidence of the influences induced by the introduction of private labels. It also benefits industry, especially manufacturers, by giving a brief standard regarding whether to cooperate or compete when faced with potential vertical competition with retailers

Production Planning with Risk Hedging

We study production planning integrated with risk hedging in a continuous-time stochastic setting. The (cumulative) demand process is modeled as a sum of two components: the demand rate is a general function in a tradable financial asset (which follows another stochastic process), and the noise component follows an independent Brownian motion. There are two decisions: a production quantity decision at the beginning of the planning horizon, and a dynamic hedging strategy throughout the horizon. Thus, the total terminal wealth has two components: production payoff, and profit/loss from the hedging strategy. The production quantity and hedging strategy are jointly optimized under the mean-variance and the shortfall criteria. For each risk objective, we derive the optimal hedging strategy in closed form and express the associated minimum risk as a function of the production quantity, the latter is then further optimized. With both production and hedging (jointly) optimized, we provide a complete characterization of the efficient frontier. By quantifying the risk reduction contributed by the hedging strategy, we demonstrate its substantial improvement over a production-only decision. To derive the mean-variance hedging strategy, we use a numeraire-based approach, and the derived optimal strategy consists of a risk mitigation component and an investment component. For the shortfall hedging, a convex duality method is used, and the optimal strategy takes the form of a put option and a digital option, which combine to close the gap from the target left by production (only). Furthermore, we extend the models and results by allowing multiple products, with demand rates depending on multiple assets. We also make extension by allowing the asset price to follow various stochastic processes (other than the geometric Brownian motion)

Economic Order Quantity (EOQ) Inventory Management - Essays in Experimental Economics

This thesis consists of six chapters to experimentally study aspects of how levels of individuals’ cognitive stress, cognitive ability and self-regulatory resource affect their decision making under the Economics Order Quantity (EOQ) inventory management environment. In Chapter 3 we use laboratory experiments to evaluate the effects of cognitive stress on inventory management decisions in a finite horizon economic order quantity model. We manipulate two sources of cognitive stress. First, we vary participants’ participation in a pin memorisation task. This exogenously increases cognitive load. Second, we introduce an intervention to reduce cognitive stress by only allowing participants to order when inventory is depleted. This intervention restricts the policy choice set. Increases in cognitive load negatively impact earnings with and without the intervention, with these impacts occurring in the first year. Participants’ in all treatments tend to adopt near optimal policies. However, only in the intervention and low cognitive load treatment do the majority of choices reach the optimal policy. Our results suggest that higher levels of multitasking lead to lower initial performance when taking on new product lines, and that the benefits of providing support and task simplicity are greatest when the task is first assigned. In Chapter 4 we use laboratory experiments to evaluate the effects of individuals’ cognitive abilities on their behaviour in a finite horizon economic order quantity model. Participants’ abilities to balance intuitive judgement with cognitive deliberations are measured by the Cognitive Reflection Test (CRT). Participants then complete a sequence of five “annual” inventory management tasks with monthly ordering decisions. Our results show that participants with higher CRT scores on average earn greater profit and choose more effective inventory management policies. However these gaps are transitory as participants with lower CRT scores exhibit faster learning. We also find a significant gender effect on CRT scores. This suggests hiring practices incorporating CRT type of instruments can lead to an unjustified bias. In Chapter 5 we use laboratory experiments to evaluate the effects of individuals’ ability to self- regulate on inventory management decisions in a finite horizon economic order quantity model. An ego depletion task is implemented aiming to diminish one’s self-regulatory resources. From a psychological point of view, self-control is impaired when the mental resource has been used up over effortful control of responses. In our experiment, participants complete an ego depletion task followed by a sequence of five “annual” inventory management tasks with monthly ordering decisions. Our results show there is no obvious treatment effect on participants’ self-regulation ability

Information and decentralization in inventory, supply chain, and transportation systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (p. 199-213).This thesis investigates the impact of lack of information and decentralization of decision-making on the performance of inventory, supply chain, and transportation systems. In the first part of the thesis, we study two extensions of a classic single-item, single-period inventory control problem: the "newsvendor problem." We first analyze the newsvendor problem when the demand distribution is only partially specified by some moments and shape parameters. We determine order quantities that are robust, in the sense that they minimize the newsvendor's maximum regret about not acting optimally, and we compute the maximum value of additional information. The minimax regret approach is scalable to solve large practical problems, such as those arising in network revenue management, since it combines an efficient solution procedure with very modest data requirements. We then analyze the newsvendor problem when the inventory decision-making is decentralized. In supply chains, inventory decisions often result from complex negotiations among supply partners and might therefore lead to a loss of efficiency (in terms of profit loss).(cont.) We quantify the loss of efficiency of decentralized supply chains that use price-only contracts under the following configurations: series, assembly, competitive procurement, and competitive distribution. In the second part of the thesis, we characterize the dynamic nature of traffic equilibria in a transportation network. Using the theory of kinematic waves, we derive an analytical model for traffic delays capturing the first-order traffic dynamics and the impact of shock waves. We then incorporate the travel-time model within a dynamic user equilibrium setting and illustrate how the model applies to solve a large network assignment problem.by Guillaume Roels.Ph.D

Base-Stock Policies with Constant Lead Time: Closed-Form Solutions and Applications

We study stationary base-stock policies for multiperiod dynamic inventory systems with a constant lead time and independently and identically distributed (iid) demands. When ambiguities in the underlying demand distribution arise, we derive the robust optimal base-stock level in closed forms using only the mean and variance of the iid demands. This simple solution performs exceptionally well in numerical experiments, and has important applications for several classes of problems in Operations Management. More important, we propose a new distribution-free method to derive robust solutions for multiperiod dynamic inventory systems. We formulate a zero-sum game in which the firm chooses a base-stock level to minimize its cost while Nature (which is the firm’s opponent) chooses an iid two-point distribution to maximize the firm’s time-average cost in the steady state. By characterizing the steady-state equilibrium, we demonstrate how lead time can affect the firm’s equilibrium strategy (i.e., the firm’s robust base-stock level), Nature’s equilibrium strategy (i.e., the firm’s most unfavorable distribution), and the value of the zero-sum game (i.e., the firm’s optimized worst-case time-average cost). With either backorders or lost sales, our numerical study shows that superior performance can be obtained using our robust base-stock policies, which mitigate the consequence of distribution mis-specification