REVENUE AND ORDER MANAGEMENT UNDER DEMAND UNCERTAINTY

We consider a firm that delivers its products across several customers or markets, each with unique revenue and uncertain demand size for a single selling season. Given that the firm experiences a long procurement lead time, the firm must decide, far in advance of the selling season not only the markets to be pursued but also the procurement quantity. In this dissertation, we present several operational scenarios in which the firm must decide which customer demands to satisfy, at what level to satisfy each customer demand, and how much to produce (or order) in total. Traditionally, a newsvendor approach to the single period problem assumes the use of an expected profit objective. However, maximizing expected profit would not be appropriate for firms that cannot afford successive losses or negligible profits over several consecutive selling seasons. Such a setting would most likely require minimizing the downside risk of accepting uncertain demands into the production plan. We consider the implications of such competing objectives. We also investigate the impact that various forms of demand can have on the flexibility of a firm in their customer/market selection process. a firm may face a small set of unconfirmed orders, and each order will often either come in at a predefined level, or it will not come in at all. We explore optimization solution methods for this all-or-nothing demand case with risk-averse objective utilizing conditional value at risk (CVaR) concept from portfolio management. Finally, in this research, we explore extensions of the market selection problem. First, we consider the impact of incorporating market-specific expediting costs into the demand selection and procurement decisions. Using a lost sales assumption instead of an expediting assumption, we perform a similar analysis using market-specific lost sales costs. For each extension we investigate two different approaches: i) Greedy approach: here we allocate order quantity to market with lowest expediting cost (lowest expected revenue) first. ii) Rationing approach: here we find the shortage (lost sale) then ration it across all the markets. We present ideas and approaches for each of these extensions to the selective newsvendor problem

Newsvendor Conditional Value-at-Risk Minimisation with a Non-Parametric Approach

In the classical Newsvendor problem, one must determine the order quantity that maximises the expected profit. Some recent works have proposed an alternative approach, in which the goal is to minimise the conditional value-at-risk (CVaR), a very popular risk measure in financial risk management. Unfortunately, CVaR estimation involves considering observations with extreme values, which poses problems for both parametric and non-parametric methods. Indeed, parametric methods often underestimate the downside risk, which leads to significant losses in extreme cases. The existing non-parametric methods, on the other hand, are extremely computationally expensive for large instances. In this paper, we propose an alternative non-parametric approach to CVaR minimisation that uses only a small proportion of the data. Using both simulation and real-life case studies, we show that the proposed method can be very useful in practice, allowing the decision makers to suffer less downside loss in extreme cases while requiring reasonable computing effort

Extensions to Newsvendor Problems

Newsvendor problems (NVPs) form an important and much-studied family of inventory control problems. Although the use of the term varies somewhat, in most situations the term NVP refers to a single-period stochastic inventory control problem involving a single product. Assuming that the demand comes from a known probability distribution, this classic problem can be solved easily with calculus (Arrow et al., 1951), and the solution appears in nearly all inventory management textbooks. In this thesis, we expand the literature in four directions. In Chapter 2, we consider an integrated approach, in which the NVP order quantities are determined directly from the data. Though the topic of integrated approaches has already been studied in the literature, the idea of constructing a robust approach that deals with nonlinear NVPs is novel. In this chapter, we introduce such an approach, and we perform extensive simulation experiments to examine the performance of the approach in different settings, including situations when the true model is known and when the underlying model is mis-specified. In Chapter 3, we consider the effect that small changes in NVP parameters would have on the optimal solution, which is commonly referred to as sensitivity analysis. We show that one can perform sensitivity analysis for NVP using techniques from stochastic programming and discrete approximation. Our method is very general and can handle changes in prices and costs, changes in demand distributions, and cross-price elasticities of demand. Moreover, computational results show that our method yields accurate estimates with very reasonable computing effort. In Chapter 4, we examine the effect of judgemental adjustments in an NVP context. Several attempts have been made to quantify the outcomes of such adjustments. However, much of this literature assumes that accurate demand forecasts are available. We consider the (more realistic) case in which the forecasts may be inaccurate, due for example to insufficient data or model mis-specification. Computational results indicate that, in some cases, judgemental adjustment can lead to an increase in profit rather than a decrease. We discuss conditions under which the adjustments are beneficial and the situations when they are not. We also propose a heuristic algorithm for “tuning” the adjustment parameters in practice. In Chapter 5, we propose an alternative non-parametric approach to the variant of the NVP in which the goal is to minimise the conditional value at risk (CVaR). Given the difficulties with treating observations with extreme values, the existing parametric methods often underestimate the downside risk and lead to a significant loss in extreme cases. The existing non-parametric methods, on the other hand, are extremely computationally expensive with large instances and depend heavily on the form of the profit function. Using both simulation and real-life case studies, we show that our proposed method can be very useful in practice, allowing decisionmakers to suffer far less downside loss in extreme cases while requiring reasonable computing effort

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes