M.Sc Student | Ezer Gad Gal |
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Subject | The Efficient Frontier of the Newsvendor Problem |

Department | Department of Industrial Engineering and Management |

Supervisor | ASSOCIATE PROF. Yale Herer |

Globalization and e-commerce have led to increased levels of competition and steadily shorter products life cycles. The newsvendor (NV) model is classically used for inventory management of products with short life cycles. The newsvendor model addresses the risk of uncertain performance as a result of demand uncertainty. While decision makers tend to avoid risk when dealing with high profit products (e.g., new products), the traditional solution of the NV problem ignores the underlying risk. Mean-variance (MV) analysis is a fundamental theory of risk management in finance. Although it is often criticized for possible lack of stochastic dominance, MV analysis is notable for being implementable and providing good recommendations even without needing to specify the utility function. Inspired by Modern Portfolio Theory (MPT), we investigate the set of all efficient solutions (i.e., the efficient frontier) of the NV problem, using a modified version of the MV analysis methodology that allows us to avoid the aforementioned pitfall.

The focus of this paper is the special case of uniformly distributed demand where identical locations are independent. While MPT uses diversification to create an efficient frontier, we show that the efficient frontier of the NV problem also exists for a single location with a single product. Defining a combination of multiple locations’ strategies as a portfolio, we show that the efficient frontier of the multilocation NV problem includes only efficient strategies of the individual problems. Moreover, when the efficient frontier of the individual problem is convex, a portfolio is efficient if and only if it includes the individual problems’ identical efficient strategies.

Creating a massive pileup of mature products, companies are encouraged not only to develop but also to launch new products or else face obsolescence as happened to Kodak, which filed for bankruptcy in 2012. Mature products’ demands have often stabilized (i.e., slight level of uncertainty) such that their profit fluctuation is negligible and so we consider a location’s choice to sell a mature product as a risk-free strategy. MPT showed that the set of all combinations of fractions between a risk-free strategy and a specific efficient portfolio (i.e., the market portfolio) results in a superior efficient frontier. The Capital Asset Pricing Model (CAPM) sets a criterion for making decisions about adding products to an existing efficient portfolio. While both MPT and CAPM focus on adding products to an existing efficient portfolio, we investigate the effect of replacing one or more locations’ strategies with risk-free strategies. We demonstrate that decision makers can gain a large reduction in risk by sacrificing only a small amount of the expected profit as more locations apply risk-free strategies.