Globalization and e-commerce have led to increased levels of competition and steadily shorter product life cycles. The newsvendor (NV) model is classically used for inventory management of short life-cycle product. It contends with demand uncertainty that leads to uncertain performances, as a result risk emerges under which decision are made. While decision makers tend to avoid risk for 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.MV analysis is notable for being implementable and providing good recommendations even without knowing the utility function. Inspired by the Modern Portfolio Theory (MPT) we investigate the set of efficient solutions (i.e., efficient frontier) of the NV problem, using the MV analysis methodology with a modification to avoid its pitfall.
We focus on the special case of uniformly distributed demand where identical locations are independent such that their decisions do not affect their demands. While MPT uses diversification to create an efficient frontier, we show that the efficient frontier of the NV problem exists also for a single location. 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 problems is convex, a portfolio is efficient if and only if it includes identical efficient strategies of the individual problems.
Mature products’ demands are often stabilized such that their profit fluctuation is negligible and so we consider location’s choice to solely sell it, as a risk-free strategy. New products have a higher expected profit, but contain uncertainty in their demand. 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 superior efficient frontier. Capital Asset Pricing Model (CAPM) set a criterion to make decision about adding products to an existing efficient portfolio. While both MPT and CAPM focus is adding products to an existing efficient portfolio, we investigate the effect of replacing locations’ strategies with risk-free strategies—within an existing portfolio. We demonstrate that we can gain large reduction in risk by sacrificing only a small amount of the expected profit.