Centre for Supply Chain Management
CMA Canada Supply Chain Managment Speaker Series: Value of a Put Option to the Newsvendor with Lexicographically Ordered Objectives
Youhua (Frank) Chen and Mahmut Parlar
published: 2005 | Research publication | CMA Cda Supply Chain Mgmt SS
ABSTRACT: In this paper we consider an extension of the single-period inventory model with stochastic demand where a put option can be purchased to reduce losses resulting from low demand. The decision maker (i.e., the newsvendor) not only chooses the order quantity but also determines the “strike price” and/or the “strike quantity” of the put option. As the buyer of the put option, the newsvendor receives from the option writer the strike price (adjusted for salvage value) for each unit the demand falls below the strike quantity. The newsvendor has two objectives which are ordered lexicographically, that is, they are assigned pre-emptive priorities: First, she maximizes the expected profit (higher priority) and then minimizes the variance of the profit (lower priority). We prove that the put option does not a.ect the newsvendor’s maximum expected profit but it a.ects the variance of the profit. We combine this result and concepts from stochastic dominance theory to prove that the lexicographic ordering of the two objectives is equivalent to maximizing the expected utility of the newsvendor when she has a quadratic utility function. Sensitivity analysis results indicate that the newsvendor can reduce her profit variance substantially when financial conditions deteriorate, i.e., when revenues decrease or when costs increase. We also find that when the option writer assumes a higher risk/return for the random option payo. (that he pays the newsvendor) the newsvendor can reduce her profit uncertainty by choosing the strike price or strike quantity optimally.
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revised Mar 3/05