Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

The classic prophet inequality states that, when faced with a finite sequence of non-negative independent random variables, a gambler who knows their distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. In this work we consider the situation in which the sequence comes in random order. We look at both a non-adaptive and an adaptive version of the problem. In the former case the gambler sets a threshold for every random variable a priori, while in the latter case the thresholds are set when a random variable arrives. For the non-adaptive case, we obtain an algorithm achieving an expected reward within at least a 1-1/e fraction of the expected maximum and prove this constant is optimal. For the adaptive case with i.i.d. random variables, we obtain a tight 0.745-approximation, solving a problem posed by Hill and Kertz in 1982. We also apply these prophet inequalities to posted price mechanisms, and prove the same tight bounds for both a non-adaptive and an adaptive posted price mechanism when buyers arrive in random order

The Application of Dynamic Models in Operations Management

The dynamic program is a principal method for analyzing stochastic optimization problems. This dissertation studies three operations management problems that arise in the dynamic environment. The principal motivation behind these comes from the applicability in three areas: the agricultural supply chain, the container shipping industry, and supply chain financing. In the first chapter, we consider the hog production industry, where the hog raising farm should decide the selling strategy among several selling options. The farm also faces the uncertain yield of different weights of hogs and spot price volatility from other interactive markets. In the second chapter, we formulate a blockchain-based cargo reservation system, where a token is designed to be used as a booking deposit to compensate the contractual party if the other side fails to honor the booking, i.e., the overbooking from the service provider and customer no-show. In the third chapter, we study advance payment as a financing instrument in a multitier supply chain to mitigate the supply disruption risk and compare the traditional system (with limited visibility) with the blockchain-enabled system (with perfect visibility). The main goal of this chapter is to shed light on how blockchain adoption impacts agents\u27 operational and financial decisions and profit levels in a multitier supply chain. We apply the genre of dynamic models to formulate all three problems, but we address them by different methodologies because of the difference in the contexts. The first two problems possess structural properties adequate to find the optimal structural policy for a dynamic program, whereas the last problem can be applied to game theory. In the hog production chapter, we find that the optimal selling strategy for the hog farm is non-monotone. The counter-intuitive situation, namely, the farm does not fulfill the long-term contract but sells to the open market to speculate the high spot price, happens when the open market is good enough. We also propose a newsvendor-like heuristic policy that improves the profit of the hog farm by over 25%. We find the service provider has different acceptance strategies for the maritime container shipping problem with and without overbooking. He always prefers reliable customers without overbooking but prefers unreliable customers with overbooking in some circumstances. In the deep-tier supplier chain finance, take a game-theoretic approach to compare how blockchain-enabled deep-tier financing schemes affect a financially constrained supply chain\u27s optimal risk-mitigation and financial strategies. We find that although improved visibility via blockchain adoption can help the manufacturer make informed supply chain financing decisions, whether it can benefit all supply chain members depends on the financing schemes in use. Blockchain-enabled delegate financing increases risk-mitigation investments and benefits all three tiers of the supply chain only when tier-2 is severely capital-constrained with the working capital below a threshold. Because delegate financing endows the intermediary tier-1 supplier leverage over the manufacturer, the inefficiency inhibits an all-win outcome when the tier-2 is not severely capital-constrained. Blockchain-enabled cross-tier direct financing exhibits a compelling performance as it always leads to win-win-win outcomes (and thus ubiquitously implementable) regardless of the supplier\u27s working capital profile

Southern Accent September 1973 - June 1974

Southern Adventist University\u27s newspaper, Southern Accent, for the academic year of 1973-1974.https://knowledge.e.southern.edu/southern_accent/1050/thumbnail.jp