Abstract: A key feature of many real-world matching markets is congestion, i.e., market participants struggle to find match partners. We characterize congestion in a model of random matching markets where an agent pair must perform an inspection to verify compatibility prior to matching with each other. Motivated by the notion of regret-free stability, we assume agents are only willing to inspect their current favorite agent and will do so only if, upon a successful inspection, that match is guaranteed. We ask when, in large random two-sided markets, will information deadlocks arise in which many agents delay inspections indefinitely awaiting a match guarantee. The market consists of N women and αN men. We obtain a sharp characterization of the existence and size of information deadlock as a function of the men-to-women ratio α, women’s average size K of the consideration set, and an inspection’s success probability p, as N grows. Our analysis is inspired by the machinery of message passing and density evolution from statistical physics. We find a phase transition from a deadlock-free regime (where a vanishingly small fraction of agents are stuck waiting) to the information deadlock regime as we increase K, decrease α or decrease p. A number of market design insights emerge from our characterization, for example, the market connectivity K which maximizes the number of matches formed is that which causes the market to be at the phase boundary between the deadlock-free regime and the deadlock regime. Vertical differentiation between agents reduces deadlock, as does a willingness by agents to perform parallel inspections.

Abstract: We study a dual sourcing problem in an increasingly volatile world. We consider two types of volatilities. The first type models fluctuating economic conditions via an underlying Markovmodulated state-of-the-world which affects the two suppliers’ cost structures, capacity limits, and demands. The other type of volatility affects the actual outputs resulting from random supply processes. We develop two approaches to show how the optimal combined ordering strategy from the two suppliers, along with a salvaging policy, can be efficiently computed, and characterize the relatively simple structure of the optimal policies. We also present various comparison results of the expected total costs under different environments. We find that the firm can, by exploiting the dual sourcing options, benefit from environmental volatilities that affect the suppliers’ cost structures or capacity limits; indeed, benefits increase as volatilities increase in specific ways. Numerical studies illustrate these results and reject other reasonable conjectures.

Abstract: We introduce a novel stochastic control model for the problem of a service firm interacting over time with one of its customers. The firm has two service modes available, which differ in their expected reward rates as well as their volatilities (risk). The firm’s objective is to maximize the rewards generated over the customer’s lifetime. Meanwhile, the customer is unsophisticated and might, probabilistically, abandon the system if unsatisfied with recent rewards. We show that the firm’s optimal policy is either myopic or a sandwich policy. A sandwich policy is one where the firm utilizes the myopically optimal service mode when the customer is either very happy or very unhappy but that utilizes the service mode with inferior reward rate when the customer happiness is in a specific interval near the satisfaction threshold. Specifically, the firm should be risk averse when the customer is marginally satisfied and risk seeking when the customer is marginally unsatisfied. We find numerically that the customer lifetime value under the optimal policy is large relative to that under the myopic policy. We also show that our results are robust to a variety of alternative model specifications.

Abstract: We study a general finite horizon, periodic review combined inventory and pricing model with N suppliers and T periods, where both the demands and the supply mechanisms are random. The random supply mechanisms are of a general type that includes most structures encountered in practice. Demands are price-dependent according to general, stochastic demand functions. We characterize the optimal combined pricing and ordering policies to all N suppliers. The general results pertain to independent supply mechanisms but under random capacities — one of the special random supply mechanisms — they also extend to suppliers that are positively dependent on each other.