Working papers

Abstract: We study a matching market with N agents who compete over M = αN opportunities. Agents must perform a costly inspection to verify compatibility prior to matching, and are willing to inspect their current favorite opportunity only if, should they find it compatible, they will be guaranteed a match. We ask when, in large random markets, will information deadlocks arise, i.e., in which markets will a constant fraction of agents get stuck waiting for a guaranteed inspection to become available. We prove, using the machinery of message passing and density evolution from statistical physics, that the existence of an information deadlock is governed by the opportunity to agent ratio α. Numerical evidence shows a phase transition from the information deadlock regime to a deadlock-free regime (where a vanishingly small fraction of agents are stuck waiting) as we gradually increase α.

2. Managing Customer Churn via Service Model Control, with Yash Kanoria and Ilan Lobel

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 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 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.

5. Sourcing with Demand Updates, with Awi Federgruen and Zhe Liu

Abstract: We address a two-stage Newsvendor model in which the mean demand -- but not the actual demand -- at first random itself, gets revealed in midstream, in time to place a second order, albeit that the unit cost price of this second order is higher than that of the original one. The two-stage process is most relevant to many retail organizations, where the retailer has access to two supply options: one with a relatively long lead time where orders need to be placed with much uncertainty about even the mean demand for the season, and a second more expensive option with a much smaller lead time that can be exercised after a signal is revealed, which provides the decision maker with an update of the mean demand. We show that the optimal first-round order can be found by solving a simple ordinary differential equation, while the second-round order is analytically available. We characterize the asymptotic behavior of the initial order, derive analytical upper and lower bounds for this initial procurement, and extend our results to the case where procurement capacities prevail. A numerical study shows the benefits of postponed procurements. We also show necessary and sufficient conditions under which a simple heuristic, suggested by the asymptotic analysis, outperforms the optimal single-stage Newsvendor solution.