**Elective Patient Admission and Scheduling under Multiple Resource Constraints.** C. Barz, K. Rajaram. April 2013.

We consider a patient admission problem to a hospital with multiple resource constraints (e.g. OR and beds) and a stochastic evolution of patient care requirements across multiple resources. There is a small but significant proportion of emergency patients who arrive randomly and have to be accepted at the hospital. However, the hospital needs to decide whether to accept, postpone or even reject the admission from a random stream of non-emergency elective patients. We formulate the control process as a Markov Decision Process to maximize expected contribution net of overbooking costs. We develop bounds using approximate dynamic programming and use this to construct heuristics. We test our methods on data from the Ronald Reagan UCLA Medical Center.

**A Unifying Approximate Dynamic Programming Model for the Economic Lot Scheduling Problem.** D. Adelman, C. Barz. January 2009.

We formulate the well-known economic lot scheduling problem (ELSP) with sequence dependent setup times and costs as a semi-Markov decision process. Using an afƒine approximation of the bias function, we obtain a semi-infinite linear program determining a lower bound for the minimum average cost rate. Under a very mild condition, we can reduce this problem to a relatively small convex quadratically constrained linear problem by exploiting the structure of the objective function and the state space. This problem is equivalent to the lower bound problem derived by Dobson (1992) and reduces to the well-known lower bound problem introduced in Bomberger (1966) for sequence-dependent setups. We thus provide a framework that unifies previous work, and opens new paths for future research on tighter lower bounds and dynamic heuristics.

**Risk-averse Capacity Control in Revenue Management.** C. Barz. *Lecture Notes in Economics and Mathematical Systems*. 597. 2007.

Deregulation had a significant impact on the U.S. airline industry in the late 1970s. Charter and low-cost airlines such as People Express and Southwest were able to offer seats at a fraction of the price charged by established carriers like Pan Am and American Airlines. Due to their different cost structure, it seemed to be impossible for the big carriers to offer tickets at the same low price. Yet they had to find a way to compete.

**Risk-sensitive Capacity Control in Revenue Management.** C. Barz, K.-H. Waldmann. *Mathematical Methods of Operations Research*. 65(3): 565-579. 2007.

Both the static and the dynamic single-leg revenue management problem are studied from the perspective of a risk-averse decision maker. Structural results well-known from the risk-neutral case are extended to the risk-averse case on the basis of an exponential utility function. In particular, using the closure properties of log-convex functions, it is shown that an optimal booking policy can be characterized by protection levels, depending on the actual booking class and the remaining time. Moreover, monotonicity of the protection levels with respect to the booking class and the remaining time are proven.