Christiane Barz

Risk-sensitive capacity control in revenue management

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.

A Unifying Approximate Dynamic Programming Model for the Economic Lot Scheduling Problem

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 affine 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 [Dobson G (1992) The cyclic lot scheduling problem with sequence-dependent setups. Oper. Res. 40:736–749] and reduces to the well-known lower bound problem introduced in Bomberger [Bomberger EE (1966) A dynamic programming approach to a lot size scheduling problem. Management Sci. 12:778–784] for sequence-dependent setups. We thus provide a framework that unifies previous work, and opens new paths for future research on tighter lower bounds ...

A price-directed heuristic for the economic lot scheduling problem

The article formulates the well-known economic lot scheduling problem (ELSP) with sequence-dependent setup times and costs as a semi-Markov decision process. Using an affine approximation of the bias function, a semi-infinite linear program is obtained and a lower bound for the minimum average total cost rate is determined. The solution of this problem is directly used in a price-directed, dynamic heuristic to determine a good cyclic schedule. As the state space of the ELSP is non-trivial for the multi-product setting with setup times, the authors further illustrate how a lookahead version of the price-directed, dynamic heuristic can be used to construct and dynamically improve an approximation of the state space. Numerical results show that the resulting heuristic performs competitively with one reported in the literature.

A tilting algorithm for the estimation of fractional age survival probabilities

Life tables used in life insurance determine the age of death distribution only at integer ages. Therefore, actuaries make fractional age assumptions to interpolate between integer age values when they have to value payments that are not restricted to integer ages. Traditional fractional age assumptions as well as the fractional independence assumption are easy to apply but result in a non-intuitive overall shape of the force of mortality. Other approaches proposed either require expensive optimization procedures or produce many discontinuities. We suggest a new, computationally inexpensive algorithm to select the parameters within the LFM-family introduced by Jones and Mereu (Insur Math Econ 27:261–276, 2000). In contrast to previously suggested methods, our algorithm enforces a monotone force of mortality between integer ages if the mortality rates are monotone and keeps the number of discontinuities small.

An Application of Markov Decision Processes to the Seat Inventory Control Problem

Airlines typically divide a pool of identical seats into several booking classes that represent e.g. different discount levels with differentiated sale conditions and restrictions. Assuming perfect market segmentation, mixing discount and higher-fare passengers in the same aircraft compartment offers the airline the potential of gaining revenue from seats that would otherwise fly empty. If too many seats are sold at a discount price, however, the airline company would loose full-fare passengers. If too many seats are protected for higher-fare demand, the flight would depart with vacant seats. Seat inventory control deals with the optimal allocation of capacity to these different classes of demand, forming a substantial part of a revenue management system.

Ant-based crossover for permutation problems

Crossover for evolutionary algorithms applied to permutation problems is a difficult and widely discussed topic. In this paper we use ideas from ant colony optimization to design a new permutation crossover operator. One of the advantages of the new crossover operator is the ease to introduce problem specific heuristic knowledge. Empirical tests on a travelling salesperson problem show that the new crossover operator yields excellent results and significantly outperforms evolutionary algorithms with edge recombination operator as well as pure ant colony optimization.

Expected Additive Time-Separable Utility Maximizing Capacity Control in Revenue Management

We briefly discuss the static capacity control problem from the perspective of an expected utility maximizing decision-maker with an additive time-separable utility function. Differences to the expected revenue maximizing case are demonstrated by means of an example.