Kyle Y. Lin

Dynamic pricing with real-time demand learning

In many service industries, the firm adjusts the product price dynamically by taking into account the current product inventory and the future demand distribution. Because the firm can easily monitor the product inventory, the success of dynamic pricing relies on an accurate demand forecast. In this paper, we consider a situation where the firm does not have an accurate demand forecast, but can only roughly estimate the customer arrival rate before the sale begins. As the sale moves forward, the firm uses real-time sales data to fine-tune this arrival rate estimation. We show how the firm can first use this modified arrival rate estimation to forecast the future demand distribution with better precision, and then use the new information to dynamically adjust the product price in order to maximize the expected total revenue. Numerical study shows that this strategy not only is nearly optimal, but also is robust when the true customer arrival rate is much different from the original forecast. Finally, we extend the results to four situations commonly encountered in practice: unobservable lost customers, time dependent arrival rate, batch demand, and discrete set of allowable prices.

Dynamic price competition with discrete customer choices

For many years, dynamic pricing has proven to be an effective tool to increase revenue in the airline and other service industries. Most studies, however, focused on monopolistic models and ignored the fact that nowadays consumers can easily compare prices on the Internet. In this paper, we develop a game-theoretic model to describe real-time dynamic price competition between firms that sell substitutable products. By assuming the real-time inventory levels of all firms are public information, we show the existence of Nash equilibrium. We then discuss how a firm can adapt if it knows only the initial - but not the real-time - inventory levels of its competitors. We compare a firms expected revenue under different information structures through numerical experiments.

A Framework Using Two-Factor Price Lattices for Generation Asset Valuation

In this paper, we use a real-options framework to value a power plant. The real option to commit or decommit a generating unit may be exercised on an hourly basis to maximize expected profit while subject to intertemporal operational constraints. The option-exercising process is modeled as a multistage stochastic problem. We develop a framework for generating discrete-time price lattices for two correlated Ito processes for electricity and fuel prices. We show that the proposed framework exceeds existing approaches in both lattice feasibility and computational efficiency. We prove that this framework guarantees existence of branching probabilities at all nodes and all stages of the lattice if the correlation between the two Ito processes is no greater than 4/√35 ≈ 0.676. With price evolution represented by a lattice, the valuation problem is solved using stochastic dynamic programming. We show how the obtained power plant value converges to the true expected value by refining the price lattice. Sensitivity analysis for the power plant value to changes of price parameters is also presented.

Optimal Discrete Search with Imperfect Specificity

A target is hidden in one of several possible locations, and the objective is to find the target as fast as possible. One common measure of effectiveness for the search process is the expected time of the search. This type of search optimization problem has been addressed and solved in the literature for the case where the searcher has imperfect sensitivity (possible false negative results), but perfect specificity (no false positive detections). In this paper, which is motivated by recent military and homeland security search situations, we extend the results to the case where the search is subject to false positive detections.

Performance analysis and simulation of cyclic code-shift keying

Cyclic code-shift keying (CCSK) is the baseband symbol modulation scheme used by Joint Tactical Information Distribution System (JTIDS), the communication terminal of Link-16. Since CCSK is non-orthogonal, an analytic evaluation of its performance in terms of probability of symbol error is nontrivial. In this paper, an analytic upper bound on the probability of symbol error of CCSK is derived for the 32-chip CCSK sequence chosen for JTIDS. The probability of symbol error obtained with the analytic method is compared with that obtained by Monte Carlo simulation for additive white Gaussian noise. The results show that the analytic method yields a tight upper bound. In addition to the 32-chip CCSK sequence chosen for JTIDS, a new 32-chip CCSK sequence with a smaller maximum off-peak cross-correlation is obtained and evaluated both analytically and by Monte Carlo simulation. The results obtained for the new CCSK sequence compare favorably with the sequence chosen for JTIDS.

Admission Control with Incomplete Information of a Queueing System

We consider a multiple-server loss model where customers arrive at a gatekeeper according to a Poisson process. A costc is incurred if a new arrival is blocked from entering the system by the gatekeeper, while a larger costK is incurred if an admitted customer finds all servers busy and therefore has to leave the system. The key assumption is that the gatekeeper is informed when an admitted customer finds all servers busy, but is not informed when served customers depart. Assuming an exponential service distribution, we show that, in the case of a single server, a threshold-type policy that blocks for a certain amount of time after a new arrival is admitted is optimal. When there are multiple servers, we propose two types of heuristic policies. We analytically compute the best policy of the first type, and use simulation to estimate that of the other.

A Graph Patrol Problem with Random Attack Times

This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and strategic attackers. A random attacker chooses which node to attack according to a probability distribution known to the patroller. A strategic attacker plays a two-person zero-sum game with the patroller. For each case, we give an exact linear program to compute the optimal solution. Because the linear programs quickly become computationally intractable as the problem size grows, we develop index-based heuristics. In the random-attacker case, our heuristic is optimal when there are two nodes, and in a suitably chosen asymptotic regime. In the strategic-attacker case, our heuristic is optimal when there are two nodes if the attack times are deterministic taking integer values. In our numerical experiments, our heuristic typically achieves within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy.

Managing Cost Overrun Risk in Project Funding Allocation

This paper discusses decision making of project funding allocation under uncertain project costs. Because project costs are uncertain and funding allocations may not necessarily match the costs required, each project is inherently subject to a cost overrun risk (COR). In this paper, a model is proposed in which project cost is treated as a factor with a probability density function. The decision maker then allocates the total funding to the projects while minimizing a weighted sum of mean and variance of the COR of the project portfolio. Some properties of project COR are derived and interpreted. Optimal funding allocation, in relationship to factors such as various project sizes and riskiness, project interdependency, and the decision maker’s risk preference, is analyzed. The proposed funding allocation model can be integrated with project selection decision-making and provides a basis for more effective project control.

Performance analysis and simulations of 32-ary cyclic code-shift keying

Cyclic code-shift keying (CCSK) is the baseband 32-ary symbol modulation scheme used by the Joint Tactical Information Distribution System (JTIDS), the communication terminal for Link-16. CCSK is not orthogonal and an analytic expression for the probability of symbol error for CCSK has thus far been elusive. In this paper, an analytic upper bound on the probability of symbol error of CCSK is derived for the 32-chip CCSK starting sequence chosen for JTIDS. The analytically obtained probability of symbol error is compared with two different Monte Carlo simulations for additive white Gaussian noise. The results of both simulations match the analytic results very well and show that the analytic method yields a tight upper bound. A new 32-chip CCSK starting sequence which has a smaller maximum off-peak cross-correlation value than the current JTIDS starting sequence is proposed and evaluated both analytically and by simulation. The results obtained for the new CCSK starting sequence compare favorably with the CCSK starting sequence chosen for JTIDS. Published in 2010 by John Wiley & Sons, Ltd. Cyclic code shift keying is used in important military communications systems designed for jamming resistance. This paper provides the most accurate analysis and simulation of CCSK performance to date in addition to a proposed improvement over the CCSK employed in the widely used Link-16 tactical communications system. (This article is a U.S. Government work and is in the public domain in the U.S.A.)

Allocation of flexible and indivisible resources with decision postponement and demand learning

We consider a firm that uses two perishable resources to satisfy two demand types. Resources are flexible such that each resource can be used to satisfy either demand type. Resources are also indivisible such that the entire resource must be allocated to the same demand type. This type of resource flexibility can be found in different applications such as movie theater complexes, cruise lines, and airlines. In our model, customers arrive according to independent Poisson processes, but the arrival rates are uncertain. Thus, the manager can learn about customer arrival rates from earlier demand figures and potentially increase the sales by postponing the resource allocation decision. We consider two settings, and derive the optimal resource allocation policy for one setting and develop a heuristic policy for the other. Our analysis provides managerial insights into the effectiveness of different resource allocation mechanisms for flexible and indivisible resources.