My research interests span modeling and analysis of supply chain management using financial, economic and game-theoretical fun

My research interests span modeling and analysis of supply chain management using financial, economic and game-theoretical fundamentals, as well as providing useful, industrial strength decision support tools using operations research models and algorithms. I intend to continue to focus on risk management in supply chains; supply contracts and supply chain competition, as well as vehicle scheduling and fleet management.

Dissertation Research

My dissertation – supervised by Professor Sridhar Tayur – consists of two parts: a theoretical part including two papers on supply chain management in the energy markets, especially the natural gas market, and an applied part based on an actual implementation of scheduling support tool for a fractional ownership business jet managing company.

Theoretical Part: 1. Equilibrium Analysis of a Natural Gas Supply Chain

Background and Motivation:

Natural gas has its own supply chain. Our original motivation came from a project at Equitable Resource Inc. (NYSE: EQT) to derive forward curves for natural gas markets by incorporating the salient dynamics in this industry. Based on fundamental economic principles, we develop a discrete time, infinite horizon and equilibrium-based model as a first step toward understanding a typical natural gas supply chain where there is a perfectly competitive market, a second market with a small number of firms and a pipeline connecting them.

Summary of Results:

We first ignore the pipeline and study the two markets separately. We extend the available literature by developing a stationary Markov perfect equilibrium (SMPE) model for the storable commodity market with a small number of capacitated firms (Market2) in several steps. First we derive the one-period profit function and explain the relationship among inventory, production and consumption. Next we define the demand shock levels for entry and exit. The necessary and sufficient conditions for strategic entry and exit are proved. The number of firms in equilibrium is showed as the smallest number that can defer the entry of an additional firm. In the third step, we show that there exists inventory equilibrium for all firms in finite and infinite horizon. Finally, we define the SMPE for Market2 with inventory, strategic entry and exit, and prove its existence and ergodicity by combining the previous results. Uniqueness of the SMPE is possible when there is a continuum of firms or there is a dominant firm who makes the others price takers. Numerically we analyze the forward curves and show that the incorporation of number of open firms is important

A general SMPE model is then developed for the entire supply chain after the consideration of the pipeline, which is assumed to be dominant in Market2. We show the existence and uniqueness of SMPE by using general equilibrium theorem. Comparative static properties are examined. Meanwhile, an optimal purchase and delivery solution is presented for the pipeline based on the equilibrium values. The features of spot and forward prices in both markets are compared and analyzed.

We believe that our paper captures the essential dynamics of the natural gas supply chain and hope that our first paper on the topic encourages more research in this area.

Theoretical Part: 2. Analysis of Firm and Interruptible Services in a Natural Gas Supply Chain (Work in Progress)

Summary:

This paper is the sister paper of the first one, expected to be ready by June 2003. In natural gas market there are two basic types of transportation contracts under which the Local Distribution Companies (LDCs) can arrange for transportation services from the pipeline company: firm and interruptible. In firm service the LDC will be delivered by the pipeline the quantity she ordered. In interruptible service, on the other hand, the LDC may not get the amount she ordered. End users purchase natural gas from the LDC and their demand is stochastic. We first study the pricing problem of interruptible contracts and firm contracts for the pipeline. Both contracts have their counterparts in financial market. Next we analyze the procurement equilibrium strategy of the LDC in finite and infinite horizon when having two supply sources with different reliability and facing stochastic demand.

Applied Part: Scheduling of Multiple Types of Time-shared Aircraft with Crew Duty Time Restrictions

Background and Motivation:

As part of its growth strategy, FlightOptions Inc., merged their fractional ownership (time-shared) operations with Raytheon Travel Air in April 2002 and became the second largest fractional ownership business jet managing company in the world. In anticipation this, they asked the authors to develop a scheduling optimization support tool.

Summary of Results:

Aircraft/crew coordination problem faced by fractional management companies has additional complication to commercial airlines. Given the additional costs in “rotating” the crew and implementation difficulties one would encounter for using separate aircraft and crew schedules, and the tendency of the requested trips to have a natural “rest” period during the evening hours, the single joint aircraft/crew scheduling approach provides a very good approximation.

We solve a multiple-type joint aircraft/crew scheduling problem in two phases. In Phase I, we present a heuristic to deal with the crew duty time restrictions for daily schedule. A direct mixed integer programming solution (MIPS) and a minimum cost network flow model with side constraints (NETIP) are developed to solve the problem. MIPS performs faster when the load ratio is high. In Phase II, we present the exact solution by formulating it as a set partitioning problem that incorporates duty time constraints for the crew. The proposed approach consists of a column generation process integrated into a branch-and-bound scheme. Each column represents a feasible routing schedule for an aircraft. The exact solution, which can provide multiple-day schedule, has a comparable performance in the computational time and a better operational efficiency compared to MIPS. Experimental results are presented and analyzed.

Our solution has been put into production in FlightOptions since Jan. 2002. Its average utility – a key performance indicator used by senior executives -- increased to over 70% compared to 62% before the implementation. In addition, its speed allows the schedulers to generate schedules dynamically over time.

Future Research Plans

Strategic Competition in a Natural Gas Supply Chain

In the equilibrium analysis paper on natural gas supply chain, only one pipeline is assumed to exist and she acts as a monopolist. In reality, there may be multiple pipelines connecting the two markets. Each pipeline’s purchase and delivery decision has an impact on the market prices, therefore on other pipelines’ strategy as well. What is the optimal policy for each pipeline? What is the equilibrium for the entire supply chain?

Contract Commitment Flexibility in Multi-Agent Systems

With the explosive growth of internet activity, there will be an increasing reliance on intelligent software agents for electronic commerce, information retrieval and supply chain management. Such multi-agent systems will be comprised of self-motivated agents that interact with each other through negotiation and task delegation. Multi-agent technology models and facilitates these interactions through automated contracting. We present a model, based on financial option pricing theory for modeling flexibility of agent contracts. In most multi-agent systems contractual commitments are binding. We explore non-binding (flexible) contracts, and model the decommitment penalties in terms of options.