MODELING AND ANALYSIS OF AN AUCTION- BASED LOGISTICS MARKET Barış Tan Semra Ağralı and Fikri Karaesmen Department of Industrial Engineering Koç University, Istanbul, Turkey May 23rd, 2005 FIFTH INTERNATIONAL CONFERENCE ON "Analysis of Manufacturing Systems - Production Management" May 20-25, Zakynthos Island, Greece

B. Tan Motivation  The Logistics Center established by Eskisehir Chamber of Industry in the Organized Industrial Zone in  The goal is to satisfy the logistics needs of the producers located in the Industrial Zone at the lowest cost by using an auction mechanism  A hub for logistics firms and truck owners  Attracts truck owners to the center with all the necessary facilities  A reduction of 20-30% in transportation costs is achieved through the market mechanism

B. Tan Eskişehir Chamber of Commerce Logistics Center Production Consumption

B. Tan Realized Transportation Prices

B. Tan Comparison with Market Price

B. Tan Modeling and Analysis Issues  Final price is determined by an auction  The number of bidders and their costs affect the price  Different costs of transportation for different trucks for the same order and the same destination  Random arrival of orders and trucks  Possible abandonment of orders and trucks  Limited capacity of the market

B. Tan Operation of the Logistics Market - 1 Istanbul 200 YTL 220 YTL 180 YTL Logistics Center Payment: 180 YTL (First Price) 200 YTL (Second Price) Industrial Zone

B. Tan Operation of the Logistics Market - 2 Adana 250 YTL Logistics Center Payment: 250 YTL Industrial Zone İzmir

B. Tan Research Questions  What is the gain that will be obtained by using an auction in logistics for the shippers and for the logistic firms?  What are the effects of various system parameters on the gains?  What will be the effect of the auction type used?  What will be the effect of the auction process?

B. Tan Approach  Analyze the second-price auction in a static setting with a given number of bidders and obtain the expected auction price.  Develop an analytical model with some simplifying assumptions and obtain closed-form expressions for the performance measures.  Develop a state-space model and determine the performance measures from the steady-state probabilities of the continuous- time Markov chain.  Develop a simulation model to validate the analytical model and also to handle other extensions

B. Tan Literature Survey  Economics – Vickrey, 1961 – Myerson, 1981 – McAfee and McMillan, 1987 – Klemperer, 1999 – Bapna et al., 2002 – Holt, 1980; Riley and Samuelson, 1981 – Milgrom and Weber, 1982 – Graham and Marshall, 1967; McAfee and McMillan, 1987 – Wilson, 1967; Weverbergh, 1979; Fibich et al., 2004; Griesmer et al., 1967; Maskin and Riley, 2000; Fibich and Gavious, 2003;Campo et al., 2003  Empirical Analysis Literature – Hendricks and Paarsch, 1995 – Paarsch, 1989 – Hendricks and Porter, 1988 – Paarsch, 1989; Laffont, Ossard, and Vuong, 1995; and Elyakime et al., 1997 – Laffont, Ossard, and Vuong, 1995 – Elyakime et al., 1997  Operations Research/Operations Management – Goldsteins, 1952 – Stark and Rothkopf, 1979 – Lucking-Reiley, 2000 – Wagner and Schwab, 2003 – Kameshwaran and Narahari, 2001 – Ledyard et al., 2002 – Song and Regan, 2003 – Chen et al., in progress – Vakrat and Seidmann, 2000 – Emiliani and Stec, 2002 – Talluri and Ragatz, 2004 – Qi, 2002

B. Tan Model Assumptions Logistics Center Industrial Zone Type L Type B l la b lb Second Price Auction Market Price PM Cost: cdf: F l (v), E[v]. Cost: cdf: F b (v), E[c]. o oa One truck load (no split) Maximum L,B trucks O orders

B. Tan Empirical Analysis: Order Arrivals

B. Tan Estimating the Cost Distribution from the Bid Distribution Bid b(v) % Izmir Cost v % First price Second price b(v) = v

B. Tan Analysis of an Auction Given that there are l carriers ( bidders) at the logistics center:  In a single-unit second-price auction, or the Vickrey auction, the carrier that submits the lowest bid wins and the winning bidder is paid at the second lowest bid.  In a second-price auction, the optimal strategy is bidding the actual cost  The expected auction price is the expected value of the second lowest cost in a group of l bidders:  When there is one bidder, it is paid at the market price without an auction p l (1)=P M.

B. Tan Analysis of an Auction  The winning carrier bids its cost which is the minimum of the costs of l bidders.  Then the expected profit is the difference between the expected auction price and the expected cost.

B. Tan Effect of the Number of Bidders Analytical Model Emprical Results Uniform cost distribution pl(l)pl(l)

B. Tan State Space Model  The state of the system: S(t) = [N o (t), N l (t), N b (t)] – N o (t):number of orders at time t – N l (t): number of Type L carriers at time t – N b (t): number of Type B carriers at time t  The process {S(t), t≥0} is a Continuous-time Markov Chain.  The steady-state probabilities:  The state space model gives the probabilities of having N o (t)=o orders and N l (t)=l, N b (t)=b carriers in the steady state.

B. Tan Steady State Analysis  Combining with the steady-state distribution of the number of carriers, all the performance measures can be determined:  P av : the expected average auction price  Q av : expected profit of the carriers  T av the expected average number of carriers waiting at the center,  O av the expected average number of waiting orders,  M o the probability of rejecting an order,  M l and M b probability of rejecting carrier because of the capacity constraint for Type L and Type B carriers

B. Tan Steady-State Analysis: Special Case  Only Type L carriers; no abandonment of orders and carriers; and no capacity constraint for arriving orders.  The state of the system: the number of outstanding orders at time t: S(t) = N o (t)- N l (t) + L,  Identical to an M/M/1 queue

B. Tan Average Auction Price and Profit where p l (k) and q l (k) are determined before

B. Tan Average Number of Carriers and Orders Rejection Probability

B. Tan Steady-State Analysis: General Case  (L+1)(B+1)+O states in the state space.  The steady state probabilities satisfy the following set of transition equations

B. Tan State-Transition Diagram L=5, B=5, O=5

B. Tan Performance Measures

B. Tan Numerical Results Table 1. Comparison with Simulation for Different Arrival and Abandonment Rates

B. Tan Validation

B. Tan Effect of Arrival Rates

B. Tan Effect of Abandonment Rates

B. Tan Observations  Average auction price is less than the market price  As the truck arrival rate or the order abandonment rate increases the auction price decreases  As the order arrival rate or the truck abandonment rate increases, the auction price increases  When different types of carriers are accepted, the average auction price decreases  The average auction price decreasing in the capacity for carriers and increasing in the capacity for orders

B. Tan Conclusions  An analytical model that captures the auction mechanism with the dynamics of the system is developed.  The model allows the users to examine the effects of various system parameters on the performance measures  The analytical results answer various design questions – Should a first price or second price auction be used? – Should the total number of bidders be revealed during the auction? –...  Utilization of the logistics auction market allows – producers to reduce their transportation costs – transporters to utilize their capacity in more efficient way – logistics companies to create value by being an intermediary between producers and transporters