MODELING AND ANALYSIS OF AN AUCTION-BASED LOGISTICS MARKET

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

2. Motivation • The Logistics Center established by Eskisehir Chamber of Industry in the Organized Industrial Zone in 2003. • 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

3. Eskişehir Chamber of Commerce Logistics Center www.esolojistik.com Production Consumption Consumption

4. Realized Transportation Prices

5. Comparison with Market Price

6. 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

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

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

9. 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?

10. 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

11. 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 Literature Survey

12. Model Assumptions Industrial Zone loa lla Type L Logistics Center lo ll One truck load (no split) Cost: cdf:Fl(v), E[v]. llb Second Price Auction Market Price PM Type B lb Maximum L,B trucks O orders Cost: cdf:Fb(v), E[c].

13. Empirical Analysis: Order Arrivals

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

15. Analysis of an Auction Given that there are lcarriers (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 lbidders: • When there is one bidder, it is paid at the market price without an auction pl(1)=PM.

16. 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.

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

18. State Space Model • The state of the system: S(t) = [No(t), Nl(t), Nb(t)] • No(t): number of orders at time t • Nl(t): number of Type L carriers at time t • Nb(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 No(t)=o orders and Nl(t)=l, Nb(t)=b carriers in the steady state.

19. Steady State Analysis • Combining with the steady-state distribution of the number of carriers, all the performance measures can be determined: • Pav:the expected average auction price • Qav: expected profit of the carriers • Tav the expected average number of carriers waiting at the center, • Oav the expected average number of waiting orders, • Mothe probability of rejecting an order, • Ml and Mbprobability of rejecting carrier because of the capacity constraint for Type L and Type B carriers

20. 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) = No(t)- Nl(t) + L, • Identical to an M/M/1 queue

21. Average Auction Price and Profit where pl(k) and ql (k) are determined before

22. Average Number of Carriers and Orders Rejection Probability

23. 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

24. 0,0,5 λO λL+ λB+5λOA 0,0,4 λO λL+ λB+4λOA 0,0,3 λO λL+ λB+3*λOA 0,0,2 λO λL+ λB+2*λOA 0,0,1 λO λB λB λB λB λB λL+ λB+λOA 0,0,0 0,1,0 0,2,0 0,3,0 0,4,0 0,5,0 λO+ 3λBA λO+ λBA λO+ 2λBA λO+4 λBA λO+5 λBA λO+ λLA λL λL λL λO+ λLA λL λL 1,0,0 1,1,0 1,2,0 1,0,0 1,3,0 1,4,0 λL λO+ 2λLA λL λO+ 2λLA λL λO+ 2λLA λL λO+ 2λLA λL λO+ 2λLA λL 2,0,0 2,1,0 2,2,0 2,0,0 2,3,0 2,4,0 λL λO+ 3λLA λL λO+ 3λLA λL λO+ 3λLA λL λO+ 3λLA λL λO+ 3λLA λL 3,0,0 3,1,0 3,2,0 3,0,0 3,3,0 3,4,0 λL λO+ 4λLA λL λO+ 4λLA λL λO+ 4λLA λL λO+ 4λLA λL λO+ 4λLA λL 4,0,0 4,1,0 4,2,0 4,0,0 4,3,0 4,4,0 λL λO+ 5λLA λB λL λB λO+ 5λLA λL λB λB λO+ 5λLA λL λO+ 5λLA λL λO+ 5λLA λL 5,0,0 5,1,0 5,2,0 5,3,0 5,4,0 λB 5,5,0 λO+ λBA λO+ 2λBA λO+ 3λBA λO+4 λBA λO+5 λBA State-Transition Diagram L=5, B=5, O=5

25. Performance Measures

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

27. Validation

28. Effect of Arrival Rates

29. Effect of Abandonment Rates

30. 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

31. 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 Conclusions