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Three Essays on Dynamic Pricing and Resource Allocation ...

Three Essays on Dynamic Pricing and Resource Allocation ...

Three Essays on Dynamic Pricing and Resource Allocation

ong>Threeong> ong>Essaysong> on Dynamic Pricing and Resource Allocation Nur (Ayvaz) Cavdaroglu Submitted in partial fulfillment of the Requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2012

  • Page 2 and 3: c○2012 Nur (Ayvaz) Cavdaroglu All
  • Page 4 and 5: performs well in our experiments. I
  • Page 6 and 7: 2.4.3 Multiple Elective Patient Cla
  • Page 8 and 9: A.3 Proof for Section 2.4.2 . . . .
  • Page 10 and 11: 3.8 Changing N . . . . . . . . . .
  • Page 12 and 13: Acknowledgement I consider myself a
  • Page 14 and 15: My sincere thanks also go to Ward W
  • Page 16 and 17: To my mother, To my father xii
  • Page 18 and 19: allocation to address this problem.
  • Page 20 and 21: investment. However, in practice, d
  • Page 22 and 23: If both cases arrive at the hospita
  • Page 24 and 25: our work and present avenues for fu
  • Page 26 and 27: Production/Service Systems. Both qu
  • Page 28 and 29: properties. The main difference of
  • Page 30 and 31: patient arrivals; the queuing-based
  • Page 32 and 33: formulated as follows: for 1 ≤ t
  • Page 34 and 35: One possible method of selecting th
  • Page 36 and 37: Table 2.4: Sensitivity Analysis wit
  • Page 38 and 39: where the capacity available in eac
  • Page 40 and 41: Rt such that the optimal value of a
  • Page 42 and 43: 2.5 Conclusion In this chapter, we
  • Page 44 and 45: conditions, the seller may enjoy in
  • Page 46 and 47: is not due to seasonality effects t
  • Page 48 and 49: generalize Ball and Queyranne’s a
  • Page 50 and 51: information is consistent with resu
  • Page 52 and 53:

    functions fb and Fb with support [

  • Page 54 and 55:

    forms: b ∗ (vb) = {b| − Fs(b) +

  • Page 56 and 57:

    evenue loss in each instance is the

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    namic pricing strategy which is cha

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    formulated as follows: max {st,t=1,

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    selling a single resource to multip

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    maximization problem of the seller

  • Page 66 and 67:

    To see how the seller behaves, note

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    gbT (.) is the pdf. The above probl

  • Page 70 and 71:

    evenue maximization problem of buye

  • Page 72 and 73:

    at each t. (Proof in Appendix B.3.)

  • Page 74 and 75:

    Since ¯ vs 2 + vb 2 ≤ vs 2 58 +

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    discrete fares and characterizing t

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    where ˆµ(t) is the forecasted val

  • Page 80 and 81:

    gramming (see Garstka and J.-B.Wets

  • Page 82 and 83:

    game under BPP setting is given by:

  • Page 84 and 85:

    If si,c = si,c, i = 1, 2 holds, for

  • Page 86 and 87:

    And the final form of the problem t

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    Table 3.2: BPP vs. SPP under variou

  • Page 90 and 91:

    Figure 3.2: Seller revenues (as a p

  • Page 92 and 93:

    fixed at vs = $1000K, and the inven

  • Page 94 and 95:

    the revenues obtained by applying t

  • Page 96 and 97:

    ased approach can account for vario

  • Page 98 and 99:

    Chapter 4 Pricing Problem of a Mono

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    sion in their paper whereas it is a

  • Page 102 and 103:

    obtained by cooperation, one of whi

  • Page 104 and 105:

    starts, the information regarding t

  • Page 106 and 107:

    forms as follows: 2 Figure 4.1: Seq

  • Page 108 and 109:

    Π i 1(γ, Λ1, qs, qi) = max p i 1

  • Page 110 and 111:

    Proposition 5. If qi ≥ 0.5C1, the

  • Page 112 and 113:

    given (qs, qi) pair, we observe at

  • Page 114 and 115:

    ( 9¯v1 42 10¯v1 , ), (ps∗ 42 1

  • Page 116 and 117:

    4.2.4 The Price Setting Problem of

  • Page 118 and 119:

    The above formulation is concave in

  • Page 120 and 121:

    • 15Λ1 42 > qs and 2 3Λ1 − 2q

  • Page 122 and 123:

    106 - 18 42 Λ1 > qi ≥ 9 23 Λ1:

  • Page 124 and 125:

    In conclusion, the additional profi

  • Page 126 and 127:

    Π s,new 1 (γ, Λ1, qs, qi,c) =

  • Page 128 and 129:

    evenue figures as stated in Table 4

  • Page 130 and 131:

    Table 4.3: Different Problem Settin

  • Page 132 and 133:

    Bibliography A. Ben-Tal, A. N., C.

  • Page 134 and 135:

    118 Deneckere, R., J. Peck. 1995. C

  • Page 136 and 137:

    120 Lan, Gao, M. Ball, I. Karaesmen

  • Page 138 and 139:

    122 Young, J. P., 1962. A queuing t

  • Page 140 and 141:

    definition of L(st, xt) in (2.1),

  • Page 142 and 143:

    fixed Ct, for all t. Thus, given th

  • Page 144 and 145:

    which implies that x ∗ t (st, Ct

  • Page 146 and 147:

    Then, the dynamic programming formu

  • Page 148 and 149:

    Therefore, from (A-5), we obtain th

  • Page 150 and 151:

    That is, if the buyer bid is less t

  • Page 152 and 153:

    id. In this note, we will analyze a

  • Page 154 and 155:

    Since buyers are naive (i.e. they p

  • Page 156 and 157:

    140 terms as in the one-to-one game

  • Page 158 and 159:

    Appendix C Appendix to Chapter 4 C.

  • Page 160 and 161:

    (φ 1(.) and φ 2(.)) lead to sales

  • Page 162 and 163:

    and the investor revenue assumes th

  • Page 164 and 165:

    It could be shown that the revenue

  • Page 166 and 167:

    C.3 Proof of Proposition 7 Consider

  • Page 168 and 169:

    152 • If qi ≥ Λ1 3 23 and qs

  • Page 170:

    for this range of (qi, qs) values s

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