Negotiation-Based Collaborative Planning Between two Partners

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 533)


In this chapter we develop a collaborative planning scheme for a single buyer-supplier pair. The underlying idea is to formalize a negotiation-like, iterative process between the supplier and buyer. Order proposals (generated by the buyer) and supply proposals (generated by the supplier) are passed between the parties in an iterative manner. A proposal received from the partner is analyzed for its consequences on local planning, and a counter-proposal is generated by introducing partial modifications. Resulting is a negotiation-based process which subsequently improves supply chain wide costs without centralized decision making and with limited exchange of information. MPM as introduced in section 3.1 are used throughout all stages of the process.


Goal Programming Order Quantity Compromise Solution Acceptance Function Collaborative Planning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 148.
    Kersten (2002), p. 16.Google Scholar
  2. 149.
    Excess supplies (vs. the initial orders) are printed bold, short supplies italic and bold.Google Scholar
  3. 150.
    Through an extensive computational evaluation presented in chapter 7.Google Scholar
  4. 151.
    Details follow below in section 4.2.4.Google Scholar
  5. 152.
    A thorough description is laid out below in section 4.3.2.Google Scholar
  6. 153.
    For a description of the symbols see Model 1, p. 30, and section 3.1.3, p. 32.Google Scholar
  7. 154.
    The original demand parameters Dj,tt are still present, as the supplier may also serve o-ther (external) sources of demand. The same set of supply items JS is used in both buyer and supplier models as the items ordered by the buyer and those supplied by the supplier are identical in a two-partner scenario.Google Scholar
  8. 155.
    See Glaser et al. (1992), pp. 237, for a procedure which combines bill-of-material and time-offset data in order to derive supply requirements in a single step.Google Scholar
  9. 156.
    See Lautenschläger (1999), pp. 81, for details. Similar proposals were made by Missbauer (1998), pp. 219, and Karmakar (1992), pp. 287.Google Scholar
  10. 157.
    The idea has been adapted from a multi-stage lot-sizing heuristic developed by Simpson (see e.g. Simpson (1999), pp. 18).Google Scholar
  11. 158.
    The example was obtained from a test instance by parametric optimization, i.e. restriction of the maximum deviation to an incrementally increased upper bound of x%.Google Scholar
  12. 159.
    The precise definition of d is develop in the next section Scholar
  13. 160.
    C.f. Hillier / Liebermann (2001), p. 654.Google Scholar
  14. 161.
    C.f. Hillier / Liebermann (2001), p. 669. Fractional programming problems with an objective function of a special type can be converted to linear programs by a variable substitution (c.f. Neumann / Morlock (1993), pp. 575). However, the above fractional program does not satisfy the necessary conditions (e.g. non-zero denominator values in the entire feasible region).Google Scholar
  15. 162.
    C.f. Domschke / Drexl (1998), p. 165. Specific solution methods only are available for special problem structures such as the “Modified Simplex Method” for quadratic programming problems (c.f. Hillier / Liebermann (2001), pp. 686).Google Scholar
  16. 163.
    Also called Method of Approximation Programming (c.f. Griffith / Stewart (1961), p. 379).Google Scholar
  17. 164.
    Griffith / Stewart (1961), p. 379.Google Scholar
  18. 165.
    C.f. Zhang et al. (1985), p. 1313. For details see e.g. Griffith / Stewart (1961), pp. 380, Palacios-Gomez (1982), pp. 1106, Zhang et al. (1985), pp. 1312.Google Scholar
  19. 166.
    See e.g. Griffith / Stewart (1961), Buzby (1974), Baker / Lasdon (1985).Google Scholar
  20. 167.
    Zhang et al. (1985) observe an average of several hundreds for some problem structures in their computational study.Google Scholar
  21. 168.
    C.f. Charnes / Cooper (1961), pp. 215, Cooper (2002), pp. 36.Google Scholar
  22. 169.
    C.f. Aouni / Kettani (2001), p. 225. See e.g. Schniederjans (1995), pp. 73, for an overview.Google Scholar
  23. 170.
    C.f. Tamiz et al. (1998), p. 570.Google Scholar
  24. 171.
    C.f. Tamiz / Jones (1996), p. 299.Google Scholar
  25. 172.
    Schniederjans (1995), p. 28.Google Scholar
  26. 173.
    C.f. Tamiz/Jones (1996), p. 202.Google Scholar
  27. 174.
    It should however be noted that percentage normalization requires non-zero target values Bj.Google Scholar
  28. 175.
    Jain et al. (1999), p. 270.Google Scholar
  29. 176.
    C.f. Backhaus et al. (1996), p. 264.Google Scholar
  30. 177.
    C.f. Härtung / Elpelt (1995), p. 72, Jain et al. (1999), pp. 271.Google Scholar
  31. 178.
    C.f. Backhaus et al. (1996), p. 274. The Euclidean distance resembles the length of a connecting line between the points xh and xk in two and three dimensional space.Google Scholar
  32. 179.
    The calculation for the supplier is equivalent but based on cumulated order quantitiesGoogle Scholar
  33. 180.
    See e.g. constraints (31) of Model 4, p. 62.Google Scholar
  34. 181.
    Mathematically, we have from constraints (31)Google Scholar
  35. MATH and hence MATH (the last two simplifications are valid because MATH by definition and only one of MATH or MATH is greater than zero at any one time). Thus, we obtain MATH(the last transformation is possible given that MATH).Google Scholar
  36. 182.
    See equation (42), p. 63.Google Scholar
  37. 183.
    if MATH equals zero, a small number 8 is added.Google Scholar
  38. 184.
    C.f. Schniederjans (1995), p. 28.Google Scholar
  39. 185.
    Principally, values greater one are permitted for d. However, the corresponding solutions proof inefficient in GP, because they are dominated by the extreme solution with Δ=0 and d=1 (Δ is non-negative by definition).Google Scholar
  40. 186.
    See section 2.3.2, p. 15.Google Scholar
  41. 187.
    See p. 44.Google Scholar
  42. 188.
    C.f. Steven (1994), p. 184.Google Scholar
  43. 189.
    See section 4.1, p. 55.Google Scholar
  44. 190.
    See Model 6, p. 72.Google Scholar
  45. 191.
    A method for determining AP is introduced shortly.Google Scholar
  46. 192.
    Local savings of up to 41,000 MU vs. partner cost increases of 35,000 MU.Google Scholar
  47. 193.
    The formula represents a linear extrapolation of MATH and the associated deviation MATH to the maximum deviation of one.Google Scholar
  48. 194.
    C.f. Chase et al. (1998), p. 510.Google Scholar
  49. 195.
    See e.g. Silver et al. (1998), pp. 89, Tempelmeier (2003), pp. 47.Google Scholar
  50. 196.
  51. 197.
    I.e. MATH.Google Scholar
  52. 198.
    A similar approach is used below in section 4.3.3, pp. 97, for accepting solutions with a degradation in total costs. It is adapted from meta-heuristic search procedures, namely Simulated Annealing. Links to Simulated Annealing and corresponding references are discussed below in 4.3.3.Google Scholar
  53. 199.
    This specification is of course still subjective. A verification or adjustment should be undertaken for individual problem settings.Google Scholar
  54. 200.
    Or any other number that seems appropriate.Google Scholar
  55. 201.
    (85) is derived from the random acceptance function of Simulated Annealing. For details see 4.3.3, pp. 97.Google Scholar
  56. 202.
    See p. 76.Google Scholar
  57. 203.
    Depending on the value of Dj (0 or 1) either positive or negative deviations can occur.Google Scholar
  58. 204.
    See p. 73 and p. 63.Google Scholar
  59. 205.
    See p. 72 and p. 62.Google Scholar
  60. 206.
    See section, p. 83.Google Scholar
  61. 207.
    See p. 83.Google Scholar
  62. 208.
    See p. 65.Google Scholar
  63. 209.
    See section 5.3, pp. 125. Also, cheating incentives and potential counter-actions are analyzed in 6.2, pp. 147.Google Scholar
  64. 210.
    MATH represents the solution to Model 3 (see p. 61) based on the buyer’s initial order pattern and MATH the (compromise) solution to Model 7 (see p. 73). The definition of an “iteration” follows below in 4.3.2, p. 94.Google Scholar
  65. 211.
    See section 0, p. 78.Google Scholar
  66. 212.
  67. 213.
    Details regarding improvement checks and stopping criteria follow in the next section.Google Scholar
  68. 214.
    That is, the “generate compromise” task in Fig. 25 actually represents an aggregate view of the compromise generation process flow shown in Fig. 23, p. 86.Google Scholar
  69. 215.
    See e.g. Pesch / Voß (1995), pp. 55, for an overview.Google Scholar
  70. 216.
    C.f. Fink (2000), p. 74.Google Scholar
  71. 217.
    See Fink (2000), pp. 77, for an overview of the various counter actions.Google Scholar
  72. 218.
    See e.g. Schocke (2000), pp. 38, Johnson et al. (1989), pp. 867, for details.Google Scholar
  73. 219.
    C.f. Johnson et al. (1989), p. 867.Google Scholar
  74. 220.
    C.f. Pesch / Voß (1995), p. 58.Google Scholar
  75. 221.
    The acceptance of new compromise proposals that display order / supply patterns partly equivalent to a former compromise is similarly dealt with by a stochastic acceptance function as described in section, pp. 83.Google Scholar
  76. 222.
    See, pp. 83.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.MainzGermany

Personalised recommendations