Computational Evaluation

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


This final chapters deals with the evaluation of the collaborative planning scheme developed in chapters 4 and 5 by computational tests. The purpose is to determine the quality of solutions attainable with the scheme on the one hand and the computational efforts necessary for realizing these solutions on the other. The focus of the computational analysis is on the basic version of the scheme as described in chapter 4, i.e. one-time planning between a single buyer and supplier. However, a somewhat smaller number of tests also considers a more general SC structure with a single supplier but several buyers, as well as planning on a rolling basis between two SC partners.


Test Problem Central Planning Test Instance Order Quantity Test Class 
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  1. 344.
    C.f. ILOG (2000), p. 17.Google Scholar
  2. 345.
    See in particular section 4.3, pp. 90.Google Scholar
  3. 346.
    Details on test instances and input parameters used in the computational study follow in the next section 7.2, pp. 168.Google Scholar
  4. 347.
    See e.g. Model 6, p. 72.Google Scholar
  5. 348.
    See p. 96.Google Scholar
  6. 349.
    See pp. 23.Google Scholar
  7. 350.
    C.f. Derstroff (1995), pp. 90.Google Scholar
  8. 351.
    See e.g. Tempelmeier / Derstroff (1993), pp. 68, Tempelmeier / Derstroff (1996), pp. 750, Ertogral / Wu (2000), pp. 937, Stadtler (2003), pp. 23.Google Scholar
  9. 352.
    I.e. units of item j required to produce one unit of a successor item k (see Model 1, p. 30).Google Scholar
  10. 353.
    C.f. Stadtler (2003), p. 24.Google Scholar
  11. 354.
    I.e. capacity units of resource r required to process one unit of item j (see Model 1, p. 30).Google Scholar
  12. 355.
    In test class L, where the planning interval is limited to 10 periods, available capacity changes in periods 3 and 9 rather than 4 and 10 as shown in the table.Google Scholar
  13. 356.
    See Model 1, p. 30. Variable production costs are neglected, assuming that unit production costs per item do not change during the planning interval and hence do not affect planning results.Google Scholar
  14. 357.
    With respect to capacity expansion, the concept used here differs from Derstroff (1995) who does not foresee capacity expansion at all. Stadtler (2003) allows for overtime only in the prohibitive expediting mode (c.f. Stadtler (2003), p. 26).Google Scholar
  15. 358.
    C.f. Tempelmeier (2003), p. 213.Google Scholar
  16. 359.
    C.f. Derstroff (1995), p. 92.Google Scholar
  17. 360.
    The abbreviations of cost rates follow the declarations laid out in Model 1, p. 30.Google Scholar
  18. 361.
    See e.g. Silver et al. (1998), pp. 151, Chase et al. (1998), pp. 587.Google Scholar
  19. 362.
    Of course, a (percentage) surplus could be added for overtime operation due to higher overtime wages etc. This is however omitted for the sake of simplicity.Google Scholar
  20. 363.
    C.f. Simpson / Erengüc (2001), p. 123. Since the negotiation scheme is intended to “close the cost gap” between Upstream Planning and centralized optimization, significant initial gaps are desired.Google Scholar
  21. 364.
    The problem structures considered here are identical to test set A+ used by Stadtler (2003) (see Stadtler / Sürie (2000), p. 5).Google Scholar
  22. 365.
    See p. 30.Google Scholar
  23. 366.
    See 7.2, pp. 168.Google Scholar
  24. 367.
    C.f. Stadtler (1996), p. 572, (non-negativity restrictions on variable values are ignored).Google Scholar
  25. 368.
    See Stadtler (1996), p. 570.Google Scholar
  26. 369.
    C.f. Stadtler (1996), pp. 574.Google Scholar
  27. 370.
    Also, the total time to find solutions for all test instances of test class L was seen at a reasonable limit with 63 hrs.Google Scholar
  28. 371.
    C.f. Stadtler (2003), pp. 1.Google Scholar
  29. 372.
    Strictly speaking, without optimal solution to the global MLCLSP, the best known solution no longer represents a lower bound on total SC costs. Nonetheless, best solutions are still used as comparison benchmarks in all test cases.Google Scholar
  30. 373.
    See 7.2, pp. 168.Google Scholar
  31. 374.
    This information is not taken from Table 23, but from the detailed records available to the author.Google Scholar
  32. 375.
    In case of S2, this observation is however not valid.Google Scholar
  33. 376.
    C.f. Simpson / Erengüc (2001), p. 123.Google Scholar
  34. 377.
    See 7.2, pp. 168.Google Scholar
  35. 378.
    See p. 170.Google Scholar
  36. 379.
    See pp. 125 for details.Google Scholar
  37. 380.
    See pp. 103.Google Scholar
  38. 381.
    See pp. 127.Google Scholar
  39. 382.
    In the two-partner scenario, in contrast, only 94 of 756 test instances proved capacity infeasible in Upstream Planning.Google Scholar
  40. 383.
    See pp. 103.Google Scholar
  41. 384.
    See p. 184.Google Scholar
  42. 385.
    See p. 185.Google Scholar
  43. 386.
    See p. 174.Google Scholar
  44. 387.
    For details see the description is 5.2, pp.115.Google Scholar
  45. 388.
    See pp. 115 (implementation and computational tests are limited to the version with full exchange of cost information as laid out in 5.2).Google Scholar
  46. 389.
    See p. 178.Google Scholar
  47. 390.
    Alternatively, costs only up to period 12 could be considered, but would need to be reduced by a “bonus” depending on inventory levels at the end of period 12, since production of the inventory positions leads to costs that are actually caused by demand occurring in period 13 or later.Google Scholar
  48. 391.
    See Table 22, p. 179.Google Scholar
  49. 392.
    See p. 180.Google Scholar
  50. 393.
    See Table 24, p. 181.Google Scholar
  51. 394.
    See e.g. the schematic overview in Fig. 33, p. 119.Google Scholar
  52. 395.
    See Model 14, p. 121.Google Scholar
  53. 396.
    See p. 170.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.MainzGermany

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