Abstract
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.
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References
Kersten (2002), p. 16.
Excess supplies (vs. the initial orders) are printed bold, short supplies italic and bold.
Through an extensive computational evaluation presented in chapter 7.
Details follow below in section 4.2.4.
A thorough description is laid out below in section 4.3.2.
For a description of the symbols see Model 1, p. 30, and section 3.1.3, p. 32.
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.
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.
See Lautenschläger (1999), pp. 81, for details. Similar proposals were made by Missbauer (1998), pp. 219, and Karmakar (1992), pp. 287.
The idea has been adapted from a multi-stage lot-sizing heuristic developed by Simpson (see e.g. Simpson (1999), pp. 18).
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%.
The precise definition of d is develop in the next section 4.2.3.2.
C.f. Hillier / Liebermann (2001), p. 654.
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).
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).
Also called Method of Approximation Programming (c.f. Griffith / Stewart (1961), p. 379).
Griffith / Stewart (1961), p. 379.
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.
See e.g. Griffith / Stewart (1961), Buzby (1974), Baker / Lasdon (1985).
Zhang et al. (1985) observe an average of several hundreds for some problem structures in their computational study.
C.f. Charnes / Cooper (1961), pp. 215, Cooper (2002), pp. 36.
C.f. Aouni / Kettani (2001), p. 225. See e.g. Schniederjans (1995), pp. 73, for an overview.
C.f. Tamiz et al. (1998), p. 570.
C.f. Tamiz / Jones (1996), p. 299.
Schniederjans (1995), p. 28.
C.f. Tamiz/Jones (1996), p. 202.
It should however be noted that percentage normalization requires non-zero target values Bj.
Jain et al. (1999), p. 270.
C.f. Backhaus et al. (1996), p. 264.
C.f. Härtung / Elpelt (1995), p. 72, Jain et al. (1999), pp. 271.
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.
The calculation for the supplier is equivalent but based on cumulated order quantities
MATH.
See e.g. constraints (31) of Model 4, p. 62.
Mathematically, we have from constraints (31)
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).
See equation (42), p. 63.
if MATH equals zero, a small number 8 is added.
C.f. Schniederjans (1995), p. 28.
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).
See section 2.3.2, p. 15.
See p. 44.
C.f. Steven (1994), p. 184.
See section 4.1, p. 55.
See Model 6, p. 72.
A method for determining AP is introduced shortly.
Local savings of up to 41,000 MU vs. partner cost increases of 35,000 MU.
The formula represents a linear extrapolation of MATH and the associated deviation MATH to the maximum deviation of one.
C.f. Chase et al. (1998), p. 510.
See e.g. Silver et al. (1998), pp. 89, Tempelmeier (2003), pp. 47.
Seep. 75.
I.e. MATH.
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.
This specification is of course still subjective. A verification or adjustment should be undertaken for individual problem settings.
Or any other number that seems appropriate.
(85) is derived from the random acceptance function of Simulated Annealing. For details see 4.3.3, pp. 97.
See p. 76.
Depending on the value of Dj (0 or 1) either positive or negative deviations can occur.
See p. 73 and p. 63.
See p. 72 and p. 62.
See section 4.2.4.1, p. 83.
See p. 83.
See p. 65.
See section 5.3, pp. 125. Also, cheating incentives and potential counter-actions are analyzed in 6.2, pp. 147.
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.
See section 0, p. 78.
Seep. 59.
Details regarding improvement checks and stopping criteria follow in the next section.
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.
See e.g. Pesch / Voß (1995), pp. 55, for an overview.
C.f. Fink (2000), p. 74.
See Fink (2000), pp. 77, for an overview of the various counter actions.
See e.g. Schocke (2000), pp. 38, Johnson et al. (1989), pp. 867, for details.
C.f. Johnson et al. (1989), p. 867.
C.f. Pesch / Voß (1995), p. 58.
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 4.2.4.1, pp. 83.
See 4.2.4.1, pp. 83.
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Dudek, G. (2004). Negotiation-Based Collaborative Planning Between two Partners. In: Collaborative Planning in Supply Chains. Lecture Notes in Economics and Mathematical Systems, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05443-7_4
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DOI: https://doi.org/10.1007/978-3-662-05443-7_4
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