By Prof. Carlos F. Daganzo (auth.)
This paintings was once motivated by means of a remark made through a former scholar (Prof. Alan Erera of Georgia Tech) in reference to a listing stabil ity online game he was once going to play in a single of his logistics periods. This was once the well known "beer-game" that's frequently performed in company faculties to illus trate the "bullwhip" influence in offer chains. Al had stated to me that he didn't have to inform his scholars tips to reorder alternative components from the opposite participants of the provision chain simply because he knew from adventure that the order sizes the gamers may generate because the online game improved may turn into chaotic anyways. in view that I had now not performed the beer video game, his asser tion was once fascinating to me. Why might such an unstructured online game consistently result in an analogous bad impact? Did it have whatever to do with psy chology? what's it that avid gamers did to generate instabilities? I posed those to folks yet couldn't get thoroughly passable an questions swers. therefore, the bullwhip secret remained, at the very least in my brain. considering that stock chains are "conservative" platforms analogous to a site visitors movement, and because site visitors movement types show related results (the instability of vehicle platoons and of convinced numerical tools being nota ble examples)' I suspected that site visitors stream idea could shed a few mild at the puzzle.
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Example text
4) also holds for the inventories and for the inventory deviations. 4) is sufficiently general to determine the stability of a policy. 40 4. 6). , of order number, N, order size, Q, or inventory, K. Stability is just a property of the vector (a, 13-A, .. ). The easiest way to determine stability-in-the-small appears to be with Von Neumann's method, as explained below, but this is not the only way to do it. The reader familiar with control theory might have been inclined to use "frequency-domain" analysis.
But if the exogenous information is subject to (small) errors, then instabilities will creep in again. 13) are needed to stabilize a chain. We will see in Sec. 13) generate order cancellations. 13) also creates other pernicious effects. , are strongly stable, reliable and have no cancellations), even in the non-linear case. 4 Thus, the least possible anticipation for a properly working chain with gain G is A = G+ 1. 13) is not the only simple, necessary, stability condition that can be developed.
8) that ~(ro) = (1+p)exp(-Aroi) pexp(Broi). 9) can be expressed as: 1~(ro)12 = 1 + 2(1+P)P[1-cos((B+A)ro)] :s; 1; "\fro. , if and only if P E [-1,0]. To see how this condition is related to the gain, express P in terms of the gain. 4c) that G = (A-I) + (A+B)p. Hence, P = (G + 1-A)/(A+B), and we see that P E [-1,0] if and only if A 2:: G+ 1. We also find after some manipulations that ~" = PB 2-(1+P)A 2 = (G+1)(B-A) - AB, which declines with A. , that extra anticipation implies extra stability, as one would expect.