A Theory of Supply Chains by Prof. Carlos F. Daganzo (auth.)

By Prof. Carlos F. Daganzo (auth.)

This paintings used to be encouraged via a remark made by means of a former pupil (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 usually performed in company colleges to illus­ trate the "bullwhip" impact in offer chains. Al had acknowledged to me that he didn't have to inform his scholars tips to reorder alternative elements from the opposite contributors of the provision chain simply because he knew from adventure that the order sizes the avid gamers might generate because the video game stepped forward may develop into chaotic in any case. considering that I had now not performed the beer online game, his asser­ tion was once interesting to me. Why might such an unstructured video game constantly bring about an analogous bad impression? Did it have anything 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. hence, the bullwhip secret remained, at the very least in my brain. when you consider that stock chains are "conservative" platforms analogous to a site visitors flow, and because site visitors circulate types convey comparable results (the instability of motor vehicle platoons and of sure numerical tools being nota­ ble examples)' I suspected that site visitors movement idea may shed a few gentle at the puzzle.

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I · ' /' t ........ ;.......... / . •••• I • I : TIME. t (c) _. ___ ' ___..... 4. Stencils for queuing and traffic models: (a) queuing; (b) queuing with blocking; (c) traffic-l (Newell, with B=l); (d) traffic-2 (cell-transmission). 24 2. Algorithms / Policies Nj,n+ 1 = Y + Nj-l,n-B (Newell, order-based). 20b) where ~ is a user-defined monotonic function that should decrease at a rate greater than or equal to -1. 3. 20) will turn out to be relevant for supply chain management because they have desirable stability properties, and can be used as a guide to construct useful inventory management policies.

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. Appendix A shows that the results with this approach are the same as those about to be derived. Von Neumann's stability test: We consider here, customer input sequences {Qo,n} with a possibly very large, but finite, number of non-zero terms.

12), which fails the ergodicity test because it does not have a fixed point if Q < (S - s), 1 but is bounded and ergodic nonetheless for non-negative orders. 12c) shows that Kj,n+ I E [S - Qmax, S] for all n. Hence the inventories are bounded. Q = S - Q and satisfy Keq,Q ::; s. Q = S -Q> S- (S-s) =s, 28 3. 12b) to reveal that Qj,n E[O, Qmax] for all n. Thus, the policy is bounded. The policy is also ergodic because under conditions of steady demand, the orders and inventories repeat themselves in a unique way with a period of I (S - s )/Ql intervals.

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