By Prof. Carlos F. Daganzo (auth.)
This paintings used to be inspired via a remark made by means of a former scholar (Prof. Alan Erera of Georgia Tech) in reference to a list stabil ity online game he used to be going to play in a single of his logistics periods. This used to be the well known "beer-game" that's usually 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 the best way to reorder alternative components from the opposite participants of the provision chain simply because he knew from adventure that the order sizes the avid gamers may generate because the video game stepped forward might turn into chaotic in any case. in view that I had now not performed the beer video game, his asser tion was once exciting to me. Why may such an unstructured video game consistently result in an identical bad impact? Did it have whatever to do with psy chology? what's it that gamers did to generate instabilities? I posed those to folks yet couldn't get thoroughly passable an questions swers. therefore, the bullwhip secret remained, a minimum of in my brain. for the reason that stock chains are "conservative" platforms analogous to a site visitors flow, and because site visitors stream versions convey related results (the instability of vehicle platoons and of definite numerical equipment being nota ble examples)' I suspected that site visitors circulate conception could shed a few gentle at the puzzle.
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Additional info for A Theory of Supply Chains
4) where (a, ~-A , ~ I-A, ... 13) evaluated at the steady state. 4) turns out to be exact if the policy is linear. 31-ANj-I,n+A-1 + ... 5). 4). Since this expression is now exact, it applies to both large and small perturbations in the linear case. , of orders or inventories) are well behaved. , This approximation holds if the Qj,n are close to a steady state, Q. e. [Q = aQ + ~-AQ + ~ l-AQ + ... ]. 7) If the identity [Q = aQ + ~-AQ + ~ I-AQ + ,.. 4) that applies to the order size deviations from the steady state.
T (a) nZ ---. , ~. .. ~ 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.
It is now shown that inventory-based policies are proper if their kernel ~(K) is continuous and monotone with a maximum absolute rate of variation, 0 :-s; 1ta < 1. 3 is proper if -1 < a < 1. To prove the assertion, note first that 1 ~(K) - ~(O) 1 :'S 1ta 1K I, since the rate of variation is bounded by 1ta in the interval [0, KJ. , the boundedness test is satisfied with 1to = 1ta and 1tl = 1~(O) I. Note too that hQ(K) = ~(K) - Q is also continuous and monotone, with the same rate of variation as ~.