By Prof. Carlos F. Daganzo (auth.)
This paintings used to be motivated through a remark made through a former scholar (Prof. Alan Erera of Georgia Tech) in reference to a listing stabil ity video game he was once going to play in a single of his logistics periods. This used to be the well known "beer-game" that's frequently performed in company faculties to illus trate the "bullwhip" impact in offer chains. Al had stated to me that he didn't have to inform his scholars how one can reorder substitute elements from the opposite contributors of the provision chain simply because he knew from adventure that the order sizes the gamers might generate because the online game advanced may develop into chaotic in any case. on account that I had now not performed the beer online game, his asser tion used to be interesting to me. Why may such an unstructured video game constantly result in an identical bad impression? Did it have whatever to do with psy chology? what's it that gamers did to generate instabilities? I posed those to other folks yet couldn't get thoroughly passable an questions swers. hence, the bullwhip secret remained, not less than in my brain. because stock chains are "conservative" structures analogous to a site visitors move, and because site visitors movement types show related results (the instability of motor vehicle platoons and of yes numerical equipment being nota ble examples)' I suspected that site visitors movement conception may well shed a few gentle at the puzzle.
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Extra resources for A Theory of Supply Chains, 1st Edition
4a and compare with Fig. 2a. In most queuing systems items cannot be processed until after they have arrived. 18) must have this property. 5). Thus, we see that the reliability of supply chains is connected with the feasibility of queuing rules. 3) that only involves the queue atj-l, K;-l,n = ~,n -~-l,n' and the order history fromj. l9a) = ~-I(K;-I,n' Qj,n-l, ... , Qj, n-B) + K;-l,n K;-l,n+l = -~-I(K;-I,n' Qj,n-l, ... 19b) where the negative of the H-kernel is the queue that server j-l would have at time n+ 1 if there were to be no further arrivals (Qj,n = 0).
This situation arises if the orders are based on forecasts, and the forecasts are based on historical averages. Policies of this type have an N-keme1 with a single argument, (Nf-l,n - Nf-l,n-B) for some B > O. Thus, linearized versions of any such policy can only have two non-zero coefficients, ~o and ~ B. Since these coefficients must add to unity they can be expressed as ~o = 1+~ and ~B = -~, for some~. Thus, the linearized generic form of these policies has only one degree of freedom. 2 is the prototype.
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.