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

By Prof. Carlos F. Daganzo (auth.)

This paintings was once inspired by way of 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 sessions. This was once the well known "beer-game" that's frequently performed in company colleges to illus­ trate the "bullwhip" influence in provide chains. Al had stated to me that he didn't have to inform his scholars how one can reorder substitute components from the opposite individuals of the provision chain simply because he knew from adventure that the order sizes the gamers could generate because the online game stepped forward might develop into chaotic in any case. seeing that I had no longer performed the beer online game, his asser­ tion used to be exciting to me. Why could such an unstructured online game continuously bring about an identical 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, not less than in my brain. due to the fact that stock chains are "conservative" structures analogous to a site visitors move, and because site visitors circulation versions convey related results (the instability of motor vehicle platoons and of definite numerical tools being nota­ ble examples)' I suspected that site visitors circulate idea may possibly shed a few gentle at the puzzle.

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11 a) I=-A Clearly the discrete gain is: L 00 G = - (1 + l~l)/(l-(l). (4. 5), we see that (4. 11 b) also holds in the non-linear case. 11b) is now explored with the help of some examples. 3 (Forecasting with moving avera2es): We examine here adaptive policies where orders are determined with a moving average rule over B > 0 prior periods. 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.

7) and the proposition for the constraints: L 00 max { G = - 1 - I=-A L ~ / = 1; 00 l~ / : ~1 ;:: 0, \;f I }. /=-A The optimum solution is obtained by setting the coefficient with the smallest sub-index equal to 1 (~-A = 1) and all others equal to zero. This yields again the familiar result, G = A-I. 13) is also a necessary condition for monotonicity. Note that this necessary condition also applies to non-linear policies, since these policies behave linearly when the input is nearly steady. Let us now tum our attention to reliability.

3. Algorithmic Properties This chapter focuses on the behavior of possible policies. It first introduces in Sec. , to be truly proper, and then examines (in Sec. 2) key properties of proper policies. 15). Two more requirements of a proper algorithm are: (i) that it should produce bounded order sizes and inventories for supplier j if the orders fromj-l are bounded, and (ii) that the time-average of these inventories (or any other statistic of the sequence) should not depend on the initial conditions if the orders from j-l are constant.

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