Logistics recalls

This route should already be familiar to us from our discussion of the logistic map in chapter 4, Prom that chapter, we recall that the Feigenbaum route calls for a sequence of period-doubling bifurcations pitchfork bifurcations versus the Hopf bifurcations of the Landau-Hopf route) such that if subharmonic bifurcations are observed at Reynolds numbers TZi and 7 2, another can be expected at TZ determined by... 

Solution The period-4 solution is bom when fi= +4ft-2 = 0. Solving this quadratic equation yields n =-2 + 6. (The other solution is negative and is not relevant.) Now recall that the origin of p. was defined such that = 0 at the birth of period-2, which occurs at r =. 3 forthe logistic map. Hence =3 + (-2-t- - /6) = 1 -t- Vb, which recovers the result obtained in Example 10.3.3. ... 

Incidentally, this gives a remarkably accurate prediction of for the logistic map. Recall that p = 0 corresponds to the birth of period-2, which occurs at r = 3 for the logistic map. Thus p corresponds to = 3.56 whereas the actual numerical result is c = 3.57 ... 

Some trajectories ofthe Henon map escape to infinity. In contrast, all trajectories of the Lorenz system are bounded they all eventually enter and stay inside a certain large ellipsoid (Exercise 9.2.2). But it is not surprising that the Henon map has some unbounded trajectories far from the origin, the quadratic term in (1) dominates and repels orbits to infinity. Similar behavior occurs in the logistic map—recall that orbits starting outside the unit interval eventually become unbounded. 

For example wrong delivery of product or filthy boxes of product by the logistic department is a major QP concern as it requires corrective actions and taking the lead in that process or the defect may even result in a recall. 

The impact of a product recall can be very detrimental to a company and causes its operations to be unsustainable. It requires reverse logistics, which is a major cost item that includes costs of customer returns, repairs, replacements, refunds, legal habiUties, disposals of returned products, and the cost of repairing brand image. According to Davidson (1984) the recall of the Ford s Pinto cost the company 125 million in punitive damages recall of Pentium microprocessors in 1994 cost Intel 500 million. 

Recalling the two forms presented for the non-binding reactivity, the Michaelis-Menten in Eq. (1.16) and the logistic in Eq. (1.37), we can clearly see that the following hierarchy exists the present discussion follows (Putz et al, 2007)... 

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