By Rainer Kleber
ReverseLogistics is a space that has attracted growingattention over the past years either from the commercial in addition to from the scienti?c aspect. the correct administration of opposite ?ows of goods and fabrics is of substantial - portance in lots of industries as a result of its in?uence on monetary functionality and environmental influence. The respective administration projects, even though, are hooked up with new hard making plans and regulate difficulties. This es- cially holds for product restoration administration touching on remanufacturing operations the place used items, after being again to the producer, are reprocessed such that they're nearly as good as new and will be re-integrated into the ahead logistics move. Amajorissueinremanufacturingishowtooptimallycoordinatethepot- tial actions directed at assembly purchaser calls for for serviceable items and to accommodate returns of goods after end-of-use.Therespectivedecisions check with ?nding a formal mixture of production unique and remanufacturing used items in addition to of stock-keeping and taking away again goods. Hereby, proper expense affects and time styles of call for and returns need to be taken into consideration.
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Extra info for Dynamic Inventory Management in Reverse Logistics
6 holds, it is never optimal to have a positive recoverables inventory. For constructing an optimal time path we suggest a forward algorithm that proceeds as follows. 6 holds. , K. Step 2 let k := 1. 9 to determine the corresponding k k interval I k = (θe,2 , θx,2 ): k k k k let θe,2 = θx,2 = θk . 9 (i) or (ii) are achieved, k k θe,2 = 0 or θx,2 = T. let k := k + 1. end while Step 3 j k while there exist two consecutive intervals with θx,2 = θe,2 , j > k and j k θx,2 − θe,2 < τu do j k let θx,2 := θx,2 .
In order to obtain results similar to the DCF solution, the value of a returned item should be set to the unweighted average of the diﬀerence of direct production and remanufacturing costs cp −cr and the opportunity cost saved by not disposing the item −cw . This makes sense if one considers that mh has been derived by using a marginal criterion regarding the ﬁrst item to be put on stock. The value of this (marginal) returned item (represented by the co-state variable) continuously increases during the interval where it is kept on inventory and for small values of α (no discounting) this movement is approximately linear.
This is intuitively clear and leads to the following proposition (presented without proof). 8 (Inventory Conditions). Let I = (θe,2 , θx,2 ) be an open time interval where yu > 0 and yu (θe,2 ) = yu (θx,2 ) = 0. 44) θe,2 (ii)at any point θ ∈ I, cumulative returns must be larger than cumulative demand θ (u(t) − d(t))dt > 0. 8 it must hold that at θe,2 , the return rate must not be smaller than the demand rate in order to start collecting returns and at θx,2 , the opposite must hold. 7. There are two reasons for this.
Dynamic Inventory Management in Reverse Logistics by Rainer Kleber