R = reorder point
is to minimize the sum of the fixed and variable(i.e.,quantitydependent)costswithintheplanning period.Variable costis the cost depend-ing on the size of the order, most of which isinventory cost.Fixed costis independent fromthe order quantity. For in-house production, thisis primarily the setup cost.Under the preconditions of this model, theoptimal order quantity is computed by minimiz-ing a cost function. LetKl¼the total quantity dependent costKr¼thetotalfixed costin theplanningperiodkl¼variable (quantity dependent) cost perunit and periodkr¼fixed cost per ordera¼frequency of placing an order within theplanning periodT¼length of the planning periody¼total demand in the planning periodx¼order quantityThen the total fixed cost isKr¼akror, becausea¼y/x,Kr¼y=xkr:Assuming a constant stock withdrawal rate,the average stock isx/2, and thus, the total vari-able cost amounts toK1¼x=2k1T:Depending on the order quantityx, the totaldecision relevant costKisKðxÞ ¼KrþK1¼y=xkrþx=2k1T:The minimum of this function, differentiatedbyx, isx¼ﬃﬃﬃﬃﬃﬃﬃﬃ2kryk1Tr:xis theoptimal order quantity(or “optimal lotsize,” “economic order quantity,” and “economiclot size”). In order to meet the demand,xmust beorderedatimes within the planning period. Froma¼y/xfollowsa¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃyk1T2kr:rAlthoughxis called an “optimal” order quan-tity, this optimum can be achieved only underrestrictive premises, including the following:•No capacity restrictions are in place regardingthe delivery (of externally procured parts),production (of in-house produced parts), andinventory capacities.•The demand for the entire planning period isknown.•The demand is the same for all periods. Thewithdrawal rate is constant for all periods.•The cost price (or the production cost, resp.)per unit is given and independent of the quan-tity.
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