This is an important concept. Machey’s managers probably favor model 2 because aservice level constraint is easier to estimate than a unit shortage cost. However, any particularservice level in model 2 is really equivalent to an appropriate unit shortage cost inmodel 1. To find the equivalent unit shortage cost p for any required service level s, we canuse SolverTable on model 1. We first calculate the fill rate as in model 2. We then runSolverTable to see how the fill rate varies with the unit shortage cost (see Figure 13.18).Note that Solver is actually minimizing total expected annual cost, but it is reporting the fillrate. We see, for example, that a fill rate of 99% is equivalent to a unit shortage cost somewherebetween $4 and $5. Similarly, a fill rate of 98% is equivalent to a unit shortage costof approximately $1. The point is that when a company specifies a required fill rate, this isreally equivalent to specifying a corresponding unit shortage cost.It is usually easier fora company to specify aservice level, but anysuch service level is reallyequivalent to someunit shortage cost.
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