Production order quantity calculator
For in-house production where the supply rate p exceeds the demand rate d, EPQ gives Q* = sqrt(2DS / [H * (1 - d/p)])[1]. The (1 - d/p) factor reduces the effective holding penalty because demand drains inventory while production builds it. Maximum on-hand never reaches Q; it tops out at Q * (1 - d/p) when the run ends.
When EPQ collapses back to Wilson
As production rate p approaches infinity, (1 - d/p) approaches 1 and Q* approaches the Wilson formula. This is the mathematical statement of "instantaneous resupply": a supplier shipping a complete batch in one drop is an EPQ with infinite p. Outside that limit, EPQ correctly accounts for the fact that the producer doesn’t hold all Q units at once.
Setup cost vs ordering cost
In the EPQ literature S is conventionally called "setup cost" rather than "ordering cost," reflecting the manufacturing context: changeover labour, scrap during ramp, quality inspection at the start of run. The math is identical to S in Wilson; only the accounting bucket changes[2]. SMED programs that shrink setup cost are the Toyota Production System’s way of driving Q* down toward 1 (see JIT).