Consider a $($s$,$S$)$ inventory model with full backlogging. Demand during each period, Dt is distributed

exponential with mean $.$ At the end of each period, the inventory position $($IPt $=$ Stock on hand $-$

Backorders $+$ Outstanding Orders$)$ is calculated and, if it is below s$,$ an order to get back up to S is placed

$($Ot $=$ max$\{$I$($IPt $<$ s$)($S $$ IPt$),0\}).$ Lead times have a Poisson distribution with mean $\backslash$theta days and all

replenishment orders are received at the beginning of the period. Note that, since orders are placed at the

end of the day, an order with lead time l placed in period n will arrive at the beginning of period n $+$ l $+1.$

A per unit holding cost h is charged for inventory on$-$hand; furthermore, there is a fixed order cost f

and a variable, per unit, cost c$.$ Our goal is to find s and S in order to minimize the E$[$Total cost per

period$]$ such that the stockout rate $\backslash$delta $$ the fraction of demand not supplied from stock on$-$hand $$ is at most

$10\%.$ To further clarify the order of events and the calculation of costs, a $5-$day example in which s $=1000$

and S $=1500,$ the initial inventory on hand is $1000$ and there are no outstanding orders is provided in Table $1.$

Recommended Parameter Settings: Take $=100,\backslash$theta $=6,$ h $=1,$ f $=36$ and c $=2.$

Starting Solutions: s $=1000,$ S $=2000.$ If multiple solutions are needed, use s $$Uniform$(700,1000),$

S $$Uniform$(1500,2000).$

Measurement of Time: Days simulated