Reorder point. This type of problem can be recognized when the demand rate(d), lead time (LT), and desired service level or stockout risk are given . Use these steps to solve this type of problem: 1. Match the choice of formula to the standard deviation (s) that are given in the problem (e.g., if both demand and lead time standard deviation are given , use Formula 13 -15 for the ROP).
ROP =\overline{d}\times \overline{LT}+ z\sqrt{\overline{LT}\sigma _d^2+ \overline{d}^2\sigma _{LT}^2 } (13–15)
2. If the problem asks for the amount of safety stock, use the second part of the appropriate ROP formula.
3. If the “expected demand during lead time” and the “standard deviation of lead time demand” are given, use Formula 13-12.
ROP = Expected demand during lead time + z \sigma _{dLT} (13–12)
ROP for variable demand and constant lead time. The housekeeping department of amotel uses approximately 400 washcloths per day . The actual number tends to vary with the number of guests on any given night . Usage can be approximated by a normal distribution that has amean of 400 and a standard deviation of nine washcloths per day. A linen supply company delivers towels and washcloths with a lead time of three days. If the motel policy is to maitain a stockout risk of 2 percent, what is the minimum number of washcloths that must be on hand at reorder time, and how much of that amount can be considered safety stock?