Weekly demand for jeans at a Gap store is normally distributed, with a mean of $100$ and a standard deviation of $50.$ The supply plant takes three weeks to supply a Gap order. The store manager monitors its inventory continuously and reorders jeans when the available inventory drops below $350.$ How much safety stock does the store carry? What CSL does the store achieve? If the store manager wants to target a CSL of $95$ percent, how much safety inventory of jeans should the store carry? What should its ROP be$?$

The integrated steel mill incurs a fixed cost of $$4,000$ for each order placed by the steel service center. Steel costs the mill $$1,000$ per ton and the mill has an annual holding cost of $20$ percent. Assuming that the mill builds up its steel $($for the service center$)$ at the rate of $50$ tons per month, what are the annual fixed cost and holding cost incurred by the mill as a result of the service center$$s ordering policy? What is the annual cost incurred by both the service center and the steel mill?

If the steel mill and the service center could work in a coordinated manner, what is the optimal order size that minimizes their joint fixed and holding costs? What annual savings could the supply chain expect as a result of coordination? Design an all unit quantity discount that the integrated steel mill could use to get the service center to order the coordinated amount without increasing annual costs at the service center.