Consider a two-stage distribution supply chain: a distribution center in the upstream and 5 retailers in the downstream. Retailer demand is normal random variables independent of each other. Use the guaranteed service-time approach. Both stages serve from inventory 98% of all the demand. Holding cost for the distribution center is 90% of the holding cost at a retailer. Distribution incoming service time is 6 days and processing time is 2 days. Processing time at each retailer is 1 day and no service time at the retailers.
What service should the distribution center quote to each retailer to minimize the expected per period cost of holding safety stocks in the supply chain?