Consider a two-stage plant-retailer supply chain. Lead time for orders is two weeks. Safety stock is equal to one weeks demand, and future demand is estimated by the average of the past two weeks.

a) Develop production planning model (equations) for the retailer that states the order-up-to rule, and order quantities as a function of time.

b) Using a table format (Columns are Week, Starting retail inventory, On order, Order-up-to target, Order quantity, and Demand) track performance of the retailer for eight weeks if demand suddenly shifts from 100 units per week to 110 units per week starting in period 3 and stays at 110 to the end.