The physical distribution channel of a major food manufacturer consists of plant stocks from which regional warehouses are restocked. These regional warehouses in turn supply the field warehouses assigned to them. There is one plant serving two regional warehouses that, in turn, serve three field warehouses each. The field warehouses have the following weekly demand forecasts for a particular item and the following inventory on hand:

The regional warehouse will supply its assigned warehouses only when the accumulated order quantity at each warehouse equals or exceeds 7,500 cases, and then in increments of 7,500 cases. The 7,500 cases are equal to a truckload shipment. In turn, the plant will supply regional warehouses in increments of 15,000 cases, which is a railcar shipment. The lead time for the supply of field warehouses is one week. Lead time is two weeks for supplying regional warehouses. Production has a lead time of three weeks for materials in lots of 20,000 cases. No shipments are in the pipeline to field warehouses; however, a previously scheduled shipment of 15,000 cases is due to arrive at regional warehouse 2 in the second week.
Over the next ten weeks, plan the materials flow through the network, estimate the average inventory in the system, and project what the production schedule should be.

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Regional Warehouse Hand (Cases) Warehouse Hand (Cases) Demand (Cases) Field Weekly Forecasted Inventory on Inventory on 1,700 3,300 1,200 2,300 2,700 4,100 1,700 900 52,300 2,300 1,200 31,700