You have been hired as a consultant by the Ontario Provincial Government to help identify "efficiencies". One potential area of cost reduction is to centralize the procurement of basic supplies across multiple school boards. Prior to conducting a detailed investigation of cost savings you have been asked to prepare a report to illustrate potential benefits by focusing on a single commodity.

One basic commodity that is procured by the individual boards is copy paper. This is a high use item and the usage and procurement details for each board are as follows $($assume that the school year is $12$ months and usage is relatively constant$).$ The unit price of a box of paper is $$60$ and the annual holding cost for a box is $$2.$

Monthly usage Cost of placing an order $($estimated fixed cost$)$ Current Order size

School Board A $500$ boxes $$10001500$ boxes

School Board B $200$ boxes $$800400$ boxes

School Board C $300$ boxes $$900300$ boxes

School Board D $400$ boxes $$10001600$ boxes

School Board E $600$ boxes $$1200900$ boxes

School Board F $100$ boxes $$400300$ boxes

School Board G $200$ boxes $$1000200$ boxes

Write a report for the government detailing your analysis and procurement recommendations. You will want to calculate the current state total purchasing costs using the given order quantities and compare them to the total purchasing costs leaving the decentralized order process in place but applying economic order quantities for each school board and to the total purchasing costs after establishing a centralized order process utilized an economic order quantity for this process as well. Clearly state all assumptions. If it was known that the lead time was $1$ week, would this change your conclusion $($consider fixed cost and order process$)?$

Within the centralized option, assume that lead time is actually $1$ week and suppose that lead time demand follows a normal distribution and the standard deviation of lead time demand is $50$ boxes. As copy paper is a critical commodity and centralizing this commodity does pose some supply risk, in making your recommendation to management, you are proposing to put some safety inventory in place to ensure that a service level of $95\%$ order fulfillment to the schools is achieved. How does this impact your reorder point? Please explain in detail showing your calculations.