PLS SOLVE ONLY PART G!!

Problem 4. (60 points] The Collins Quarter Restaurant in Savannah, Georgia, is a popular place for weekend brunch. The restaurant serves real maple syrup with French toast and pancakes. The restaurant man- ager, Bob, buys the maple syrup from a company in Maine that requires 3 weeks for delivery. The syrup costs Bob $4 a bottle and may be purchased in any quantity. Fixed costs of or- dering amount to about $75 for bookkeeping expenses, and holding costs are based on 20% annual rate. Based on past experience, the weekly demand for the syrup is normal with mean 12 and variance 16 (in bottles). Assume that there are 52 weeks in a year and that all excess demand is backordered. (a) (5 points) What is the expected demand and variance during lead time? (b) (10 points) What inventory policy should Bob use if a Type I service level of 95% is desired and demand is normally distributed, assuming that Bob is allowed to order at any time? Give the optimal solution of such an inventory policy. (c) (5 points) What is the expected number of backordered units under Type I service levels? (d) (10 points) What inventory policy should Bob use if a Type II service level of 95% is desired and demand is normally distributed, assuming that Bob is allowed to order at any time? Give the optimal solution of such an inventory policy. (e) (10 points) Suppose that Bob's supplier requires a minimum order size of 500 bottles. Find the reorder level that Bob should use if he wishes to satisfy type II service level of 99% assuming normal distribution for the demand. (f) (10 points) Forget about the calculations in (a)-(e). Suppose Bob's suppliers require him to place orders at regular intervals (the quantity of each order is allowed to change). What inventory policy does this correspond to? What would be a good frequency for placing orders? (g) (10 points) Suppose Bob's suppliers require him to order every week instead of the frequency given in (f). After looking at his desired service level, Bob finds that the cor- 2 responding z value is 1. Give the optimal solution. Illustrate how your solution works by filling out the table below: 1 4 5 6 7 15 12 12 4 Cycle number Demand during cycle Inventory level at end of cycle Pipeline Inventory at end of cycle before ordering Inventory position at end of cycle before ordering Inventory ordered at end of cycle 0 2 3 0 10 8 25 30 20 0 0 0 20 0 Problem 4. (60 points] The Collins Quarter Restaurant in Savannah, Georgia, is a popular place for weekend brunch. The restaurant serves real maple syrup with French toast and pancakes. The restaurant man- ager, Bob, buys the maple syrup from a company in Maine that requires 3 weeks for delivery. The syrup costs Bob $4 a bottle and may be purchased in any quantity. Fixed costs of or- dering amount to about $75 for bookkeeping expenses, and holding costs are based on 20% annual rate. Based on past experience, the weekly demand for the syrup is normal with mean 12 and variance 16 (in bottles). Assume that there are 52 weeks in a year and that all excess demand is backordered. (a) (5 points) What is the expected demand and variance during lead time? (b) (10 points) What inventory policy should Bob use if a Type I service level of 95% is desired and demand is normally distributed, assuming that Bob is allowed to order at any time? Give the optimal solution of such an inventory policy. (c) (5 points) What is the expected number of backordered units under Type I service levels? (d) (10 points) What inventory policy should Bob use if a Type II service level of 95% is desired and demand is normally distributed, assuming that Bob is allowed to order at any time? Give the optimal solution of such an inventory policy. (e) (10 points) Suppose that Bob's supplier requires a minimum order size of 500 bottles. Find the reorder level that Bob should use if he wishes to satisfy type II service level of 99% assuming normal distribution for the demand. (f) (10 points) Forget about the calculations in (a)-(e). Suppose Bob's suppliers require him to place orders at regular intervals (the quantity of each order is allowed to change). What inventory policy does this correspond to? What would be a good frequency for placing orders? (g) (10 points) Suppose Bob's suppliers require him to order every week instead of the frequency given in (f). After looking at his desired service level, Bob finds that the cor- 2 responding z value is 1. Give the optimal solution. Illustrate how your solution works by filling out the table below: 1 4 5 6 7 15 12 12 4 Cycle number Demand during cycle Inventory level at end of cycle Pipeline Inventory at end of cycle before ordering Inventory position at end of cycle before ordering Inventory ordered at end of cycle 0 2 3 0 10 8 25 30 20 0 0 0 20 0