Problem
This question is motivated by the Littlefield game, and is on (Q,r) inventory control model. Notes about data: No Littlefield game play is needed to answer this question. The data here may not correspond to the data in the dry-run or actual Littlefield game play. In fact, the data in this question is customized to each student. Let n = integer corresponding to the sum of the last four digits of your UC M# - if you are taking this in a group, you may pick either student's M# to answer this question. For instance, if the last 4 digits of your M# is 1234, n = 1+2+3+4 = 10. Suppose you will play the Littlefield Game and you forecast that the daily demand rate is stable at a mean value of 10.5 units per day with a standard deviation of 3.24 units per day, where std.dev. is approximately sqrt(mean). Each customer demand unit consists of (is made from) 60 kits of material. The cost per kit is 10$ and so the unit material cost is 600 $/unit. The effective annual interest rate for working capital (carrying WIP inventory) is 10%$/$ per year; and the company operates for 350 working days each year. The fixed order cost is 500*(1+) $/order, where n was discussed above; you may round the fixed order cost to the nearest integer. The lead time for delivery of kit replenishment orders placed with the supplier is 4 days. Item inventory replenishment is automatically controlled using a computer program that follows a (Q,r) policy
A. Calculate a good value for the order quantity Q and a good Power-of-Two reorder interval in days (clearly show the approach you used to pick your Power-of-two reorder interval). Calculate the order quantity corresponding to your Power-of-Two Interval. By what percentage does the power-of-two reorder interval increase relevant annual fixed order and inventory cycle-stock holding costs, relative to the optimal [economic] reorder interval?
Demand annually, D = 11 * 350 = 3850 units
Cost of Fixed Order, S = 1000
B. Calculate a good reorder point, r, corresponding to a target in-stock service level probability or critical ratio of min(70+n, 98)%, where n was discussed in the preface to these (Q,r) questions. For instance, if n = 10, the target in-stock service level is min(70+10, 98) = 80%; if n = 35, the target in-stock level is min(70+35, 98) = 98%. How much cost does the demand uncertainty add to your relevant annual inventory cost (due to the safety stock)?
C. If you are asked to replace the above (Q,r) system with a (R,r) system where R is an order-up-to level and r is the reorder point, what value of order-up-to level R would you recommend using and why?