(25points)EOQ / (Q,r) policy: This question is motivated by the Littlefield game, but is on (Q,r) inventory control. Notes about data:The data here may or 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 yourUC 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 growing from day 1till day 120 and then stabilizes (stays flat after simulated day 120) at a mean value of 9units per day with a standard deviation of 3 units per day, where std.dev. is approximated by sqrt(mean). In answering these Littlefield related questions, pretend that you are planning for the interval of time after day 120. Each customer demand unit consists of (is made from) 60 kits of material. The cost per kit is 10$ and so the unit cost is 600 $/unit. The effective annual interest rate for working capital (carrying WIP inventory) is 10%$/$, year; and the company operates for 350 working days each year. The fixed order cost is 500*(1+??18)$/order, where n was discussed above; where 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) policya)

a.) (9points)Calculate a good value for the order quantity Qand 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?

b)(*9points)Calculate a good reorder point, r, corresponding to a target in-stock service level probability or critical ratio of min(70+n, 98)%, where nwas 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)? How would you decide if these costs areworth adding or not?

c.) (*7points)This question is not related to a and b above. Answer any one of questions, below either EOQ or Reorder Point; treat each question as ceteris paribus (all other things being equal / unchanged).EOQ/ Cycle Stock:Suppose you take one large warehouse serving demand in all of the United States for a single product (with an annual demand of 20,000 units) and you replaced it with four similar-sized warehouses (each with an annual demand of 5,000 units). Each warehouse independently follows its EOQ for reordering the product from the supplier. Assuming the cost parameters A and h remain the same, quantify the effect of splitting the large warehouse into four smaller warehouses on the system’s total cycle stock. Pick your answer from the following (circle all that apply)and explain your choice: 1. It doubles2. It increases by less than double 3. It increases by more than double4. It is halved. 5. It decreases6. It does not change7. Cannot say what will happenWhat is a summary takeaway lesson from this question and its answer?OR

Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of $350 on each Aqua-Spa he sells and $300 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs he produces. The production of each Aqua-Spa generates 15 pounds of a toxic resin, whereas each Hydro-Lux produces 10 pounds of toxic resin. Howie has identified two different objectives that could apply to his problem: He can maximize profit or he can minimize the production of toxic resin. Suppose Howie considers the maximization of profit as half as important as the minimization of toxic resin.

1. Formulate an MOLP model for Howie’s decision problem.

2. Implement your model in a spreadsheet and solve it.

3. What is the solution to Howie’s MOLP problem?