Question

PART A: Suppose that a liquor distributor has an average known weekly demand of 10000 units of 1 Liter Makers Mark Bourbon. Each bottle of Makers Mark costs the distributor $25 per bottle. Specifically for the space for this product, it costs the distributor $0.50 per bottle per week to hold in inventory. When the distributor purchases from the manufacturer, they are incurred a $2000 fixed ordering cost. Use this information to answer the following questions

a: What is the optimal order quantity that the distributor should order when they order?

b: How often should the distributor place an order for this quantity?

c: If the distributor follows this ordering policy, what is the total weekly cost of the distributor? Suppose that the distributor makes a mistake, and order 1% more than the optimal policy. What is the percentage difference in cost as a result of ordering 1% more than required?

PART B: Now suppose that the distributor is able to sell each bottle for $35 per bottle. The cost per bottle is the same, namely $25 per bottle. Assume now, however, that demand is random, and that it follows a normal distribution. Use this information to answer the questions below.

a: Assume the average weekly demand is µ = 10000. Find the optimal solution for σ = 500, σ = 1000, σ = 5000, σ = 10000.

b: Let y be the set of optimal solutions, let x be the sigmas from the previous problem. Run a linear regression to find an equation for Q = a + bσ. What are the respective values for a and b?

c: What does this tell us about the optimal ordering policy with respect to the variation in our demand data?

PLEASE SHOW ALL WORK.

Answer 1

ANS

Part A:

Given	Weekly Demand	d	10,000	bottles per week
	Cost per order	S	$2000	Per order
	Cost per bottle	C	$25	Per bottle
	Holding cost per unit per week ($)	H	$0.50	Per bottle per week
Part a.	EOQ	Q*	= √(2 x d x S/H) Q* = √(2 x 10,000 x 2000/0.50)Q* = 8944.27 Or Q* = 8945	bottles per order
ANS a.	Optimal Order Quantity = 8945 units per order
Part b.	Frequency of ordering	n	n = demand/order size n = 10000/8945 n = 1.12 orders per week
Ans b.	Frequency of order = 1.12 orders per week
Part c.
Weekly inventory Cost calculation for optimal order Quantity, Q* = 8945
	Total weekly inventory Cost = Weekly ordering cost + weekly holding cost	TC = AHC + AOC TC = [Q/2 x H] + [d/Q x S]	TC1 = [8945/2 x 0.50] + [10000/8945 x 2000] TC = $2235.89 + $2236.25 TC1 = $4,472.14	Per week
Weekly inventory Cost calculation for order Quantity, Q* = 8945 + (0.01*8945) = 9034.45
	Total weekly inventory Cost = Weekly ordering cost + weekly holding cost	TC = AHC + AOC TC = [Q/2 x H] + [d/Q x S]	TC2 = [9034.45/2 x 0.50] + [10000/9034.45 x 2000] TC = $2236.07 + $2258.61 TC2 = $4,494.38	Per week
Percentage difference in cost as a result of ordering 1% more than required optimal quantity
	Percentage Difference	% change = (TC2 – TC1) / TC2	% change = (4494.38 – 4472.14) / 4472.14 x 100 % change = 0.5%	Per week
ANS c.	percentage difference in cost as a result of ordering 1% more than required optimal quantity = 0.5% per week