PART A: You are expected to type (or scan your hand-written solutions into one pdf document) for Questions 1,2 and 3:

1. XYZ Inc. stocks a certain switch connector at its central warehouse for supplying field service offices. The yearly demand for these connectors is 32,000 units. XYZ estimates its annual holding cost for this item to be $20 per unit. The cost to place and process an order from the supplier is $50. The company operates 320 days per year and the lead time to receive an order from the supplier is 2 working days. The company's current inventory policy states that they should place 64 orders throughout the year and each order must be for 500 units. The new supply chain manager who just joined XYZ questions the optimality of this policy and wonders how much XYZ would save if they had implemented EOQ.

a) What is the total cost of current inventory policy (ordering 500 units)? (10 points)

b) What is the economic order quantity (EOQ) for this product? (5 points)

c) What is the total cost of following EOQ policy? How much XYZ would save by switching toEOQ? (10 points)

d) What should be the reorder point? (5 points)

2. A manufacturer makes an electronic component used in many electronic appliances. It has orders for about 100,000 units of its product for the entire year and has the capability of producing 500 units per day. The manufacturer operates its facility 250 days per year. Setting up the production costs $50. The per unit cost of producing the component is $1. The holding cost is estimated to be $2 per unit per year.

a) What is the optimal production order quantity for this product? (10 points)

b) What is the total annual cost (including the production cost) the manufacturer incurs using this optimal production orderquantity? (10 points)

3. Consider a retail store that sells t-shirts during the summer season. The manager of the store needsto make a stocking decision for the upcoming summer season. She believes that the demand is normally distributed with mean 4000 and standard deviation of 300 t-shirts. The retailer buys the t-shirt from the manufacturer at $12 a t-shirt and can sell it at $25. At the end of the season, the retailer can return any unsold t-shirt to the manufacturer at $5.

a) What is the optimal service level for this retailer? (5 points)

b) What would be the manager's optimal stocking decision? (10 points)

c) How does your answer change if the retailer is not paid anything for any unsold t-shirts at the end of the season? Observe how your answer changed (increase vs. decrease) and provide an explanation. (5 points)

PART B: You are expected to develop an Excel spreadsheet model for Question 4 and upload it together with your solutions for Part A on Blackboard following the Assignment 1 link.

4. The owner of a newsstand believes that the demand is normally distributed for the newspaper with a mean of 80 and standard deviation of 18. The paper costs 70 cents, which sells for $2.5. For each unsold paper, the owner receives 30 cents credit.

Create a simulation model using Excel and run it for 100 days.

a) What is the average profit of the newsstand if the owner decides to buy 80 papers every day? (10 points)

b) What is the average profit of the newsstand if the owner decides to buy 88 papers every day? (10 points)

c) Comparing your results in (a) and (b), what do you observe? Using the optimal fill rate formula used earlier in class, find the optimal number of papers the owner needs to buy. Is it consistent with the observation you made in the simulation outcome? (10 points)

[HINT: To create the above model, you should first generate samples for a normally distributed random variable with mean 80 and standard deviation 18, which will correspond to demand realizations for each day. The excel function "=NORMINV(RAND(),80, 18)" generates normally distributed random numbers with mean 80 and standard deviation 18. Then, you need to copy the formula for 100 rows to create 100 demand samples. Below is an example of how the first row of the spreadsheet model will look like. As discussed in Lecture 3 (slide 16), based on how many papers are purchased, the realized demand and cost/price values given above, you need to write the profit function in another cell and (copy this function as well for 100 rows). Finally take an average of profits (using "=AVERAGE()") which will represent the "expected value" in the original profit formula. Now you need to do the same profit calculation for a different amount for part b. You can do that by entering the same profit function in another column.

A B (for part C (for part (b))

= NORMINV(RAND(),80, 18) =Profit Function =Profit Function.

(as discussed in

(Will generate normally Lecture 3 slide 16).

distributed random number).