PART 1 – EOQ AND NEWSVENDOR EXAMPLES | ASSIGNMENT HELP

Question 1 (10 points)

Give an example (not mentioned in class) of a real-world problem that fits the EOQ model. You can draw from your personal experience, previous job or internship, or an example you observed in the real-world. For this example, explain the variable unit cost, the fixed ordering cost, the holding cost, and the demand. If you can, provide values for these parameters. If you cannot find precise parameter values, explain how you would obtain these costs.

Question 2 (10 points)

Give an example (not mentioned in class) of a real-world that fits the Newsvendor model. You can draw from your personal experience, previous job or internship, or an example you observed in the real-world. For this example, explain the decision, the uncertainty, the underage cost, and the overage cost. If you can, provide specific values for underage and overage costs. If you cannot find specific values, explain what data and other information you need to compute underage and overage costs.

PART 2 – ORDERING GT LAPTOP CASES (20 POINTS)

Question 1 (8 points)

The demand for GT-branded laptop cases in the campus bookstore is fairly regular throughout the year, at 200 cases per year. The wholesale cost of each laptop case is $50. Assuming a fixed shipping cost of $20/order and a holding cost of $2 per case per year, determine the optimal order quantity, re-ordering interval, and the yearly average costs using the EOQ model.

Question 2 (5 points)

Assume a year consists of 52 weeks. Also, assume a fixed 4-week lead time for an order (it takes four weeks for the supplier to deliver the cases). What is your on-hand inventory level when you place the order? This value is called the reorder point.

Question 3 (7 points)

Your supplier offers you a 2% per-unit discount for all cases if you order 100 cases or more. Would your optimal order quantity change in such a case? If so, what is the new recommended order quantity and reorder interval?

PART 3 – SENSITIVITY OF THE EOQ MODEL (20 POINTS)

After graduating from Georgia Tech, you accept a job offer to work at BuzzBread, an Atlantan bakery chain created by your uncle George P. Burdell. Your uncle, who is an expert in “leading” organizations but not so much in handling day-to-day business operations, makes you responsible for managing the inventory of various bread and pastry ingredients.

Your first task is to set-up the reorder policy for the flour supply of BuzzBead’s Atlanta locations. You estimate the cost of flour to be about $1 per kg and the demand to be stable at 50,000kg per year. After analyzing data, talking to the managers of several BuzzBread bakeries, and accounting for your uncle’s “business intuition,” you estimate that:

• The fixed ordering cost, K, of flour is between $50 and $70 per order.
• The holding cost, h, of flour is between $0.02 per kg per year and $0.05 per kg per year.

Question 1 (10 points)

You decide to set-up a flour reordering policy according to the EOQ model. Given the fixed and holding costs parameter ranges, what is the range of possible optimal ordering quantities?

Question 2 (10 points)

You now examine how much money could be “left on the table” by misestimating the cost parameters. Specifically, let OPT_COST(K, h) be the minimum average holding and fixed ordering costs (i.e., the EOQ cost excluding the variable cost of $50,000 per year of flour) for parameters (K, h). Also, let COST(Q, K, h) be the average holding and fixed ordering costs for order quantity Q and parameters (K, h).

a) For ordering quantities in the range in Question 1, and for the parameters (K, h) in the range from the problem statement, what is the maximum value of the ratio COST(Q, K, h)/OPT_COST(K, h)? Note that, for a given Q, the parameters (K, h) should be the same in the numerator and the denominator of the ratio for a proper comparison. Hint: you only need to consider combinations of the extreme values for h, K, and Q.

b) How does this maximum ratio compare to the range of ordering quantities in Question 1?

PART 4 – BACK TO THE BAGEL STORE (20 POINTS + 10 BONUS POINTS)(DO NOT PLAY GAME I HAVE ATTACHED FILES TO THIS)

In this part of the assignment, we revisit the bagel store from Assignment 5. There is a new game. Feel free to enter the game and check out the instructions.

In this new game, the daily demand for bagels follows a Uniform distribution with a range [0, 475]. The wholesale price for a bagel is $2.00, and the retail price is $3.00. Any leftover inventory at the end of the day is donated for free. The dynamics are the same as in Assignment 5.

Question 1 (6 points)

Calculate:

1. The underage and overage costs.
2. The service level (also called the critical ratio) and optimal ordering quantity.
3. The expected sales, lost sales, expected leftover inventory, and expected profit.

Question 2 (10 bonus)

Are the total profits you obtain consistent with what you calculated in Question 1?

Question 3 (6 points)

A local organization offers to purchase any leftover bagels you have for $1.00 per bagel (they then resell them to factories that have a night shift).

1. How do your underage and overage costs change? What is your new ordering quantity?
2. How many bagels do you expect to sell to the local organization at the end of the day?
3. What is your expected profit in this case?

Question 4 (8 points)

You are considering purchasing a small oven for your store. The oven allows you to “bake fresh bagels to order.” However, in-store baking is more expensive than sourcing from suppliers, and you estimate that each in-store baked bagel costs $2.50 to make and bake (in-store baked bagels are still sold for $3.00). The oven allows you to capture all demand: if demand exceeds what you ordered from your supplier at the start of the day, you can just “bake-to-order.” Conversely, if there are any leftover bagels, you can still sell them to the local organization for $1.00 per bagel.

1. If you purchase the oven, how many bagels would you order from your supplier at the start of the day?
2. If you purchase the oven, how many bagels do you expect to bake in-store each day? How many leftover bagels do you expect to sell to the local organization at the end of each day?
3. How much are you willing to pay for the oven?

PART 5 – BECOMING CARBON NEUTRAL (20 POINTS)

Georgina Burdell has recently become the CEO of a company that manufactures highly specialized heavy equipment. One of her first projects as a CEO is ordering a report of the company’s environmental performance. She is surprised to find the company is very far from being green. Furthermore, customers and shareholders are pressuring Georgina to reduce the company’s carbon footprint. Drastic times call for drastic measures, so Georgina decides to make the company CO2 neutral.

To enact her plan, she commissions a team of scientists to understand the necessary steps to becoming CO2 neutral. It turns out that the production of one piece of equipment can be offset by planting ten trees. Furthermore, your CO2 emissions depend on how much heavy equipment you produce, which, in turn, depends on the demand for that equipment. Since future demand is uncertain, your future CO2 emissions are also uncertain.

Georgina then asks you, an undergraduate intern,-to find the most economical way to proceed. She is considering a mix of two options:

A) The company can buy deforested land in Brazil at $100 per square meter. Planting a tree requires two square meters and costs $50 per tree. While planting trees is fast, buying land in Brazil as a foreign company is complex. As a result, to claim CO2 offsets next year, you need to decide how much land to buy this year. Thus, the land purchasing decision is made before you observe your CO2

B) The company can buy fallow land in the USA at any time for $500 per square meter and start planting trees immediately. Because of the different ecology, trees require only one square meter Moreover, planting a tree in this land comes at the cost of $150.

Question 1 (5 points)

What are some of the pros and cons of each option?

Question 2 (5 points)

Formulate the problem of how much land to buy in Brazil as a Newsvendor Problem. What is the “order quantity” in this case? What are the underage and overage costs?

Question 3 (10 points)

You next consider how many trees you will need to plant. Luckily, another intern is well trained in forecasting. Based on the historical sales and current industry trends, they estimate that the number of heavy equipment pieces you will produce next year follows a Normal Distribution with a mean of 40 pieces and a standard deviation of 8 pieces.

1. How much land do you optimally buy (on average) in Brazil and the USA, and how many trees do you optimally plant (on average) in both countries?
2. What are the minimum expected costs for becoming neutral?