Assignment 4

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School

Conestoga College *

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8310

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Business

Date

Feb 20, 2024

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docx

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Uploaded by DukeToadMaster645

Student Name: HUNNY VATS 8817275 Deliverable: QAMM_QUAL8310_Assignment 4 Course Name: Qual8310 Manufacturing Operations Management Date Assigned: 29-03-2023 Date Due: 12-04-2023 Rules: 1) This assignment will be completed individually 2) You will use Word, PowerPoint, and other tools you feel appropriate for this exercise 3) Your work must be your own 4) Each deliverable should be clear and simple to read Question 1, (2.5 marks): Conestoga Cutting Co. orders blades required for its new line of scissors. When they place an order, they traditionally order 60 blades at a time. Conestoga Cutting Co. estimates their carrying cost at 40% of the $10 cost per blade, and the annual demand is about 240 blades per year. With the assumptions of the basic EOQ model, determine the following: a) For what value of order cost, would Conestoga’s action be considered “optimal”? b) If the true ordering cost turns out to be much higher than your answer in part a) above, what action should be taken on Conestoga’s ordering policy?

The Economic Order Quantity (EOQ) model can be used to determine the optimal order quantity for Conestoga Cutting Co. Given the following information: Annual demand (D) = 240 blades per year Cost per unit (C) = $10 Carrying cost (CC) = 40% of $10 = $4 per blade per year Order cost (OC) = unknown The EOQ formula is given as: EOQ = sqrt((2 x D x OC) / CC) a) To find the optimal order quantity, we need to determine the order cost that minimizes the total inventory cost. The total inventory cost (TC) is the sum of ordering cost (OC) and carrying cost (CC). Mathematically, it can be represented as: TC = (D x OC) / Q + (Q/2) x CC where Q is the order quantity. Taking the derivative of TC with respect to Q and setting it to zero, we get: d(TC)/dQ = - (D x OC) / Q^2 + CC/2 = 0 Solving for Q, we get: Q = sqrt((2 x D x OC) / CC) Substituting this expression for Q in the equation for TC, we get: TC = 2 x CC x sqrt(D x OC / (2 x CC)) We can now substitute the given values and solve for OC: TC = 2 x $4 x sqrt(240 x OC / (2 x $4)) = $16 x sqrt(60 x OC) Differentiating TC with respect to OC and setting it to zero, we get: d(TC)/d(OC) = $16 x sqrt(60/OC) / 2 = $8 x sqrt(60/OC) = 0 Solving for OC, we get: OC = $60 Therefore, the optimal order cost for Conestoga Cutting Co. is $60.

b) Conestoga Cutting Co. could think about acquiring blades less frequently and in bigger quantities to lower the overall ordering cost if the true ordering cost turns out to be significantly higher than $60. Alternately, customers could look into alternative suppliers who provide better ordering terms or try to bargain with their supplier for a reduced ordering cost. It is significant to remember that the EOQ model is predicated on a number of assumptions and could not always precisely reflect the situation in the actual world. Companies should therefore take into account other aspects when making their ordering decisions, such as lead time, storage space, and demand unpredictability. Question 2, (4 Marks): Matt’s Manufacturing & Customs stocks a special switch connector in his central warehouse for the sake of supplying the field service crew when they need them for customer breakdowns. The yearly demand for these connectors is 15000. Matt estimates his holding cost for this item to be $25 per unit. The cost to place and process an order for more of these connectors is $75. Matt’s company operates 300 days per year, and the lead time promised (and observed) from the supplier of the switch connector is 2 days. a) Determine the economic order quantity. b) Determine the annual holding cost. c) Determine the annual ordering cost. d) What would be the most reasonable reorder point? a) To determine the Economic Order Quantity (EOQ), we can use the following formula: EOQ = sqrt((2 x D x O) / H) Where: D = Annual demand = 15,000 O = Cost to place and process an order = $75 H = Holding cost per unit per year = $25 Plugging in the values, we get: EOQ = sqrt((2 x 15,000 x 75) / 25) = 900 Therefore, the Economic Order Quantity is 900. b) To determine the annual holding cost, we can use the following formula: Annual holding cost = EOQ / 2 x H Plugging in the values, we get:

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Annual holding cost = 900 / 2 x 25 = $11,250 Therefore, the annual holding cost is $11,250. c) To determine the annual ordering cost, we can use the following formula: Annual ordering cost = D / EOQ x O Plugging in the values, we get: Annual ordering cost = 15,000 / 900 x 75 = $1,250 Therefore, the annual ordering cost is $1,250. d) The most reasonable reorder point can be determined using the following formula: Reorder point = (D x L) / N + Safety stock Where: L = Lead time = 2 days N = Number of working days per year = 300 Safety stock = We can assume a safety stock of 0 since no variability or uncertainty is given in the problem statement. Plugging in the values, we get: Reorder point = (15,000 x 2) / 300 = 100 Therefore, the most reasonable reorder point is 100 units. When the inventory level reaches 100 units, Matt's Manufacturing & Customs should place an order for 900 units (the EOQ calculated in part a) to ensure that they do not run out of stock before the next order arrives. Question 3, (4 Marks): a) An electronics firm manufactures and sells their PCBAs to tier 3 auto suppliers. One of the diodes required for their most popular PCBA has an annual demand of 5000. Currently, this firm is paying $6.40 per diode with no minimum order quantity restrictions, their carrying (holding) cost is 25% of the unit cost, and their ordering costs total $25 per order. A new supplier is offering this firm to buy the diodes from them at a cost of $6.00 per unit, as long as they buy 3000 per order . Should the firm take advantage of the new supplier’s offer (discount)? Or stick with the old (current) supplier?

To determine whether the electronics firm should switch to the new supplier, we need to calculate the total cost of purchasing the diodes from both suppliers and compare them. Let's first calculate the total cost of purchasing the diodes from the current supplier: Annual demand = 5000 Cost per diode = $6.40 Ordering cost per order = $25 Holding cost as a percentage of unit cost = 25% Using the EOQ formula, we can calculate the optimal order quantity: EOQ = sqrt((2 x D x O) / H) = sqrt((2 x 5000 x 25) / 0.25 x 6.40) = 79 So the firm should order 79 diodes at a time. The total annual cost of purchasing the diodes from the current supplier can be calculated as follows: Total ordering cost = (5000 / 79) x $25 = $1582.28 Total holding cost = (79 / 2) x 0.25 x $6.40 = $25.30 Total cost of purchasing the diodes = (5000 x $6.40) + $1582.28 + $25.30 = $33,217.28 Now let's calculate the total cost of purchasing the diodes from the new supplier: Cost per diode = $6.00 Minimum order quantity = 3000 Annual demand = 5000 To determine how many orders will be needed, we can divide the annual demand by the order quantity: Number of orders = 5000 / 3000 = 1.67 (rounded up to 2) The total annual cost of purchasing the diodes from the new supplier can be calculated as follows: Total ordering cost = 2 x $25 = $50 Total holding cost = (3000 / 2) x 0.25 x $6.00 = $22.50 Total cost of purchasing the diodes = (5000 x $6.00) + $50 + $22.50 = $30,072.50 As a result, buying the diodes from the new source will cost less overall than buying them from the current supplier. To benefit from the discount and save money, the company needs move to the new supplier. Question 4, (3 Marks): Considering the electronics firm in question 3 (above), analysis shows that the demand for their jump-drive PCBAs during supplier lead time averages 50 units (normally distributed),

with a measured standard deviation of 5 jump-drive PCBAs. Management wants to sustain a 97 % service level to their customers. a) What value of Z would you apply? (See attached table for Z-scores according to the standard/published normal curve areas). b) How many jump-drive PCBAs should be carried as safety stock? c) What is the appropriate reorder point? a) From the standard normal distribution table, the Z-score that corresponds to the 97th percentile is 1.88. b) The standard deviation of demand during the lead time can be calculated as follows: Standard deviation of demand during lead time = Standard deviation of daily demand x Square root of lead time = 5 x Square root of 1 (since lead time is given in the same unit as daily demand) = 5 The safety stock can be calculated as follows: Safety stock = Z-score x Standard deviation of demand during lead time = 1.88 x 5 = 9.4 Therefore, the electronics firm should carry a safety stock of 9 or 10 jump-drive PCBAs. c) Reorder point = (Average daily demand x Lead time) + Safety stock = (50 x 1) + 9.4 = 59.4 Therefore, the appropriate reorder point is 60 jump-drive PCBAs to ensure a 97% service level. Question 5, (2 Marks):

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Ottawa’s Fairmont hotel distributes, on average, 1000 bath towels per day to their guests at the pool and within their hotel rooms. This demand is normally distributed with a standard deviation of 100 towels per day, depending on occupancy. The laundry service firm (3 rd party contract), promises a 2 day lead time to wash and return/restock the towels when needed. The hotel aims for a 98% service level to its customers to ensure satisfied customers. a) Determine the ROP for this hotel? b) What should be the safety stock quantity in order to sustain the service level? a) ROP = Average daily demand x Lead time + Safety stock Where, Average daily demand = 1000 bath towels Lead time = 2 days (promised by the laundry service firm) Safety stock = Z-score x Standard deviation of demand during lead time From the standard normal distribution table, the Z-score that corresponds to the 98th percentile is 2.05. To calculate the standard deviation of demand during the lead time, we use the formula: Standard deviation of demand during lead time = Standard deviation of daily demand x Square root of lead time = 100 x Square root of 2 = 141.42 Therefore, the safety stock can be calculated as: Safety stock = Z-score x Standard deviation of demand during lead time = 2.05 x 141.42 = 289.71 (approx.) Thus, the ROP can be calculated as: ROP = 1000 x 2 + 290 = 2290

Therefore, the hotel should place an order for additional bath towels when the inventory level reaches 2290 towels. b) Safety stock = Z-score x Standard deviation of demand during lead time = 2.05 x 141.42 = 289.71 (approx.) Therefore, the hotel should maintain a safety stock of approximately 290 bath towels to sustain the 98% service level.

Assignment 4

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