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Economic order quantity (EOQ) is the order quantity at which

The components of inventory holding cost are. 

(Service Level Questions) Ava runs an outdoor gear rental company specializing in luxury camping tents. Each tent costs $200, and restocking takes one year. She applies a 10% annual holding cost rate and estimates a $50 goodwill loss for each stockout. Ordering costs $120. Ava expects to rent 500 tents per year, with a demand standard deviation of 150 tents. Demand is normally distributed. NOTE: The question statement above is the same for all 7 questions in this exam. Question: What is the optimal order quantity (Q) if Ava wants to have 85% of Type 2 Service?

(Greedy Heuristic and Optimization Questions) A company operates four plants that supply goods to five warehouses. The goal is to minimize the total transportation cost while meeting the demand at the warehouses and not exceeding the supply capacities of the plants. Plant Capacity (in units) 1 60 2 110 3 90   Warehouse Demand (in units) 1 80 2 50 3 60 4 70   Plant / Warehouse (Shipping cost, $) 1 2 3 4 1 10 13 12 11 2 15 14 17 18 3 19 16 20 21 NOTE: The question statement above is the same for all 3 questions in this exam. Question: The demand satisfaction constraint for Warehouse 2 can be written as the following:  x12 + x22 + x32 + x42 = 50

(Service Level Questions) Ava runs an outdoor gear rental company specializing in luxury camping tents. Each tent costs $200, and restocking takes one year. She applies a 10% annual holding cost rate and estimates a $50 goodwill loss for each stockout. Ordering costs $120. Ava expects to rent 500 tents per year, with a demand standard deviation of 150 tents. Demand is normally distributed. NOTE: The question statement above is the same for all 7 questions in this exam. Question: What is the optimal reorder point (R) if Ava wants to have 85% of Type 2 Service?

(Greedy Heuristic and Optimization Questions) A company operates four plants that supply goods to five warehouses. The goal is to minimize the total transportation cost while meeting the demand at the warehouses and not exceeding the supply capacities of the plants. Plant Capacity (in units) 1 60 2 110 3 90   Warehouse Demand (in units) 1 80 2 50 3 60 4 70   Plant / Warehouse (Shipping cost, $) 1 2 3 4 1 10 13 12 11 2 15 14 17 18 3 19 16 20 21 NOTE: The question statement above is the same for all 3 questions in this exam. Question: The Capacity constraint for Plant 1 can be written as the following:  x11 + x12 + x13 + x14 = 80

 (Iterative (Q, R) System Problem) Fatih owns a boutique coffee shop called Bean & Brew, specializing in handcrafted artisan coffee blends sourced from a small cooperative in Costa Rica. Each 1-pound bag of coffee beans costs Fatih $10 to purchase. Because of the limited seasonal harvest and processing time, it takes a full year to receive new shipments. Fatih applies an annual holding cost rate of 15% to account for storage and spoilage risks. If a customer request cannot be fulfilled due to stockouts, Fatih estimates a goodwill loss of $20 per missed sale. Every time he places an order, he incurs a $25 import and processing fee. Based on past sales records, Fatih expects to sell approximately 300 bags per year, with a standard deviation of 50 bags. Assume that the demand for the coffee beans follows a normal distribution. NOTE: The question statement above is the same for all 4 questions in this exam. Question: Assuming a normal demand distribution, determine the optimal (Q,R) policy. Continue iterating until the gap between successive iterations of the Q value is less than 5%. (i.e., 

(Service Level Questions) Ava runs an outdoor gear rental company specializing in luxury camping tents. Each tent costs $200, and restocking takes one year. She applies a 10% annual holding cost rate and estimates a $50 goodwill loss for each stockout. Ordering costs $120. Ava expects to rent 500 tents per year, with a demand standard deviation of 150 tents. Demand is normally distributed. NOTE: The question statement above is the same for all 7 questions in this exam. Question: What is the optimal order quantity (Q) if Ava wants to prevent stockouts in 85% of order cycles (Type 1 Service)?

 (Iterative (Q, R) System Problem) Fatih owns a boutique coffee shop called Bean & Brew, specializing in handcrafted artisan coffee blends sourced from a small cooperative in Costa Rica. Each 1-pound bag of coffee beans costs Fatih $10 to purchase. Because of the limited seasonal harvest and processing time, it takes a full year to receive new shipments. Fatih applies an annual holding cost rate of 15% to account for storage and spoilage risks. If a customer request cannot be fulfilled due to stockouts, Fatih estimates a goodwill loss of $20 per missed sale. Every time he places an order, he incurs a $25 import and processing fee. Based on past sales records, Fatih expects to sell approximately 300 bags per year, with a standard deviation of 50 bags. Assume that the demand for the coffee beans follows a normal distribution. NOTE: The question statement above is the same for all 4 questions in this exam. Question: Assume that the optimal order size is 100, and optimal reorder point is 450. Calculate the safety stock.