Question number 6 and onwards

Economic order quantity: The ideal amount of inventory that will be ordered with each replenishment cycle to minimize inventory related costs e.g., holding costs, shortage costs, order costs etc. Reorder point: The inventory level at which a replenishment order will be triggered Lead time: Time lapse between the release and the receipt of an order Cycle stock: Amount of inventory that is planned to be used during a given time Safety stock: Difference between the reorder point and the mean demand during lead time Fill rate: Fraction of demand that will be filled from the stock; it is also referred to as service level Maximum stock level: the maximum inventory level that cannot be exceeded. The periodic review and continuous review models provide mathematical formulation to estimate this level Freshly Baked an upscale specialty cupcake bakery is headquartered in Islamabad. Freshly Baked grew from one retail outlet in 2015 to fourteen retail stores in 2020. Most stores are owned by company itself while a few are operated by franchisees. Demand for cupcakes exhibits patters based on seasons, store location, day of the week, and time of day. The freshness promise implicit in Freshly Baked had to be supported by the daily baking and topping of thousands of cupcakes at Islamabad bakery as well as early-morning delivery of cupcakes to each store. Your task is to compute a variety of inventory management parameter values for Freshly Baked, with the assistance of a list of hints provided at the end of exercise. Retail store level cupcake inventory planning Freshly Baked cupcakes sold at retail stores for prices ranging from about Rs. 50 each for simpler cupcakes by the dozen up to about Rs. 80 for the fanciest cupcakes sold individually. Most of the cupcakes were sold in 2-packs priced at Rs. 200. An approximate overall average selling price was Rs. 75 per cupcake. Franchisees were charged Rs. 30 per cupcake. Company-owned stores were also charged the same transfer price of Rs. 30 per cupcake. Total variable costs per cupcake out of the Islamabad bakery were about Rs. 20, representing Rs. 10 in direct material and Rs. 10 in variable labor. Cupcakes not sold by the end of the day were discarded. Freshly Baked credited stores Rs. 25 for each unsold/discarded cupcake. Research indicated that customers were generally willing to purchase cupcakes from those available, even if they had to substitute a second choice for a most-preferred flavor. For the purpose of this exercise, understocking costs are confined to the immediate lost sales profit. In practice, Freshly Baked did not permit franchisees to make their own cupcake-ordering decisions. Instead, cupcakes were baked and delivered to all stores based on centralized decision. Raw material inventory planning Freshly Baked uses a particular brand of packaged cake mix in two flavors (vanilla and chocolate) as the basic material on which all the Freshly Baked flavor recipes were variations. Even though the business had grown dramatically, this recipe structure remained. The cake mixes were bought in pallet-load quantities for Freshly Baked. Due to the strong weekly sales pattern, inventory planning for cake mix was done on weekly basis. Cake mix orders were placed with grocery store chain distribution warehouse. Cake mixes were delivered 5 days after the order placement. Occasionally, the grocery warehouse had insufficient inventory to fill Freshly Baked orders, resulting in insufficient raw material to support Freshly Baked baking operations. When this happened, Freshly Baked employees would drive to grocery stores in Islamabad vicinity and buy boxes of cake mix off the store shelves until they had enough to support the baking operations. This typically required visits to about 25 retail stores and took whole day. Coping this situation required an average of 15 hours of employee overtime and cost Rs. 300 per hour inclusive of mileage expenses. Prices paid in the stores were also higher, amounting to an extra cost per pallet of Rs. 350. Although Freshly Baked had grown via reinvestment of retained earning, 13% is a reasonable approximation for the relevant annual cost of capital i which should be considered to apply to inventory holding of cake mix. Assume 358 days per year. Physical holding costs are negligible at the margin, since the Islamabad facility has sufficient warehouse space to accommodate all reasonable inventory required. Obsolescence and shelf-life considerations also do not apply to the cake mixes, which are typically coded for sale up to eighteen months after packing. The value of a pallet of cake mix C, at Freshly Baked including delivery charges is Rs. 30,000. Real butter and fresh eggs are also important ingredients in Freshly baked cupcakes. There are managed according to a continuous review system and ordered whenever inventory levels reach a reorder point. Annual demand D for eggs is 600,000. The cost of placing an egg order S including delivery charges is Rs. 250. Lead time for eggs is two days. Holding costs H for eggs are dominated by their limited shelf life and the requirement that they be held in cold storage and handled with care. Freshly Baked has capacity to keep an inventory of 5000 eggs at any one time, however average inventory of eggs is around 4500. These costs total Rs. 1.5 per egg per day. Financial holding costs are negligible. Daily demand for eggs averages about 1600, but there are significant variations from day to day. The standard deviation of daily egg demand is 350. Daily demand for eggs is approximately normally distributed. Freshly Baked also has to keep an inventory of packing material which it manages centrally for both company owned stores and franchisees. Monthly demand for packing boxes averages 35,000 and the cost of placing order including transportation cost per consignment is Rs. 5000. The store manager has estimated that the annual holding cost of packing material including damages incurred during storing is Rs. 5 per box per day. Warehouse capacity permits Freshly Baked to have an average inventory of 60,000 boxes. Computing inventory management related parameter values Please calculate the following values. You may use hints at the end of this exercise 1. Compute the cost of understocking Cu for franchisees and for company owned stores. 2. Compute the overstocking cost Co for franchisees and for company owned stores 3. Compute the best service level SL for cupcake stocking at franchisees stores 4. Compute the best service level SL for cupcake stocking at company owned stores 5. Based on your answers to 3 & 4 does a centralized decision making for store-level inventory lead to higher profitability for the entire Freshly Baked supply chain than the alternative model of allowing franchisees to do their own ordering? 6. Compute the inventory review period for cake mix in days. 7. Compute the lead time for cake mix in days. 8. Compute the exposure period for cake mix inventory planning 9. Compute the cost of a stockout of cake mix 10. Compute the annual holding cost of a pallet of cake mix 11. Compute the cost of overstocking through 1 review period (weekly holding cost per pallet of cake mix) 12. Compute the best service level SL for pallets of cake mix 13. Compute the total holding cost of eggs. 14. Compute the economic order quantity EOQ for eggs 15. Compute the safety stock of eggs it would take to assure a 99.87% service level. 16. Compute the reorder point ROP for eggs, using the safety stock that you calculated in 14. 17. We could express the reorder point rule from 15 this way: order more eggs when the supply is X days. Give an expression for X. 18. Compute the average daily quantity of eggs on hand, using your answers to 13 & 14. 19. What is the economic order quantity of packing material 20. What shall be the order frequency of packing material on per year basis. 21. Compute the cycle stock for eggs and packaging material Hints Cost of understocking: for franchisee, running out of cupcakes before the end of the day imposes an immediate opportunity cost of lost sales equal to the difference between their cost and selling price of cupcakes. For company owned stores, the understocking cost is equal to the difference between their variable cost and selling price. Cost of overstocking: for franchisees, cupcakes leftover at the end of the day cost them the difference between the price they pay and the credit form Freshly Baked corporation. For company owned stores, cupcakes leftover cost them only the variable cost of Freshly Baked. Franchisee best service level: SL = Cu / (Cu + Co) Company owned store best service level: SL = Cu / (Cu + Co) Central decision making: Compare answers for 3 & 4