Problem
To ensure a full line of outdoor clothing and accessories, the marketing department at Crane Mountain, a full time of outdoor clothing and accessories chain, insists that they sell high-tech winter parkas. Unfortunately, Crane Mountain does not have expertise in manufacturing those kinds of parkas. They found a Canada-based supplier, Moose Knuckles, that was able to provide a quote of $275 per parka. Moose Knuckles can manufacture parkas at a cost of $150 per parka. Crane Mountain knows that it cannot sell the parkas for more than $350. Given the retail price, Crane Mountain's demand forecast is for 600 parkas (normally distributed), with a standard deviation of 300. In addition, Crane Mountain anticipates excess inventory will need to be sold off at a 75% discount at the end of the season.
I. If Crane Mountain decides to include these parkas in its assortment, what is the optimal service level it should target to maximize expected profits?
II. Crane Mountain's marketing department conducted a study of the market for high tech parkas. They decided that they can increase their revenues by increasing the retail price of parkas to have an optimal service level of 40%. Given the new price, Crane Mountain's demand forecast is for 400 parkas (normally distributed), with a standard deviation of 300. How many parkas should Crane Mountain keep in stock?
III. Suppose that Crane Mountain decides to keep an inventory level of 200 parkas. What is Moose Knuckles' profit?
IV. What is the optimal service level for this two-tier supply chain? (i.e., maximizes the expected profit of Crane Mountain's and Moose Knuckles).
V. Suppose that the retail price of parkas is $350. In order to encourage Crane Mountain to increase its order of winter parkas, Moose Knuckles proposes a buy-back contract. Under the contract, Moose Knuckles would buy back any unsold parkas at the buy-back price. A shipping cost of $25 per parka is incurred by Moose Knuckles. Supposing that the optimal service level for the two-tier supply chain is 80%, at what buy-back price would Crane Mountain's optimal service level be equal to the optimal service level for the chain?
VI. Crane Mountain has realised that while some customers like hooded parkas and appreciate the hooded version of the high-tech parka, others don't like it. Suppose the demand for the hooded and un-hooded versions of the parka are independent from each other and are both normally distributed with mean 200 and standard deviation 100. Instead of ordering the two versions separately, Crane Mountain is considering ordering a "generic parka" and add the hood on demand (free of charge) in the store. The design is such that this option would not affect how the un-hooded version looks. Suppose the company would like to keep the same service level for the individual as well as generic parkas at 98%. With this option, ignoring the inventory of hoods that are added later, what happens to the total inventory of the parkas at the beginning of the winter season?
Given a buy-back contract with buy-back price of $200, Moose Knuckles decides to order 850 parkas. At the end of the winter season, Crane Mountain was able to sell 650 parkas. With the buy-back contract, what is Moose Knuckle's profit at the end of the season? Suppose that there is no salvage value to Moose Knuckles for any unsold parkas, and a unit shipping cost of $25 is incurred by Moose Knuckles.
VII. Crane Mountain also rents out tents for outdoor enthusiasts. A major music festival weekend is expected to occur next month during which tent rentals are in high demand. Customers decide to rent a tent one month in advance. Crane Mountain has a total of 100 tents available for rental. Customers pay a non- refundable $30 to rent a tent for the weekend. Based on past data, Crane Mountain estimates that on average 15 customers who have paid for the tent would not show up to collect their tent (Normally distributed with a standard deviation of 15). If a customer with reservation shows up, but there is no tent for them, Crane Mountain offers them a new, smaller tent for free without the need to return-an option that all customer would accept happily. The smaller tent costs Crane Mountain $100. How many reservations should Crane Mountain accept?