郭玉靜

Abstract： The page research on Reebok through many factors，such as uncertainties，risks，inventory and profits trade-off.Finally I get the optimal service level of Reebok.

Keywords： supply chain；service level；inventory

1）

Uncertainties

There are mainly two reasons contributing to the player demand uncertainties，the first one is player trades and free agent signings，and the second one is team and player performance during the season.If the player is traded，the demand for his old team jersey will drop immediately，while the demand for his new team jersey is created. During the season，the demand will fluctuate based on the players performance as well as the anticipation of the playoffs for their team，during the playoff.

Risks

Reebok has the option to order blank jersey and dressed jersey.If there are any leftover of dressed jerseys they have to sell them at savage cost which incurs about $ 2.5 loss，and if the dressed jerseys are not enough they can print dressed jerseys from blank jerseys which costs $1 more than buy dressed jersey directly.If the blank jerseys are left over，they can store and sell them in the next season which incurs a $1 holding cost.

Inventory

The retailers normally place approximately 20% of annual order for delivery in May and place orders for another 30% of anticipated sales between May and August when the season hasnt started yet.For these 20% early orders Reebok can just place the order to CM so there is no inventory required.For the other 30% orders the only risk is trading of players.Thus they can order dressed jerseys for those players which are capable of fulfilling the minimum order requirement and not possible to be traded.And all the other orders should be blank jerseys.During the season，since the demand is highly fluctuating， they should have minimum amount of dressed jerseys，and fulfill the “hot-market” by printing the blank jerseys to dressed jerseys.

2）

Maximize Profits

Bearing in mind that end-of-season inventory level and profits may be in conflict， the intuitive answer is for Reebok to maximize profit in spite of a probable non-zero end-of-season inventory level.In fact，we can look at the cost of stock out and the cost of overstock to investigate on the costs and benefits of keeping inventory in hope of generating more profits.

Costs/Benefits Analysis

Generally，the costs of stock out amount at most $13.1 per jersey of lost sales while costs of overstock of dressed jerseys amount to just $2.50 of salvage costs and costs of overstock of blank jerseys amount to only $1.045 per jersey in holding costs until the next season.

Risks Consideration

However，it should also be noted that since Reebok has two means of satisfying demand，the details of costs and benefits between these two options should also be studied together as they make decision based on the goal of maximizing profits.The overstock cost of a dressed jersey is about $1.50 more than that for a blank jersey.However， there is a risk of overstock blank jerseys being outdated the next season，so Reebok cannot simply count on always being able to sell overstock blank jerseys from previous seasons.

Inventory and Profits Trade-off

Since profit is essentially equal to sales revenues minus all costs，it can be maximized while keeping the end-of-season inventory level in mind and the results would be a plan that requires the minimum possible end-of-season inventory to get most profits.

Theoretically，the only possible way for Reebok to minimize end-of-season inventory and yet maximize profits at the same time is if they are able to order exactly the same number of jerseys as the demand for that season. Admittedly，this is practically impossible due to variations in demand. Nonetheless，it is possible to maximize profits while keeping inventory at the lowest possible level required to attain that profit and the trade-off can be balanced to give the most profits.

Service Level

In general，Reebok is expected to provide a high service level to its customers.For Reebok themselves，they should aim to maintain a high level of service in order to respond quickly to fluctuating and new arising demand like hot-market items.At the same time， they have to maintain a competitive edge over other competitors.Overall，considering the need to reduce risk of overstocking， jerseys getting outdated etc.，I feel that a 90% service level should be sufficient.

3）

Newsboy model is applicable for dressed jersey since they have a possibility of over-stock and they will be salvaged at the end of season.For blank jerseys，the newsboy model formulas are still applicable in this case.

Dressed Jerseys

For dressed jersey，underage cost is the loss that Reebok runs out of dressed jerseys from CM and has to print in DC.We assume Reebok has enough stock of blank jerseys to be printed into dressed jerseys.

Underage Cost cud= Cost of printing in DC –Difference in the cost between blank jersey and dressed jersey.

=$2.4-（$10.9-$9.5） = $1

Since Reeboks general practice is to sell leftover dressed jerseys at a discount but hold blank jerseys for the next season.We assume they dont hold inventory for dressed jerseys at the end of season.

Overage Cost c0d=Cost of dressed jersey-Discounted price

=$10.9-$7=$3.9

Service Level=0.204=20.4%

Blank Jerseys

For blank jerseys，the potential profit of a sold blank jersey in that season is the wholesale price subtracted by combined cost of the blank jersey and the cost of printing in DC.

Pb =$24.0-$9.50-$2.40=$12.1

The underage cost of a blank jersey is the opportunity cost of the lost revenue of that jersey.

cub=$12.1

The overage cost of a blank jersey is the holding cost the jersey until next season.We assume the blank jerseys are equally profitable in the coming season.

cob=$1.045

Service Level =92.05%

For the dressed jerseys，Reebok is capable to provide only 20.4% service level. For the minimal 90% of service level，79.6% of time that Reebok has to print from blank jerseys.The underage cost of $1 is much smaller than the overage cost of $3.9.So my suggestion is that Reebok should rely more on blank jerseys rather than ordering dressed ones directly from CM.The 92.05% of service level for blank jerseys is another strong indication for that since the blank jerseys will stock out only 7.95% of time.

4）

From Part （3），the optimal service level of dressed jerseys to maximize the profit will be 20.4%；and the optimal service level of blank jerseys to maximize the profit will be 92.1%.

The optimal order quantity for the dressed jersey of Antowain Smith is only 1067 that is lower than the minimum order level of 1728.Thus all the jerseys for Antowain Smith will be ordered as blank jerseys.

For the jerseys of all the other players，they are all ordered as blank jerseys. For 92.1% service level，the number of blank jerseys needs to be ordered for the other players is 38027.

Profits

The expected sale volume for all jerseys are the mean in the demand forecast， thus all the dressed jerseys will be sold.

The total profit from dressed jerseys=37516 × （24.0-10.9） = $491，459.6

For the total expected demand for the top 6 players =64405，thus the remaining demand will be satisfied by the blank jerseys.The expected amount of blank jersey sold for the top 6 players= 64405 – 37516 = 26889.

The total expected demand for the other players = 23275 and they are all sold as blank jerseys.Thus the total amount of blank jersey sold = 26889 + 23275 =50164.

Therefore，the total profit from blank jerseys = 50164 × （24.0-9.5-2.4） = $606，984.4.

Thus the total profit will be = $491，459.6 + $606，984.4 = $1，098，444.

Inventory

Since all the dressed jerseys are expected to be sold，thus there will be no inventory left over for dressed jerseys at the end of the season.However there will be a large amount of blank jerseys left over.The amount of left over blank jerseys = the total blank jerseys ordered – the total blank jerseys sold = 66898 + 38027 – 50164 = 54761.The total inventory holding cost until next season will be 54761 × 1.045 = $ 57225.25.This is only 5.21% of the total profit，thus it is reasonable.

Service Level

For the top 5 players （with dressed jerseys ordered），the expected service level is 90%，this is the minimal service level set by me.For Antowain Smith and the remaining players，the service level is 92.1%，which is the optimal service level for blank jerseys.