Inventory Simulation Case Study

SCM $475$

Sports$-$related stores often stock championship$-$related apparel in advance of a significant championship game. These items are then available $($on$-$hand$)$ for sale minutes after the game is over. There is obvious risk in this strategy. For example, some stores in the Seattle area were stocked and ready to immediately sell Seahawks Super Bowl championship apparel in the event that the Seahawks defeated the New England Patriots. What happened to this apparel when the Patriots won the Super Bowl? Often the apparel is donated to charities.

It is interesting to think that there are many children in an impoverished nation somewhere that will live their lives thinking that the Seahawks were Super Bowl champions because they have a t$-$shirt that says so$.$

In this case, consider a small sporting goods store in a suburb of Houston, Texas. Assume that the Houston Texans have won their way into the next Super Bowl and will play the Seattle Seahawks. The store can order Super Bowl championship t$-$shirts for $\backslash (\backslash$$ $10\backslash )$ per shirt and must order in multiples of $50.$ Given the potentially high demand for championship shirts $($the Texans have never won a Super Bowl$),$ the store can order no more than $500$ shirts. The store will sell each shirt for $\backslash (\backslash$$ $30\backslash ).$ We are only concerned with sales immediately after the Super Bowl, so there is a salvage value of $\backslash (\backslash$$ $6\backslash )$ at the end of the game.

The store recently hired a graduate of an operations management program. This new hire has estimated the probabilities that the store will sell certain quantities of shirts. Assume, to simplify the problem, that the store will experience demand in exact multiples of $50$ shirts. The employee's estimated demand probabilities are shown in the table below:

What is the optimal purchase quantity and what is the associated expected profit?