Sample question $($weight: $20\%)$ this question consists of parts a$)$ and b$)$

CookiePalooza $($CP$)$ is a manufacturer of $$home$-$baked$$ high$-$end $($non$-$perishable$)$ cookies. As a key account manager working for CP$,$ you are responsible for sales to GourmetShoppe, a fairly large chain of upscale grocery stores. The retailer carries four of CP$$s SKUs $($all part of the same $$Ole$$ Style$$ series$).$ Since CP owns all inventory carried in GourmetShoppe$$s distribution centers and stores, CPs senior management pays close attention to inventory figures and is concerned with maximizing inventory management efficiency. Here are some key figures for the $2020$ fiscal year:

SKU Total avg. inventory held by GourmetShoppe Total annual sales to GourmetShoppe Inventory$-$to$-$sales ratio

Ole$$ Style Caramel $$6,500$ $$50,0000\mathrm{.}13$

Ole$$ Style Chocolate $$10,800$ $$140,0000\mathrm{.}08$

Ole$$ Style Butter $$8,100$ $$80,0000\mathrm{.}10$

Ole$$ Style Chunky Nut $$7,000$ $$60,0000\mathrm{.}12$

In your role as key account manager you decide when and how many cookies to ship to GourmetShoppe. Thankfully, sales are very stable throughout the year and predictable to within less than $1\%$ of actual demand. Lead times from CP$$s bakery to any of GourmetShoppe$$s distribution centers are two days and do not vary. For technical reasons, each SKU must be managed and shipped separately. Shipments from CP to GourmetShoppe cost a fixed $ amount, can be of any size and can be initiated at any time. There are no constraints with respect to shelf capacity. Lastly, it should be noted that all relevant costs $($unit costs, shipping costs, etc.$)$ are the same for all SKUs.

Upon reviewing the figures shown above, the VP of Sales commends you for the efficient management of the $$Ole$$ Style Chocolate$$ SKU but is particularly displeased with the seemingly inefficient management of inventories of the $$Ole$$ Style Caramel$$ SKU. At the annual sales summit meeting of all key account managers, the VP of Sales asks you to comment on what he perceives to be an inconsistent performance in terms of inventory management efficiency. Just as you start choking up$,$ you realize that you actually have a really good explanation.

a$)$ Please respond to the VP of Sales$$ assertion that your performance in terms of inventory management efficiency has been $$inconsistent$.$

The obnoxious guy sitting next to you is the key account manager for GoodFoods $($another upscale retailer that carries the same lineup of Ole$$ Style cookies$).$ He gloats that his inventory$-$to$-$sales ratios are much better than yours even though GoodFoods$$ market is comparable to that of GourmetShoppe in terms of size and all other relevant characteristics. The VP of Sales wants to avoid any further conflict in the meeting but pulls you aside at the end of the day and asks you to offer an explanation for your obnoxious colleague$$s observation. You have been suspicious of your colleague$$s seemingly better performance for a while and are more than happy to discuss this with the VP of Sales

b$)$ What are the potential reasons for the observed differences in inventory$-$to$-$sales ratios? How could the VP of Sales assess whether the reasons you offer actually do explain those differences?