Case Study $11\mathrm{.}1$

Jack$$s Hardware

Several years ago, Jack Adams decided he had been working as a skilled building contractor long enough. He wanted to establish himself in a more predictable and pleasant work environment. He realized that there was an opportunity in the medium$-$sized village where he lived, in that there was no local hardware store. People from the village would have to travel by car more than $30$ minutes to find the nearest hardware store, and Jack figured many in his village $($and surrounding countryside$)$ would rather come to a local store for their needs. His knowledge of hardware gained from his years as a contractor would serve him well in the hardware business.

The venture turned out to be quite successful and his business grew. The problem he was currently facing is that the village was also growing and at least one large hardware chain company was starting to look at the village as a possible opportunity for a new store. Jack realized that if he had competition in town, he needed to evaluate his own business.

Jack had never paid a lot of attention to what he considered the $$small details$$ of his cost structure. He knew that his prices were somewhat higher than what the chain hardware stores in the nearby city charged, but he knew that his customer still came to him because he was in their village and also because they knew that Jack had lots of knowledge about hardware and could almost always answer their questions. His customers were loyal, but he also knew that if another store opened in the village with lower prices that he would certainly lose at least some of his business. Since those chains could order in bulk and get quantity discounts, they could charge less for their products.

One of Jack$$s clerks had recently had experience in a warehouse setting and suggested to Jack that he might want to evaluate his inventory policies. If he could save some money with inventory, he might be able to lower his prices enough to stay reasonably price competitive, especially in view of his great reputation for customer service.

Jack had a good friend who had a daughter who was a business student studying operations management at a well$-$known university, so Jack asked if his friend if his daughter might be able to help. She agreed, and asked Jack to provide some basic data about two of his more important products. She said she would evaluate options for Jack, and if it turned out successful, he could potentially expand the approach to more of his items.

Here is the data that Jack provided for the two items:

ITEM A

Item$$cost$=$$$2\mathrm{.}80$each

Order$$cost$=$$$15\mathrm{.}00$per$$order

Inventory$$holding$$cost$=18\%$per$$year

Average$$demand$$per$$year$=1000$

Currently $($at the recommendation of the supplier$)$ the amount ordered per order$=100$

ITEM B

Item$$cost$=$$$12\mathrm{.}50$each

Order$$cost$=$$$22\mathrm{.}50$per$$order

Inventory$$holding$$cost$=18\%$per$$year

Average$$demand$$per$$year$=750$

Currently $($at the recommendation of the supplier$)$ amount ordered per order$=60$

Actual demand over the last $20$ weeks:

Eleven$\mathrm{.}5-13$ Full Alternative Text

Eleven$\mathrm{.}5-14$ Full Alternative Text

The current inventory $($at the beginning of week $1)$ for Item A is $30,$ and for Item B is $25.$

The student doing the evaluation said she wanted to evaluate using and economic order quantity $($EOQ$)$ and a periodic order quantity $($POQ$)$ and compare both to the existing policy using the same criteria $($the only difference being the order size$).$ The current policy on reordering items was to order when the inventory level dropped to one week$$s average usage $($the supplier was able to respond to all orders from Jack in about one week$),$ but just in case that week$$s demand was a little higher than average, he wanted to add a bit of a buffer of $15\%$ weekly demand. He didn$$t want to lose a sale if he ran out before his new order from the supplier came in$.$ In the past he didn$$t care so much because most of his customers could wait for a day or two for a part that was out of stock, but Jack knew that with a potential new competitor coming to town that many of his customers might go to the new store if Jack was out of stock, and he thought that even though the $15\%$ extra might cost him a bit more in inventory cost it was likely worth it to prevent lost sales and perhaps lost customer loyalty.

The student was a bit concerned about evaluating the POQ situation because it meant the inventory would not be monitored on a regular basis until the end of the defined period. While that was an advantage for saving constant inventory counts, it might mean that if the demand was unusually high, they could run out of stock without even knowing it was low. Given that the items are sold on demand, there is no opportunity to $$look ahead$$ at demand.

For the two items in question, the average weekly usage is as follows:

The$$average$$weekly$$usage$$for$$A$=1000/52=19\mathrm{.}2$or$19$units

The$$average$$weekly$$usage$$for$$B$=750/52=14\mathrm{.}4$or$14$units

Applying the $15\%$buffer$,$ the critical inventory values are $22$ un