The Western Plumbing Company (Western) started as a family business...

The Western Plumbing Company (Western) started as a family business by three brothers in Kamloops in 1998 who left their general contractor business to venture into construction supplies. Besides offering wholesale supply of lighting products, pre-wired fixtures, electrical components, and heating as well as ventilating supplies, the company built quite a reputation as a wholesaler for plumbing supplies to trades in the residential, commercial, home improvement, and renovation business. Over time, Western's business leaned more towards plumbing supplies as the company streamlined its operations. Benefitting from their network of contacts with construction companies, independent contractors, and various handy men from their previous general contractor business, Western plumbing supplies never looked back. The company expanded to become the main plumbing wholesaler and distributor in the Thompson-Nicola region and eventually expanded by opening branches in Vernon, Kelowna, Abbotsford, Surrey, and Burnaby that enabled them to set a foothold in the lower mainland market. What began as a small family business grew into six branches employing 54 staff members. The Kamloops branch remained their head office, showing their bond to the community where the three brothers were raised and still maintain their family home in the Valleyview neighborhood. Western works withor, more accurately, collaborates withall the reputed suppliers of plumbing and electrical products using a distributor in Vancouver as its single source who is dedicated to Western. Western's plumbing

Figure 1: Plumbing pipe fitting 2 TRU OPEN LEARNING | WESTERN PLUMBING COMPANY | CC BY-NC-SA 4.0 line consists of seven different adapters, five bushings, three sizes of clean-outs, six different couplings, four tees, three wyes, four S-traps, and five copper elbow fittings. Their 1.5 inch, 90-degree copper elbow (see below) is a very popular item in the plumbing line that comes packaged in 10 elbows per box. The box costs about $65 to Western, and Western sells it at $100 per box, gaining a $35 profit margin. Course Fit Supply Chain Management, Production and Operations Management, Logistics and Transportation

CASE PROBLEM In the construction and renovation business, any stockout can pose a serious threat to the business as it not only results in lost sales but the risk may be as high as losing a business client to the competitors. Western maintains a benchmark policy to keep 98% stock availability for the popular items such as 90-degree elbows. Western uses a periodic ordering policy with its distributor in Vancouver and keeps a safety stock of popular items like elbows to minimize the chances of stockouts. Stockouts may happen due to a number of reasons. Prominent among them are two reasons: the variability in the demand by the customers and the variability in the lead-time from the suppliers. For analysis of this case, we will focus on the 90-degree elbow item. Note that a similar analysis would be necessary for other items. The weekly demand of copper elbows, although stable throughout the year, varies from week to week in accordance with the construction and renovation activities in the region. The demand pattern is influenced by time of the year, holidays, new permits, weather, and so on. Similarly, the lead-time from the distributormeasured as the time from placing the order to receiving the orderalso varies depending on the stock availability, consolidation with other orders, weather, traffic, packaging requirements, and so on. Western operates 52 weeks in a year. The weekly demand pattern and order lead-time for copper elbows are recorded over the last 52 weeks and are given in Table 1 and Table 2 respectively (see below). Although the leadtime is recorded in hours from the order placement time to the order receipt time, for safety stock computations it is converted into weeks. Each complete order arrives in the same shipment, and splitting the order amount is not an option for the distributor. Although owing to variation in weekly demand, the safety stock carried over from one cycle to the next may vary, though not substantially, but it can be safely assumed that the average safety stock will still be constant throughout the year. This average safety stock to manage the variation in demand and lead times is calculated as follows: Safety Stock = Z*SQRT {average Lead Time * (Standard Deviation of weekly Demand)2 + average weekly demand * (Standard Deviation of Lead Time)2 } Fig 2: 1.5 Inch, 90-degree elbow.

Note: The Z-score in this would be the standard normal deviate corresponding the desired customer service level. The holding cost is applied on each box worth $65 that is held in inventory. This includes the interest payments on inventory of this product, stacking and handling of boxes and the cost of storage space.

The holding cost as a percentage of the value of inventory stays more or less the same in each year. According to a recent past estimate, the company carried $1.5 million worth of copper elbows and the holding cost in accounting records was listed as $225,000.

The holding costs are not only incurred on the regular depleting inventory under economic order modeling but also on the constant safety stock that is required to manage the variations in weekly consumption and the variation in lead times.

The management carries safety stock that allows it to maintain a 98% stock availability at all times.

The management is well aware of the negative consequences that a stock-out situation can inflict on their as well as on their customer's business. Although the customer orders are fillable 98% of the time from the regular orders and safety stocks that come from their Vancouver vendor, the management is not prepared even to take 2% chances.

Therefore, the management decided to respond to those 2% out-of-stock chances through an out-of-pocket policy. Similar copper elbows from a different vendor are available from local Home Depot in loose quantities at $8.50 a piece.

Western packages these replacement copper elbows for its customers costing them $90 a box that includes the purchase cost and the packaging time. This replacement product is acceptable to customers during desperate times provided there is a price discount from Western. Western decided to sell this replacement box to its valued customers at $50 a box which costed them $90. The $40 loss per box is treated as a stock-out cost for Western to avoid losing their valued customers. This is to what extent Western management can go to provide unsurpassed service to its valued customers.

Western management estimates that each order costs about $2500 in terms of placing the order, clerical time, receiving, off-loading, counting and verifying the quantity against the order. The management had concerns about the frequency of ordering. If fewer orders in large quantities are placed, it lowers the ordering cost but it results in more regular inventory cost.

If smaller orders are placed more frequently, it reduces the inventory costs but increases the ordering cost. Therefore, the management would like to explore various order length cycles to get some guidance on what would be an optimal order cycle length for western.

Exploring various order cycle lengths varying from 2 weeks to 10 weeks, the management wants advice on the optimal order length they need to choose to minimize their total combined ordering, holding and stock-out costs.

For each length of the order cycle, the annual number of orders and average order sizes need to be calculated. Two percent of these orders are unfillable from regular and safety stock inventory and hence result in out-of-stock cost for the plumbing supply company. This provides the basis for computing out-of-stock costs. The average weekly demand can be assumed to be constant for this high level of customer service level. The expected order size therefore would be the total usage or demand during the order cycle. In essence, the case analysis involves four types of costs for each cycle length: The annual ordering cost The annual regular inventory holding cost The annual constant safety stock holding cost to maintain a 98% service level due tdemand and lead time variations The out-of-stock costs. The objective is to determine the order length in number of weeks that would minimize the total combined costs representing the above four cost categories. STUDY NOTES To work on the case questions, please use the Western Inventory Data Set Excel document. The Excel workbook has data sets under multiple tabs that you will need for your analysis.

Questions:

A).Starting with T=2, change the value of the order cycle length, i.e. order length T=2, 3, 4, 5, 6, 7, 8, 9, and 10 weeks. For each length, calculate the order size, number of orders, the afore-mentioned four costs and the total cost.

B).Make a plot of the four costs and the total costs against the order cycle length.

2. Using the analysis in part (A) and part (B), recommend a good order cycle length to Western's management. Justify your recommendation and discuss any interesting cost behavior that you noticed.

3. Western is a highly leveraged company, funding inventory and operations mostly through business loans. Therefore, a major part of the holding cost percentage is the interest payments made.

i).If interest rates go up, it can potentially raise the holding costs as a percentage of the product value therefore motivating the company to reduce its order cycle length.

ii).What is the impact of a 20% increase (i.e. current holding cost percent *1.20), a 30% increase in holding cost percentage, or a 70% increase in holding cost percentage? Does a new order cycle length become optimal?

4. The management would also like to assess the possibility to, rather than occasionally buying the elbows from Home Depot, manage the 2% stock-out and package them into boxes, if it would be more cost-effective to carry some extra safety stock to have a 100% service level (Z=3) and product availability. The extra holding cost on safety stock may very well off-set the cost of stock-outs but management would like Western plumbing supplies became an independent company in 1998