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.

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

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. 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. 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.

CASE DISCUSSION QUESTIONS

1. 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.

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

3. Using the analysis from Question 1 and Question 2 above, recommend a good order cycle length to the Western management team. Justify your recommendation, and discuss any interesting cost behaviour that you noticed.

4. Western is a highly-leveraged company and mostly funds the inventory and operations through business loans. Therefore, a major part of the holding cost percentage is the interest payments made. If interest rates go up in future, it can potentially raise the holding costs as a percentage of the product value, therefore motivating the company to reduce its order cycle length. What is the impact of a 20% (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?

Table 1: Weekly Demand for 90-Degree Elbow Boxes Demand Week Demand 400 27 410 450 28 440 425 29 427 430 30 418 460 31 370 390 37 380 405 33 410 416 34 428 430 35 412 10 440 36 450 11 395 37 376 12 360 38 360 13 370 39 417 14 410 40 422 15 390 41 440 16 440 47 380 17 460 43 415 18 425 44 432 19 448 45 396 20 462 46 460 21 380 47 422 22 395 48 446 23 414 49 398 24 423 50 428 25 448 51 410 26 422 52 415 10888 10762 Table 1 Weekly Demand Table 2 Lead timesTable 2: Lead-Times in Hours and Weeks (Weeks = Hours/24x7) Lead-Time Lead-Time Lead-Time Week Lead-Time (Hours) (Weeks) Week (Hours) (Weeks) 1 96 0.57 27 99 0.59 2 83 0.49 28 88 0.52 3 110 0.65 29 120 0.71 120 0.71 30 100 0.60 90 0.54 31 110 0.65 75 0.45 32 76 0.45 CO 130 0.77 33 110 0.65 120 0.71 34 140 0.83 140 0.83 35 120 0.71 10 92 0.55 36 100 0.60 11 90 0.54 37 110 0.65 12 99 0.59 38 95 13 0.57 110 0.65 39 108 0.64 14 120 0.71 40 112 0.67 15 130 0.77 41 118 16 0.70 125 0.74 42 122 0.73 17 80 0.48 43 85 18 0.51 0.52 14 76 0.45 19 110 0.65 45 126 0.75 20 86 0.51 46 134 0.80 21 92 0.55 47 99 22 0.59 95 0.57 48 91 0.54 23 100 0.60 49 110 0.65 24 112 0.67 50 104 0.62 25 108 0.64 51 112 0.67 26 120 0.71 52 118 0.70