10.7 Tools: Location Decisions

Deciding how many warehouses you need to operate is the ultimate total costing decision. Not only does the number of warehouses affect operating efficiencies (i.e., fixed and variable costs) but it also influences other cost categories like transportation, inventory, and order processing. It also has a huge impact on customer service—and the cost of poor service (e.g., lost sales or even lost customers). Your job is to configure your network to minimize the sum of all these costs. Figure 10-10 shows how these different costs typically behave when you add or subtract warehouse locations. Notice that you minimize your total costs at a point where no single activity cost curve is at its minimum. You really do need to look at all of your costs together.

Let's reemphasize a point we made in the last section (yes, it's that important). Your biggest challenge in calculating total costs is to identify your relevant costs and gather accurate data. You need to understand the nature of each cost category. Let's take a closer look at two of the cost categories: cost of poor customer service and inventory carrying costs.

• Cost of Poor Customer Service: Having fewer warehouses increases your distance to customers, decreasing your service levels. Specifically, your order fulfillment cycle time goes up. So does your cycle time variability. You are likely to suffer more late deliveries and cause more stock outs. Customers may defect—taking their business to suppliers who promise more responsive service. If you add more warehouses in the right locations, you will reduce distance and improve service. But, at some point, the service benefit begins to diminish. The question is, where? You need the numbers to know for sure.

• Inventory Carrying Costs: You may have noticed that the inventory carrying costs go up as you increase the number of warehouses? This happens because safety stocks tend to increase as you add facilities to your network. Why, you ask? Think about a one-facility network. That one facility serves all of your customers. Some customers will order more than you expect and other customers will order less. When you have a lot of customers, these "overs" and "unders" cancel each other out. You benefit from a portfolio effectA situation when some customers order less than expected, and other customers order more than expected, and they cancel each other out. . Total variation is reduced. Let's reiterate this point: When you have a broad and diverse portfolio of customers, variations in orders tend to return to the mean (in statistics, we call this the "central tendency" theorem). When you add warehouses, you reduce the number of customers each warehouse serves. In other words, you reduce the portfolio effect at the individual warehouse level. What does this mean? Answer: Your overall network safety stock will increase. However, because you have more warehouses, the actual safety stock held at each warehouse will typically decrease.

  In logistics, we refer to this relationship between the number of warehouses and the amount of safety stock as the Square Root of N RuleThe rule that states that the system-wide safety stock is directly related to the square root of the number of warehouses in the network. : which states that your system-wide safety stock is directly related to the square root of the number of warehouses in your network. The equation for the Square Root of N Rule is simple:

  $$x_2=(x_1)\cdot \sqrt{n_2/n_1}$$

  Where:

  n ₁ = number of existing warehouses

  X ₁ = total safety stock in existing warehouses

  n ₂ = number of proposed future warehouses

  X ₂ = total safety stock in proposed future warehouses

  Now, let's work through a simple example. Suppose you operate a single-warehouse that holds 100 units of safety stock. You are thinking about adding three new warehouses—each located closer to different key customers. So, what do you know? n ₁ = 1, n ₂ = 4 (1+3), and X ₁ = 100. Let's plug these numbers into the equation.

  $$x_2=(100)\cdot \sqrt{\frac{4}{1}}=(100)\cdot 2=200$$

  When you quadruple the number of warehouses, you double your safety stock. Let's make one final point about the Square Root of N Rule: It is just a rule of thumb. The unique nature of your network may mean that the relationship looks a little (or maybe a lot) different. This is why you need to collect accurate data as you do your total cost analysis.

Finally, when it comes to total costing for warehouse network design, you face another challenge: Managers in different departments have different opinions about the costs—and thus the number of warehouses you should operate. Sales and Marketing places special emphasis on cost of poor—or non-competitive—service and often prefers more facilities so they can promise faster, more responsive delivery. Finance, however, tends to prefer fewer facilities to minimize required investment. Since logistics is managed as a cost center, you may side with finance—especially since the cost of lost sales is hard to quantify.

You might think, "Now that you've determined how many facilities to use, the question is, where should you build them?" The reality is that the two decisions are interconnected. Where you build affects how many you need to build. The math required to identify the best number and location requires a PhD in optimizing techniques. Don't be discouraged. You'll have team members with those skills. What you need to know are the basics so that you can understand their analysis. So, let's look at the basics. You've heard it said the three keys to success in real estate and retail are "location, location, and location." Location analysis begins with understanding the geography of supply and demand. Simply put, where do you buy from and where do you sell to?

Your goal is to find the geographic center; that is, the location that minimizes the distance between you and your supply chain partners (suppliers and customers). What do we mean by geographic center? If you look at a map of the United States, the geographic center for continental U.S. (the 48 contiguous states) is near Wichita, Kansas. Is this the right place to set up your warehouse? Maybe. But, you are probably already asking,"Where are your customers located?" Did you know that 47% of the U.S. population lives in the Eastern time zone? By contrast, 32% live in the Central time zone, 14% in the Pacific, and a mere 5% in the Mountain. Thus, your real "center" of interest is the weighted center of economic activity. Such models are called Center-of-Gravity Models An approach used to compute the geographic center for a set of demand/supply volumes. The goal is to minimize the weighted distance/cost to ship goods from suppliers to the distribution facility as well as to ship goods from the distribution facility to customers.. Center-of-gravity Models assess the "pull" of supply and demand locations, assigning proportionately more weight to bigger sources of supply and bigger customers. When you realize that almost 80% of the population lives in the Eastern and Central time zones, it makes sense that FedEx built its air hub in Memphis, Tennessee and UPS set up operations in Louisville, Kentucky.

Of course, you don't want to ignore customers in Seattle—or anywhere else. This is where your analysis becomes complex. How many geographic centers make sense—and where are they? CPG companies used zip-code analysis of population centers to come up with the rule of thumb that five centers were needed to supply a nationwide network of retail stores: Los Angeles, California; Dallas, Texas; Atlanta, Georgia; Mechanicsburg, Pennsylvania; and Chicago, Illinois. By contrast, to reach its goal of affordable one-day delivery, Amazon has built 84 North American distribution centers (78 in the U.S., 5 in Canada, and 1 in Mexico). 3 So, you really need to add service goals and idiosyncratic location costs to your analysis. If you're doing business globally, you also have to consider the unique challenge of crossing national borders.

You can find a more complete list of factors to consider in Table 10-2. The factors are divided into two columns. The left column lists factors that help you select the region (perhaps country or state) in which to place a facility. The right column identifies criteria that you would evaluate to choose a specific building site. As you consider site location, be sure to plan for the 10-20 year future. For example, Zappo's, a US online retailer of shoes, clothing, and accessories, built its first distribution center in Shepherdsville, Kentucky twice the required size for the volume at the time the facility was opened. Within the first year, Zappos began using the additional space. If you don't already own the land, it can be very difficult—and expensive—to expand a warehouse. One final thought on warehouse location: Because warehousing brings economic activity and jobs, you might be able to negotiate incentives and tax abatements from countries, states, and cities that want your business.