Time Drivers and Bottlenecks

Managing customer-response time and on-time performance requires managers to understand the causes and costs of delays, for example, at a machine in a manufacturing plant or at a checkout counter in a store. A time driver is any factor that causes a change in the speed of an activity when the factor changes. Two time drivers are described below:

UNCERTAINTY ABOUT WHEN CUSTOMERS WILL ORDER PRODUCTS OR SERVICES. For example, the more randomly Airbus receives orders for its airplanes, the more likely queues will form and delays will occur.
BOTTLENECKS DUE TO LIMITED CAPACITY. A bottleneck occurs in an operation when the work to be performed approaches or exceeds the capacity available to do it. For example, a bottleneck results and causes delays when products that must be processed at a particular machine arrive while the machine is being used to process other products. Bottlenecks also occur on the Internet, for example, when many users try to operate wireless mobile devices at the same time (see Concepts in Action: Facebook Works to Overcome Mobile Data Bottlenecks).

Many banks, such as Bank of China; grocery stores, such as Kroger; and entertainment parks, such as Disneyland, actively work to reduce queues and delays to better serve their customers.

Consider again Formrob Corporation, which uses one turning machine to convert steel bars into a heating block for its 3D printers. The heating block is the only product the company makes on the turning machine. Formrob makes and sells the heating blocks as spare parts for its 3D printers after receiving orders from wholesalers. Each order is for 750 heating blocks.

Formrob’s managers are examining opportunities to produce and sell other products to increase the firm’s profits without sacrificing its short customer-response times. The managers examine these opportunities using the five-step decision-making process introduced in Chapter 1.

IDENTIFY THE PROBLEM AND UNCERTAINTIES. Formrob’s managers are considering introducing a second product, a motor front panel, which will use the same turning machine currently used to make heating blocks. The primary uncertainty is how the introduction of a second product will affect the manufacturing cycle times for heating blocks. (We focus on Formrob’s manufacturing cycle time because the receipt time and delivery time for the heating blocks and motor front panels are minimal.)
OBTAIN INFORMATION. Managers gather data on the number of past orders for heating blocks, the time it takes to manufacture them, the available capacity, and their average manufacturing cycle time. Formrob typically receives 30 orders for heating blocks each year, but it could receive 10, 30, or 50 orders. Each order is for 750 units and takes 100 hours of manufacturing time (8 hours of setup time to clean and prepare the machine that makes the heating blocks and 92 hours of processing time). The annual capacity of the machine is 4,000 hours.
MAKE PREDICTIONS ABOUT THE FUTURE. If Formrob only makes heating blocks in 2020, it expects to receive 30 orders of 750 units each requiring 100 hours of manufacturing time. The total amount of manufacturing time required on the machine is $inline style begin inline style text 3,000 end text thin space text hours end text thin space left parenthesis 100 thin space text hours per order?? end text cross times ? 30 thin space text orders end text right parenthesis end style$ , which is less than the available machine capacity of 4,000 hours. Queues and delays will still occur because wholesalers can place their orders at any time, while the machine is processing an earlier order.

Concepts in Action

Facebook Works to Overcome Mobile Data Bottlenecks^*

Wachiwit/Shutterstock

Facebook is the world’s largest social networking company. More than 2.6 billion people around the world use its core Facebook, Messenger, Instagram, and WhatsApp services to communicate with each other every month. Forty-seven percent of users globally access Facebook via mobile phones, including 68% in the United States. As a result, Facebook consumes a large amount of mobile data.

Ensuring ample mobile bandwidth is critical to Facebook’s success. The more people access Facebook services on their phones, the more they see Facebook ads, which are the company’s primary sources of income. But Facebook contends for mobile bandwidth with everything from competing services such as Twitter and WeChat to personal and industrial devices connected as part of the Internet of Things. With data traffic from mobile devices increasing by an estimated 53% per year, the demand for mobile bandwidth is fast outstripping the best efforts of providers like Facebook to supply it.

Aware of this challenge, Facebook actively works behind the scenes to alleviate mobile data bottlenecks that slow the delivery of its content. In recent years, Facebook has deployed various strategies to overcome mobile bottlenecks that affect the delivery of its content:

Facebook spends billions of dollars annually operating geographically distributed data centers. By 2018, Facebook had nearly 15 million square feet of data center space completed or under construction around the world storing replicas of its data to route queries from mobile devices to the closest server. Content cached at these data centers is what allows viewers to fast-forward video as if the file were stored on a home device.
Facebook is also experimenting with new ways to improve mobile network access around the world. From testing the use of drones to deploy mobile bandwidth in hard-to-reach places to using high-frequency radio waves to speed up networks in dense urban areas, the company is constantly investing in new technologies to help clear mobile traffic jams and keep the multimedia content (and ads) flowing to its billions of users.

Looking ahead, Facebook will continue to invest in new technologies to help overcome mobile bandwidth bottlenecks, as well as continuously improve the underlying technical infrastructure of its own apps to increase efficiency—for example, by unifying the code used for its WhatsApp, Instagram, and Messenger apps—to help overcome mobile data choke points and meet the ever-growing demand for its services around the world.

Average waiting time, the average amount of time that an order waits in line before the machine is set up and the order is processed, equals^*

$\begin{array}{l} \frac{\begin{matrix} \begin{array}{c} Annual average \\ number of \\ orders for heating blocks \end{array} & \times & {(\begin{array}{c} Manufacturing \\ time per order \\ for heating blocks \end{array})}^{2} \end{matrix}}{2 \times [\begin{matrix} \begin{array}{c} Annual machine \\ capacity \end{array} & - & (\begin{matrix} \begin{array}{c} Annual average number \\ of orders for heating blocks \end{array} & \times & \begin{array}{c} Manufacturing \\ time per order for heating blocks \end{array} \end{matrix}) \end{matrix}]} \\ = \frac{30 \times 100^{2}}{2 \times [4,000 - (30 \times 100)]} = \frac{30 \times 10,000}{2 \times (4,000 - 3,000)} = \frac{300,000}{2 \times 1,000} = \frac{300,000}{2,000} \\ = 150 hours per order (for heating blocks) \end{array}$

Therefore, the average manufacturing cycle time for an order is 250 hours $begin inline style left parenthesis 150 space text hours of average waiting time? end text plus 100 text ?hours of manufacturing time). end text end style$ Note that manufacturing time per order is a squared term in the numerator. The squared term indicates the disproportionately large impact that manufacturing time has on the waiting time. As the manufacturing time lengthens, there is a much greater chance that the machine will be in use when an order arrives, leading to longer delays. The denominator in this formula is a measure of the unused capacity, or cushion. As the unused capacity becomes smaller, the chance that the machine is processing an earlier order becomes more likely, leading to greater delays.

The formula describes only the average waiting time. A particular order might arrive when the machine is free, in which case manufacturing will start immediately. In another situation, Formrob may receive an order while two other orders are waiting to be processed, which means the delay will be longer than 150 hours.

If Formrob makes heating blocks and motor front panels in 2020, it expects to receive the following:

Heating blocks: 30 orders of 750 units each requiring 100 hours of manufacturing time per order.
Motor front panels: 10 orders for motor panels of 800 units each requiring 50 hours of manufacturing time per order, composed of 3 hours for setup and 47 hours of processing.
The expected demand for heating blocks will be unaffected by whether Formrob produces and sells motor front panels.

If Formrob makes both heating blocks and motor panels, the average waiting time before the machine setup begins is expected to be as follows (the formula is an extension of the preceding formula for the single-product case):

$\begin{array}{l} \frac{[\begin{matrix} \begin{array}{l} Annual average number \\ of orders for heating blocks \end{array} & \times & {(\begin{array}{l} Manufacturing \\ time per order \\ for heating blocks \end{array})}^{2} \end{matrix}] + [{\begin{matrix} \begin{array}{l} Annual average number \\ of orders for motor panels \end{array} & \times & (\begin{array}{l} Manufacturing \\ time per order \\ for motor panels \end{array}) \end{matrix}}^{2}]}{2 \times [\begin{matrix} \begin{array}{l} Annual machine \\ capacity \end{array} & - & (\begin{matrix} \begin{array}{l} Annual average number \\ of orders for heating blocks \end{array} & \times & \begin{array}{l} Manufacturing \\ time per order \\ for heating blocks \end{array} \end{matrix}) & - & (\begin{matrix} \begin{array}{l} Annual average number \\ of orders for motor panels \end{array} & \times & \begin{array}{l} Manufacturing \\ time per order \\ for motor panels \end{array} \end{matrix}) \end{matrix}]} \\ = \frac{[30 \times {(100)}^{2}] + [10 \times {(50)}^{2}]}{2 \times [4,000 - (30 \times 100) - (10 \times 50)]} = \frac{(30 \times 10,000) + (10 \times 2,500)}{2 \times (4,000 - 3,000 - 500)} \\ = \frac{300,000 + 25,000}{2 \times 500} = \frac{325,000}{1, 000} = 325 hours per order (for heating blocks and motor panels) \end{array}$

Producing motor panels will cause the average waiting time for an order to more than double, from 150 hours to 325 hours. The waiting time increases because the production of motor panels will cause the machine’s unused capacity to shrink, increasing the probability that new orders will arrive while current orders are being manufactured or waiting to be manufactured. The average waiting time is very sensitive to the shrinking of unused capacity.

If Formrob’s managers decide to make motor panels as well as heating blocks, the average manufacturing cycle time will be 425 hours for a heating block order $inline style begin inline style left parenthesis 325 text hours of average waiting time end text plus 100 text hours of manufacturing time end text right parenthesis end style$ and 375 hours for a motor panel order $inline style begin inline style left parenthesis 325 text hours of average waiting time end text plus 50 text hours of manufacturing time). end text end style$ A heating block order will, on average, spend $begin inline style 76.5 percent sign thin space left parenthesis 325 thin space text hours end text divided by 425 thin space text hours end text right parenthesis end style$ of its manufacturing cycle time just waiting for its manufacturing to start!

MAKE DECISIONS BY CHOOSING AMONG ALTERNATIVES. Should Formrob produce motor panels, given how much it would slow down the manufacturing cycle time for heating blocks? To help the company’s managers make a decision, the management accountant identifies and analyzes the relevant revenues and relevant costs of producing motor panels and, in particular, the cost of delays on all products. The next section focuses on this step.