Valley of Hope Hospital has been under recent pressure from stakeholders to improve cost efficiency and customer service. In response, the hospital has undertaken a series of process-improvement initiatives. One of the first processes targeted for improvement was the X-ray service. A major concern identified by both physicians and patients has been the amount of time required to obtain an X-ray. In addition, management would like to make sure that available resources are utilized efficiently.

A process-improvement team was set up to study the X-ray service process and recommend improvements. The team identified the point of entry into the process as the instant that a patient leaves the physician's office to walk to the X-ray lab. The point of exit was defined as the instant that both the patient and the completed X-ray film are ready to enter the physician's office for diagnosis. The unit of flow is a patient.

To determine the flow time of the existing process, a random sample of 50 patients was observed over a two-week period. The X-ray unit processes, on average, 44 patients per eight-hour day, or 5.5 patients per hour. All resources are scheduled for operation from 9:00am to 5:00pm each day, six days per week. For each patient, the team recorded times of entry and exit from the X-ray service process. The difference between these two times was then used as a measure of flow time for each patient. The average of the 50 data points was 154 minutes. This figure, then, serves as an estimate of the average flow time for the X-ray service process.

Each process step, their estimated theoretical times (work content), and their required resources are shown in Table 1. In addition, each activity is identified as value-added (VA) or non-value-added (NVA).

The corresponding process flowchart is shown in Figure 1. It depicts all activities and the precedence relationships among them. For example, Activity 2 must be completed before Activity 3 can begin. Meanwhile, Activity 1 can be carried out simultaneously with Activities 2 and 3. Note that the classification of activities to VA and NVA is somewhat subjective, and may depend on the specific details of the situation.

The team analyzing the process flowchart identified four activity paths:

• Path 1: Start -> 1->4->5->6->7->8->9->10->End
• Path 2: Start->2->3->4->5->6->7->8->9->10->End
• Path 3: Start->1->4->5->6->7->8->11->End
• Path 4: Start->2->3->4->5->6->7->8->11->End

The theoretical flow time along these four paths are:

• Path 1 = 50 minutes
• Path 2 = 69 minutes
• Path 3 = 60 minutes
• Path 4 = 79 minutes

Path 4, therefore, is the critical path, yielding a theoretical flow time of the process as 79 minutes.

What is the flow-time efficiency of the process?

Flow-time efficiency = Theoretical flow time/Average flow time = 79/154 = 51%

This means that waiting represents about half of the time in this process. The challenge this poses to the management of the hospital is whether some of this waiting can be eliminated. Note that of the 79 minutes of theoretical flow time, the only activities which are value adding are Activities 6 and 7. Thus the value adding time of the process is 7.5 + 15 = 22.5 minutes, which is less than 15 percent of the average flow time. (You could argue further that the rework is non-value adding time.)

To analyze the capacity of the process, we need to know the nature of the resources and the number of resources available. Table 2 shows the resource pools, their unit load, number of resources, and theoretical capacity.

The theoretical bottleneck resource is the darkroom, with a capacity for processing only 8 patients per hour. The theoretical maximum capacity of the process itself therefore is 8 patients per hour.

Question 1:What is the capacity utilization of the entire process?