1 International Joint Conference - CIO-ICIEOM-IIE-AIM (IJC 2016) San Sebastián, Spain, July 13-15, 2016 Common Service Demand Pattern for Service Capacity Planning. Yuval Cohen 1, Shai Rozenes 2, Efrat Perel 3, Maya Golan 4 Abstract This research is based on analysis of empirical data of various service demand patterns such as banks, hospitals, communications and others. The research findings show similar patterns of demand of various different services in different parts of the world. The double hump demand pattern appears to be a typical pattern for daytime services around the globe having typical peak hours during a workday. Analysis shows a striking demand similarity of the same weekdays, and a significant difference between the demand of workdays and weekend days. The paper discusses ways to efficiently plan the service workforce and capacity based on the relevant demand patterns. Keywords: Demand pattern, Service capacity, Load pattern, Rush hour, Service level. 1 Yuval Cohen ( e-mail: yuvalc@afeka.ac.il) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. 38 Mivtsa Kadesh, Tel-Aviv 69988, Israel. 2 Shai Rozenes ( e-mail: rozenes@ afeka.ac.il) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. Tel-Aviv 69988. 3 Efrat Perel ( e-mail: efratp@afeka.ac.il) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. Tel-Aviv 69988. 4 Maya Golan (e-mail : mayag@ afeka.ac.il) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. Tel-Aviv 69988.
2 1 Introduction While inventory could be used for satisfying demand, services typically cannot be stored (Shtub and Cohen, 2016). Therefore the daily demand pattern for a particular service reflects the actual load on the system (Daskin, 2011). Plenty of daily service demand patterns were gathered and described for specific products or services, but to the best of our knowledge there was no research effort to find commonality across different organizations or services. In this paper we present characteristic demand behavior for various services. This paper focuses on examination of daily patterns of different services and products in an effort to detect similarities and certain characterizing patterns or phenomena. The research questions are described next. 2 The research questions and hypotheses The following are the research questions we tried to answer in this paper: Question 1: Are there similar daily patterns that characterize different services? Hypothesis: Different services share similar daily patterns. Question 2: Are different days of the work week (Monday to Friday) have different patterns? Hypothesis: Workdays share similar demand pattern. Question 3: Do weekends have different demand profile then work days? Hypothesis: Weekends have different demand pattern than weekends. These hypotheses are checked statistically with high significance level. 3 Finding similarity in patterns In this section we show the similarity of daily demand patterns for services around the world. Figure 1 shows a demand pattern we collected during 2010 at a major hospital in Israel. It clearly shows a double hump pattern of calls.
3 2000 1800 1600 1400 1200 1000 800 600 400 200 0 Hospital Patient Arrivals per Hour During Workdays of First Two Quarters of 2010 (Israel) Sunday Monday Tuesday Wednesday Thursday Fig 1. Average hourly arrival rates of patients to an Israeli hospital (annual -2010) While the workdays in the hospital have very similar behavior, the weekend has a different pattern as shown in figure 2. 6 4 3 3 Hospital Daily Average Arrivals: Saturday (2010) 2 2 2 3 4 6 9 10 9 9 9 7 8 8 12 12 14 14 12 10 Fig 2. Average hourly arrival rates on Saturdays of patients to an Israeli hospital (annual - 2010) The regular double-hump pattern is found in other home consumption areas such as water, and communications. However, the peaks may shift considerably based on drinking/watering habits as shown in figure 3.
4 Fig 3. Daily water consumption in Croatia (Margeta, 2010) This two peak pattern is even more extreme in road and train traffic where the commute to work and back produces rush hours with sharper peaks (e.g. figures 4 and 5). Fig 4. Average US daily traffic pattern and the effect of different congestion percentages (Margiotta et al, 1999).
5 VISTA07 HIST78 Fig 5. Weekday person trips by car and public transport in Melbourne Statistical Division by quarter-hour, 1978=HIS78 and 2007=VISTA07 (McGeoch, 2011). Figure 6 shows a striking similarity that exists between the daily traffic pattern and the call intensity to 511 (Traveler information service). Workdays Profile Fig 6. Hourly call distribution during average workday for 2004 (based on 670,369calls to 511 traveler information) Source US Department of Transportation (US DOT) Federal Highway Administration report - 2006.
6 4. Validation Study To validate our findings we processed annual information collected in the call center of an major Israeli bank. This helped us to examine and validate our assumptions related to the daily demand patterns. The results are depicted in figure 7. Fig 7. Daily demand pattern of average call per hour in a call center of a major bank (2015) The two peaks are clearly visible in figure 7. Moreover, the differences between workdays are statistically insignificant (Chi-squared test on deviations from the daily average) with the exception of Sunday (under all standard confidence levels). This justifies planning capacity based on an average workday profile. The corresponding profile is depicted in figure 8. Hospital Daily Average Arrivals: Monday - Thursday (2010) 19 19 18 16 6 4 3 2 2 2 2 4 8 15 14 12 11 14 15 16 15 14 10 8 Fig 8. Average hourly workday arrival rates to an Israeli hospital (2010)
7 5. Discussion The patient arrivals in figure 8 are independent of each other, and such independent processes constitute a non-homogeneous Poisson process [8]. Therefore the hourly averages are also the hourly variances. Thus, using the approximation of the Poisson ( ) distribution to the Normal distribution, helps to ensure the keeping the desired level of service. For example, if the goal is to give treatment to 95% of the arriving patients within an hour from the arrival, the medical workforce should be able to treat a number of patients that is equal to two standard deviations above the average. Thus, for the morning peak hours of figure 12 the capacity should be based on treating 28 patients per hour 19 2 19 28, while the evening capacity could be planned for treating 24 patients per hour 16 2 16 24. To answer the hypothesis regarding the difference of the weekend we tested statistically the weekend profile, and found that it is significantly different than the average workday profile (p<0.005). While the workdays have very similar behavior, the weekend has a different pattern as shown in figure 9. Fig. 9. Average weekday total arrival rates of calls to an Israeli bank (2015) Call centers use standard method such as Erlang-B and Erlang-C formulas for capacity planning (Yom-Tov and Mendelbaum, 2014). These methods are based on having the demand profile and estimating the demand during rush hours. While the average demand curve is important, it presents only averages and does not provide all the information needed for planning. The finding of this study support the conclusion that demand during regular week days can be modeled by an average hourly demand pattern, while weekend days should be modeled through their daily average demand.
8 6. Conclusion In this paper we discussed and analyzed a recurring demand pattern. We found the double hump pattern as characterizing demand in many different services (utilities, hospitals, transportation etc.). The demand patterns are reflecting the level of related activity, and the double-hump appears when there are two peak activity periods during the day. We found striking similarity between the workday profiles (Monday to Thursday demand profiles). However workday demand profiles are not similar to the weekend profiles. The difference is reflected both in the intensity and the pattern of the daily profiles of demand. Estimating the peak (rush) hours demand distributions of these patterns is critical for the capacity planning. Capacity planning must take into account the demand variability and the desired service level. Further research is required to establish the typical workday demand pattern as a stable and global tool for planning the workforce. 9 References Daskin M S (2011) Service Science: Service Operations for Managers and Engineers, Wiley, Haboken NJ. Margeta J, (2010) Water Supply: Planning, Design, Management and Water Purification; Technical report, Faculty of Civil Engineering and Architecture, University of Split: Split, Croatia (In Croatian). Margiotta R, Cohen H, DeCorla-Souza P (1999) Speed and Delay Prediction Models forplanning Applications, Sixth National Conference on Transportation Planning for Small and Medium- Sized Communities, Spokane, Washington, (1999) McGeoch A. C, (2011). 30 years of travel in Melbourne: 1978/79 and 2007/08, Australasian Transport Research Forum 2011 Proceedings, Adelaide, Australia. Shtub A, Cohen Y (2016) Introduction to Industrial Engineering, CRC press, Boca Raton FL. U.S. Department of Transportation, (2006) Federal Highway Administration. 2006 status of nation s highways bridges and transit- report to congress. www.fhwa.dot.gov/policy/2006cpr/ U.S. Department of Transportation, (2008) Federal Highway Administration. 2008 status of nation s highways bridges and transit- report to congress. www.fhwa.dot.gov/policy/2008cpr/ Yom-Tov GB, and Mendelbaum A (2014) Erlang-R: A Time-Varying Queue with Reentrant Customers, in Support of Healthcare Staffing, Manufacturing & Service Operations Management, 16 (2), 283-299.