University:
California State University, Northridge
Course:
SOM 686 | Operations Management
Academic year:

2024
Views:

55

Pages:

12
Author:

absolument20yzj

Safety Capacity Capacity Investment Decisions The Economics of Buffer Capacity Cost of servers wages =$20/hour Cost of leasing a telephone line=$5 per line per hour Cost of lost contribution margin =$100 per blocked call Cost of waiting by callers on hold =$2 per minute per customer Total Operating Cost is $386.6/hour 40 Example 8.9 - Effect of Buffer Capacity on Total Cost Safety Capacity 41 Number of lines n 5 6 7 8 9 Number of CSR’s c 1 1 1 1 1 Buffer capacity K=n-c 4 5 6 7 8 Cost of servers ($/hr)=20c 20 20 20 20 20 Cost of tel.lines ($/hr)=5n 25 30 35 40 45 Blocking Probability Pb (%) 10.04 7.71 6.03 4.78 3.83 Lost margin = $100RiPb 200.8 154.2 120.6 95.6 76.6 Average number of calls in queue Ii 1.23 1.52 1.79 2.04 2.27 Hourly cost of waiting=120Ii 147.6 182.4 214.8 244.8 272.4 Total cost of service, blocking and waiting ($/hr) 393.4 386.6 390.4 400.4 414 Safety Capacity Example 8.10 - The Economics of Processing Capacity The number of line is fixed: n=6 The buffer capacity K=6-c c K Blocking Pb(%) Lost Calls RiPb (number/hr) Queue length Ii Total Cost ($/hour) 1 5 7.71% 1.542 1.52 30+20+(1.542x100)+(1.52x120)=386.6 2 4 0.43% 0.086 0.16 30+40+(0.086x100)+(0.16x120)=97.8 3 3 0.09% 0.018 0.02 30+60+(0.018x100)+(0.02x120)=94.2 4 2 0.04% 0.008 0.00 30+80+(0.008x100)+(0.00x120)110.8 42 Safety Capacity Variability in Process Performance Why considering the average queue length and waiting time as performance measures may not be sufficient? Average waiting time includes both customers with very long wait and customers with short or no wait. We would like to look at the entire probability distribution of the waiting time across all customers. Thus we need to focus on the upper tail of the probability distribution of the waiting time, not just its average value. 43 Safety Capacity Example 8.11 - WalCo Drugs One pharmacist, Dave Average of 20 customers per hour Dave takes Average of 2.5 min to fill prescription Process rate 24 per hour Assume exponentially distributed interarrival and processing time; we have single phase, single server exponential model Average total process is; T = 1/(Rp – Ri) = 1/(24 -20) = 0.25 or 15 min 44 Safety Capacity Example 8.11 - Probability distribution of the actual time customer spends in process (obtained by simulation) 14000 10000 8000 6000 4000 2000 Total Time in Process 74 68 62 56 50 44 38 32 26 20 14 8 0 2 Frequency 12000 45 Safety Capacity Example 8.11 - Probability Distribution Analysis 65% of customers will spend 15 min or less in process 95% of customers are served within 40 min 5% of customers are the ones who will bitterly complain. Imagine if they new that the average customer spends 15 min in the system. 35% may experience delays longer than Average T,15min 46 Tduedate Service Promise: , Service Level & Safety Time Safety Capacity 47 SL; The probability of fulfilling the stated promise. The Firm will set the SL and calculate the Tduedate from the probability distribution of the total time in process (T). Safety time is the time margin that we should allow over and above the expected time to deliver service in order to ensure that we will be able to meet the required date with high probability Tduedate = T + Tsafety Prob(Total time in process <= Tduedate) = SL Larger SL results in grater probability of fulfilling the promise. Safety Capacity Due Date Quotation Due Date Quotation is the practice of promising a time frame within which the product will be delivered. 48 We know that in single-phase single server service process; the Actual total time a customer spends in the process is exponentially distributed with mean T. SL = Prob(Total time in process <= Tduedate) = 1 – EXP( - Tduedate /T) Which is the fraction of customers who will no longer be delayed more than promised. Tduedate = -T ln(1 – SL) Safety Capacity Example 8.12 - WalCo Drug WalCo has set SL = 0.95 Assuming total time for customers is exponential Tduedate = -T ln(1 – SL) Tduedate = -T ln(0.05) = 3T Flow time for 95 percentile of exponential distribution is three times the average T Tduedate = 3 * 15 = 45 95% of customers will get served within 45 min Tduedate = T + Tsafety Tsafety = 45 – 15 = 30 min 30 min is the extra margin that WalCo should allow as protection against variability 49 Safety Capacity Relating Utilization and Safety Time: Safety Time Vs. Capacity Utilization Capacity utilization ρ Waiting time Ti Total flow time T= Ti + Tp Promised time Tduedate Safety time Tsafety = Tduedate – T 60 % 1.5Tp 2.5Tp 7.7Tp 5Tp 70% 2.33Tp 3.33Tp 10Tp 6.67Tp 50 80% 4Tp 5Tp 15Tp 10Tp 90% 9Tp 10Tp 30Tp 20Tp Higher the utilization; Longer the promised time and Safety time Safety Capacity decreases when capacity utilization increases Larger safety capacity, the smaller safety time and therefore we can promise a shorter wait Safety Capacity Managing Customer Perceptions and Expectations Uncertainty about the length of wait (Blind waits) makes customers more impatient. Solution is Behavioral Strategies Making the waiting customers comfortable Creating distractions Offering entertainment 51

Capacity Planning in Services Industry, Part 3

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