ISM 270 Service Engineering and Management Lecture 5: Facility Location, Project Management

Announcements  Project 2 proposal due today  Homework 4 today  Online game next week

Dave Nielsen  Director with StrikeIron  Manages West coast Operations  Background working with developer community  PayPal Pro release  Persistent Web – Internet Consulting

Some key concepts for capacity management  Economic Order Quantity  Queueing Dynamics

Economic Order Quantity  Consider a process that uses raw material Fixed known demand rate r (per minute/day/year) Fixed known demand rate r (per minute/day/year) Orders are in batches, costing: Orders are in batches, costing: Fixed cost B for each batchFixed cost B for each batch Unit cost per item c in batchUnit cost per item c in batch Unit storage/holding cost h to have extra supplyUnit storage/holding cost h to have extra supply Cost (penalty) p for missing order due to stock-outCost (penalty) p for missing order due to stock-out 1. When do you place an order? 2. How big should the batch be?

Economic Order Quantity Fixed known demand rate r (per minute/day/year) Fixed cost B for each batch Unit cost per item c in batch Unit storage/holding cost h to have extra supply Cost (penalty) p for missing order due to stock-out

Economic Order Quantity  Variations: Lead-time from order to arrival of batch Lead-time from order to arrival of batch Uncertain/varying demand Uncertain/varying demand Option to back-order Option to back-order

Forecasting/Estimating

N Period Moving Average Let : MA T = The N period moving average at the end of period T A T = Actual observation for period T Then: MA T = (A T + A T-1 + A T-2 + …..+ A T-N+1 )/N Characteristics: Need N observations to make a forecast Very inexpensive and easy to understand Gives equal weight to all observations Does not consider observations older than N periods

Moving Average Example Saturday Occupancy at a 100-room Hotel Three-period Saturday Period Occupancy Moving Average Forecast Aug Sept

Exponential Smoothing Let : S T = Smoothed value at end of period T A T = Actual observation for period T F T+1 = Forecast for period T+1 Feedback control nature of exponential smoothing New value (S T ) = Old value (S T-1 ) + [ observed error ] or :

Exponential Smoothing Weight Distribution Relationship Between and N (exponential smoothing constant) : N (periods in moving average) :

Saturday Hotel Occupancy Effect of Alpha ( =0.1 vs. =0.5) Actual Forecast

Exponential Smoothing With Trend Adjustment Commuter Airline Load Factor Week Actual load factor Smoothed value Smoothed trend Forecast Forecast error t A t S t T t F t | A t - F t | MAD = 6.7

Exponential Smoothing with Seasonal Adjustment Ferry Passengers taken to a Resort Island Actual Smoothed IndexForecast Error Period t A t value S t I t F t | A t - F t| 2003 January … ….. February … ….. March … ….. April … ….. May … ….. June … ….. July … ….. August … ….. September … ….. October … ….. November … ….. December … January February March

Managing Waiting Lines

Laws of Service  Maister’s First Law: Customers compare expectations with perceptions.  Maister’s Second Law: Is hard to play catch-up ball.  Skinner’s Law: The other line always moves faster.  Jenkin’s Corollary: However, when you switch to another other line, the line you left moves faster.

Essential Features of Queuing Systems Departure Queue discipline Arrival process Queue configuration Service process Renege Balk Calling population No future need for service

Arrival Process StaticDynamic AppointmentsPrice Accept/Reject BalkingReneging Random arrivals with constant rate Random arrival rate varying with time Facility- controlled Customer- exercised control Arrival process

Distribution of Patient Interarrival Times

Temporal Variation in Arrival Rates

Poisson and Exponential Equivalence Poisson distribution for number of arrivals per hour (top view) Poisson distribution for number of arrivals per hour (top view) One-hour One-hour interval interval Arrival Arrivals Arrivals Arrival Arrival Arrivals Arrivals Arrival 62 min. 40 min. 123 min. Exponential distribution of time between arrivals in minutes (bottom view)

Queue Configurations Multiple Queue Single queue Take a Number Enter

Queue Discipline Queue discipline Static (FCFS rule) Dynamic selection based on status of queue Selection based on individual customer attributes Number of customers waiting Round robinPriorityPreemptive Processing time of customers (SPT rule)

Outpatient Service Process Distributions

Capacity Planning and Queuing Models

Queuing System Cost Tradeoff Let: C w = Cost of one customer waiting in queue for an hour C s = Hourly cost per server C = Number of servers Total Cost/hour = Hourly Service Cost + Hourly Customer Waiting Cost Total Cost/hour = C s C + C w L q Note: Only consider systems where Note: Only consider systems where

Queuing Formulas Single Server Model with Poisson Arrival and Service Rates: M/M/1 1. Mean arrival rate: 2. Mean service rate: 3. Mean number in service: 4. Probability of exactly “n” customers in the system: 5. Probability of “k” or more customers in the system: 6. Mean number of customers in the system: 7. Mean number of customers in queue: 8. Mean time in system: 9. Mean time in queue:

Queuing Formulas (cont.) Single Server General Service Distribution Model: M/G/1 Mean number of customers in queue for two servers: M/M/2 Relationships among system characteristics:

Congestion as With: Then:

Single Server General Service Distribution Model : M/G/1 1. For Exponential Distribution: 2. For Constant Service Time: 3. Conclusion: Congestion measured by L q is accounted for equally by variability in arrivals and service times.

General Queuing Observations 1. Variability in arrivals and service times contribute equally to congestion as measured by L q. 2. Service capacity must exceed demand. 3. Servers must be idle some of the time. 4. Single queue preferred to multiple queue unless jockeying is permitted. 5. Large single server (team) preferred to multiple-servers if minimizing mean time in system, W S. 6. Multiple-servers preferred to single large server (team) if minimizing mean time in queue, W Q.

Managing Capacity and Demand

Segmenting Demand at a Health Clinic Smoothing Demand by Appointment Scheduling Day Appointments Monday 84 Tuesday 89 Wednesday 124 Thursday 129 Friday 114

Hotel Overbooking Loss Table Number of Reservations Overbooked Number of Reservations Overbooked No- Prob- shows ability Expected loss, $

Daily Scheduling of Telephone Operator Workshifts Scheduler program assigns tours so that the number of operators present each half hour adds up to the number required Topline profile Tour

LP Model for Weekly Workshift Schedule with Two Days-off Constraint Schedule matrix, x = day off Operator Su M Tu W Th F Sa 1 x x … … … …... 2 … x x … … … … 3 …... x x … … … 4 …... x x … … … 5 … … … … x x … 6 … … … … x x … 7 … … … … x x … 8 x … … … … … x Total Required Excess

Seasonal Allocation of Rooms by Service Class for Resort Hotel First class Standard Budget Percentage of capacity allocated to different service classes 60% 50% 30% 20% 50% Peak Shoulder Off-peak Shoulder (30%) (20%) (40%) (10%) Summer Fall Winter Spring Percentage of capacity allocated to different seasons 30% 20% 10% 30% 50% 30%

Demand Control Chart for a Hotel Expected Reservation Accumulation 2 standard deviation control limits

Yield Management Using the Critical Fractile Model Where x = seats reserved for full-fare passengers d = demand for full-fare tickets p = proportion of economizing (discount) passengers C u = lost revenue associated with reserving one too few seats at full fare (underestimating demand). The lost opportunity is the difference between the fares (F-D) assuming a passenger, willing to pay full-fare (F), purchased a seat at the discount (D) price. C o = cost of reserving one to many seats for sale at full-fare (overestimating demand). Assume the empty full-fare seat would have been sold at the discount price. However, C o takes on two values, depending on the buying behavior of the passenger who would have purchased the seat if not reserved for full-fare. if an economizing passenger if a full fare passenger (marginal gain) Expected value of C o = pD-(1-p)(F-D) = pF - (F-D)

Next Week: Littlefield Challenge  Scenario handed out: Managing testing system