1. Previously Optimization Probability Review Inventory Models Markov Decision Processes Queues

2. Logistics Office Hours: –Friday 2-3? Monday: –Case: staffing call-center for hospital Will post: –Case details –Sample problems for final

3. Agenda Simulation of Queues Review

4. Queues ORMM Excel add-in

5. How It Works (15.5) Keep track of customers –Not discretizing time –Called “Discrete Event Simulation” Define for nth customer –A(n), Q(n), S(n), T(n) arrival, waiting, service and total time Calculate them using (n-1)th customer –A(n), S(n) realization of random variables –Q(n) = max {0, T(n-1) - A(n) } –T(n) = Q(n) + S(n)

6. Simulation Review Confidence intervals –For E[X],  [X], P(E) Creating simulations in Excel –Random numbers, Queues Optimizing Simulations What is the confidence interval? What sample size is necessary? Run and interpret a queueing simulation. Tweak an existing simulation

7. Queuing Review Networks of M/M/s –W, W q, L, L q G/G/s (with Excel add-in / simulation) –W, W q, L, L q, P(T q >c) –distributions Optimize cost, service, #servers

8. Inventory Review Newsvendor model Base-stock model Economic Order Quantity Which model is appropriate? How much inventory to have?

9. MDP Review When appropriate? What does f(i) mean? Given MDP solution, what is the optimal action? Implement it –Given reward R(i,k) –Transition probabilities P(j | i,k) Tweak an existing MDP

10. Children’s Hospital Case *Hillier and Lieberman

11. Children’s Hospital Case Appointments, referrals a mess –Each department separate –Some phone number not listed –Not clear which department appropriate –Lack of communication –Takes time, annoys clients Wants to consolidate appointment scheduling into one call-center.

12. Organizational Issues Jobs? Departments must adopt centralized appointment system –Loss of control –Loss of flexibility

13. Operational Issues How many people do we need? English and Spanish speakers? Part time vs. full time? Staffing schedule? Wait times? Costs?

14. Data Available Avg. # calls per hour % of callers speak Spanish Wages Staff availability