1. Service Manager Forecasting (traffic, orders, …) Determine the Level of Service (Newsboy) Estimate Manpower Requirements Shift Scheduling (LP, IP) Assigning Shifts to Workers (Assignment, LP) Job Sequencing and Scheduling

2. Determine the Level of Service Choose Service Criteria (t.d. Average Waiting Time or P(wait>T) P(wait) or P(balking) “Newsboy Problem” Probability Distribution of Demand Estimate Cost Under & Over Usually difficult => Service Level

3. Manpower Requirements Experience Statistics Queueing Theory QTP, Armann Ingolfsson Simulation: @Risk, Crystal Ball Simul8 ProModel

4. Queueing Theory Analytical Models of Waiting Systems Markov-assumptions, i.e. expon (both arrivals & service) Poisson Memoryless Process! Open/Closed System (“Limited Source”) Wait/Balk (“Limited Queue”) Steady State: Arrivals < Capacity

5. Open Systems, M/M/s M/M/1 og M/M/s TEMPLATE.XLS Given: Arrival og cap. s*µ,Ws=1/µ Steady State: U = Ls/s = / s*µ < 1 Key Results: L, Lq, W, Wq L = Lq + Ls, W = Wq + Ws Little: L = *W og Lq= *Wq

6. Optimizing Waiting Systems Given (beside, µ): Cs og Cq Find economical no of servers s Difficult to estimate Cq, therefore service level Other models, see G/G/s (approx) etc LIMITED_Q_TEMPLATE.XLS LIMITED_SOURCE_TEMPLATE.XLS

7. Simulating Waiting Systems Simulation more realistic, “you can always simulate”! Not limited to Markov assumptions Sometimes expensive model building Sometimes too great expectations MULTISERVERSIM.XLS Simul8, ProModel, …

8. Shift Scheduling Scheduling shifts on days/weeks See p. 148 in Rardin Based on known manpower requirements Ex p. 142 í W&A, WorkerScheduling.xls, Work 5 days, off 2 days Determine how many start at time t Min no of employees needed, LP

9. Assigning shifts or tasks “Assignment”, see p 235- in W&A Transport Model with all RHS = 1 Assigning jobs to men/machines Swim Teams, Exam Shedules, Fishing Vessels Landings, … See p 58 in Rardin “Crew Scheduling”, See p 572 in Rardin Assigning Shifts: Employees grade shifts

10. Job Sequencing See p 609- in Rardin Orders or Batches Given: Processing Times, Due Dates Criteria: Flow and/or Due Dates Rules: FCFS, SPT, Slack, EDD Complexity: n jobs to m machines, min setup time, …