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MGTSC 352 Lecture 25: Congestion Management MEC example Manufacturing example.

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Presentation on theme: "MGTSC 352 Lecture 25: Congestion Management MEC example Manufacturing example."— Presentation transcript:

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2 MGTSC 352 Lecture 25: Congestion Management MEC example Manufacturing example

3 MEC (p. 181) One operator, two lines to take orders –Average call duration: 4 minutes exp –Average call rate: 10 calls per hour exp –Average profit from call: $24.76 Third call gets busy signal How many lines/agents? –Line cost: $4.00/ hr –Agent cost: $12.00/hr –Avg. time on hold < 1 min.

4 Modeling Approaches Waiting line analysis template Simulation We’ll use both for this example To Excel …

5 The Laws of Queueing eff =  (1 – PrBalk)  Effective service rate = entering rate * % sticking around  = eff /(s  )  utilization = demand / capacity W = Wq + 1/   Time in the system = time in the Q + time in service L = = Lq + S*   # people in the system = # in the line + # in service  # in service = # servers * probability of server being busy Little’s Law: L = eff W Little’s Law for the queue: Lq = eff Wq Little’s Law for the servers: s*  = eff (1/  )

6 Manufacturing Example (p. 184) Machine (1.2 or 1.8/minute) 1/minute Poisson arrivals Exponential service times

7 Manufacturing Example Arrival rate for jobs: 1 per minute Machine 1: –Processing rate: 1.20/minute –Cost: $1.20/minute Machine 2: –Processing rate: 1.80/minute –Cost: $2.00/minute Cost of idle jobs: $2.50/minute Which machine should be chosen? To Excel …

8 Manufacturing Example Cost of machine 1 = $1.20 / min. + ($2.50 / min. / job)  (5.00 jobs) = $13.70 / min. Cost of machine 2 = $2.00 / min. + ($2.50 / min. / job)  (1.25 jobs) = $5.13 / min.  Switching to machine 2 saves money – reduction in lost revenue outweighs higher operating cost.

9 Cost of waiting (Mach. 1) Method 1: –Unit cost × L = ($2.50 / min. job)  (5.00 jobs) = $13.70 / min Method 2: –Unit cost × × W  = ($2.50 / min. job)  (5.00 min)  (1 job/min) = $13.70 / min Little’s LawL = × W

10 Manufacturing Example 2 (p. 184) Machine (1.2 or 1.8/minute) 1.1/minute Poisson arrivals Exponential service times Changed from 1 to 1.1 Reminder: Cost of idle jobs = holding cost = $2.50 / minute / job

11 Manufacturing Example 3 (p. 184) Machine (1.2 or 2 at.6/min) 1/minute Poisson arrivals Exponential service times Reminder: Cost of idle jobs = holding cost = $2.50 / minute / job Two machines, each taking twice as long

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