Chapter 13 Part 2 - Chapter 13 Simulation – Part 2...

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Unformatted text preview: Chapter 13 Simulation – Part 2 Brew-Thru Example Service entrance Car 3 Car 2 Service lane Car 1 Exit Waiting area Note: Customers balk if more than 4 cars in line Monte Carlo Simulation 1. Set up probability distributions for the exogenous variables 2. Build cumulative probability distributions 3. Establish an interval of random numbers for each exogenous variable 4. Generate a set of random numbers 5. Simulate the situation for many trials Brew-Thru Example Number of customers Number arriving every 3 min. arriving 0 1 2 3 4 Probability 0.19 0.39 0.19 0.15 0.08 1.00 Brew-Thru Example Order size Average time Average Average Average Probability to fill order profit to Small Medium Large 0.39 0.50 0.11 1.00 3 min. 6 min. 9 min. $ .75 1.50 1.50 3.00 3.00 Monte Carlo Simulation 1. Set up probability distributions for the exogenous variables 2. Build cumulative probability distributions 3. Establish an interval of random numbers for each exogenous variable 4. Generate a set of random numbers 5. Simulate the situation for many trials Brew-Thru Example # of customers arriving every 3 min. Prob. Cumulative Prob. Interval 0 1 2 3 4 0.19 0.39 0.19 0.15 0.08 1.00 0.19 0.58 0.77 0.92 1.00 0<RN<=0.19 0.19<RN<=0.58 0.58<RN<=0.77 0.77<RN<=0.92 0.92<RN<=1.00 Brew-Thru Example Order Order size size Small Medium Large Prob. 0.39 0.50 0.11 1.00 Cumulative Cumulative probability probability 0.39 0.89 0.89 1.00 1.00 Interval 0<RN<=0.39 0.39<RN<=0.89 0.89<RN<=1.00 Monte Carlo Simulation 1. Set up probability distributions for the exogenous variables 2. Build cumulative probability distributions 3. Establish an interval of random numbers for each exogenous variable 4. Generate a set of random numbers 5. Simulate the situation for many trials Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 Brew-Thru Example Period Period 1 2 3 4 5 6 7 8 Service Service completed? completed? Profit Profit Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 yes yes Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 yes .41 yes Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 Med yes .41 Med 2 yes Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 Med yes .41 Med 2 yes 0 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 Med yes .41 Med 2 yes 0 1 Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No --- Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 Med yes .41 Med 2 yes 0 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 Med yes .41 Med 2 yes 0 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 Med yes .41 Med 2 yes no no 0 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 Med yes .41 Med 2 yes no -- -- -no 0 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 Med yes .41 Med 2 yes no -- -- -no 0 0 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 Med yes .41 Med 2 yes no -- -- -no 0 0 1 2 Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No Yes(1) --1.50 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 Med yes .41 Med 2 yes no -- -- -no 0 0 1 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 Med yes .41 Med 2 yes no -- -- -no 0 0 1 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 Med yes .41 Med 2 yes no -- -- -no yes yes 0 0 1 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 yes yes no no yes yes .41 -.73 Med 2 Med -- -- 0 0 1 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 yes yes no no yes yes .41 -.73 Med 2 Med -Small 1 Small -- 0 0 1 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 yes yes no no yes yes .41 -.73 Med 2 Med -Small 1 Small -- 0 0 0 1 2 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 yes yes no no yes yes .41 -.73 Med 2 Med -Small 1 Small -- 0 0 0 1 2 1 Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No Yes(1) Yes(2) --1.50 .75 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 2 .32 1 .15 0 .95 yes yes no no yes yes .41 -.73 Med 2 Med -Small 1 Small -- 0 0 0 1 2 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 2 1 0 4 yes yes no no yes yes .41 -.73 Med 2 Med -Small 1 Small -- 0 0 0 1 2 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 2 1 0 4 yes yes no no yes yes yes yes .41 -.73 Med 2 Med -Small 1 Small -- 0 0 0 1 2 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 2 1 0 4 yes yes no no yes yes yes yes .41 -.73 .50 Med 2 Med -Small 1 Small -- 0 0 0 1 2 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 2 1 0 4 yes yes no no yes yes yes yes .41 -.73 .50 Med 2 Med -Small 1 Small Med Med -- 0 0 0 1 2 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 2 1 0 4 yes yes no no yes yes yes yes .41 -.73 .50 Med 2 Med -Small 1 Small Med 2 Med -- 0 0 0 0 1 2 1 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 2 1 0 4 yes yes no no yes yes yes yes .41 -.73 .50 Med 2 Med -Small 1 Small Med 2 Med -- 0 0 0 0 1 2 1 4 Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No Yes(1) Yes(2) No --1.50 .75 Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No Yes(1) Yes(2) No --1.50 .75 --- Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 2 1 0 4 yes yes no no yes yes yes yes .41 -.73 .50 Med 2 Med -Small 1 Small Med 2 Med -- 0 0 0 0 1 2 1 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 2 1 0 4 2 yes yes no no yes yes yes yes .41 -.73 .50 Med 2 Med -Small 1 Small Med 2 Med -- 0 0 0 0 1 2 1 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 2 1 0 4 2 yes yes no no yes yes yes yes no no .41 -.73 .50 Med 2 Med -Small 1 Small Med 2 Med -- 0 0 0 0 1 2 1 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 2 1 0 4 2 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 1 2 1 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 2 1 0 4 2 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 2 1 0 4 2 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 4 Brew-Thru Example Period Period Service Service completed? completed? Profit Profit 1 2 3 4 5 6 7 No Yes(1) Yes(2) No Yes(3) --1.50 .75 --- Brew-Thru Example Period Period Service Service completed completed ? Profit Profit 1 2 3 4 5 6 7 No Yes(1) Yes(2) No Yes(3) --1.50 .75 --1.50 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 1 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 1 yes yes no no yes yes yes yes no no yes yes .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 1 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 4 yes .89 yes Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 1 yes yes no no yes yes yes yes no no .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med --- -- 0 0 0 0 2 1 2 1 4 4 Large yes .89 Large yes Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 1 yes yes no no yes yes yes yes no no -Large yes .89 Large 3 yes .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med -- -- 0 0 0 0 2 1 2 1 4 4 Brew-Thru Example # of # of of of Order Service Lost Number New Service Order Service Lost Number New Service avail? Period RN Cust. avail? RN Size Periods Cust. waiting Size Periods waiting Period 1 2 3 4 5 6 7 .63 .32 .15 .95 .68 .23 2 1 0 4 2 1 yes yes no no yes yes yes yes no no -Large yes .89 Large 3 yes .41 -.73 .50 -- Med 2 Med -Small 1 Small Med 2 Med -- -- 0 0 0 0 2 0 1 2 1 4 4 4 Brew-Thru Example Period Period Service Service completed completed ? Profit Profit 1 2 3 4 5 6 7 No Yes(1) Yes(2) No Yes(3) No --1.50 .75 --1.50 --- Brew-Thru Example Total revenue =$8.25 Average revenue per period = 8.25/6 = $1.38 Average profit per customer = 8.25/6 = $1.38 Opportunity cost due to balking = 0 (1.25) = $ 0 Total profit = 8.25 – 0 = $8.25 ...
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