SS3751 Soo Hyun Shin SY2513 Sung Woo Yoo JK3362 Jae Yoon Kim XZ2345 Xixi Zhao JL4126 Jun Li

Transcription

1 Queuing Theory Application: Improve Food Distribution Efficiency of City Harvest s Washington Height Mobile Market by at least 20% with Multiple Suggestions SS3751 Soo Hyun Shin SY2513 Sung Woo Yoo JK3362 Jae Yoon Kim XZ2345 Xixi Zhao JL4126 Jun Li

2 Agenda 1. Background & Description 2. Model 3. Suggestions & Simulations

3 Background City Harvest 1. The world s first food rescue organization for people in need - Healthy neighborhood program 2. Mobile markets since Serving fruits and vegetable in low income communities in NYC through farmers market-style distribution 3. Mobile market in Washington Heights - The largest mobile market currently - Around 22,000lbs of food provided (85% of average distribution rate) - Around 1,200 registered people (48% of average attendance)

4 Description 1. Membership - Local community members with proof of home address - Four categories according to the number of family members Category A B C D E Number of people Unregistered 2. Operation - Bi-monthly operation from 9:00 a.m. to 11:00 a.m. - A ticket for each category with their membership card at the market - Market set-up and prepackaging from 8:30 a.m. - # of volunteers: approximately 20-25

5 Washington Heights Mobile Market

6 Setting

7 Objectives 1. Improving serving rate of food-distributing system 2. Reducing Line-up time of waiting area

8 Model Set-up: Stochastic Queuing Basic Inputs indicated by the model Arrival rate : λ, average No. of customers arriving in a unit of time; Serving rate : μ, average No. of customers the server is able to serve in a unit of time Departure rate is 1/ Max(1/ λ, 1/ μ) λ μ, 1/ λ << 1/ μ. The interval between departures is exactly 1/ μ, dependent solely on serving rate

9 Model Set-up: Stochastic Queuing Basic Inputs indicated by the model Arrival rate at each server: λ 1, λ 2,..., λ n Serving rate at each server: μ 1, μ 2,., μ n We are assuming: a). Suffiently large arrival rate b). System in stable status so that no transferring time between stations c). All volunteers have the same energy level and productivity System-level serving time μ =1/ n 1 i=1 Min(P i,d i ) Specifically: P i is the Packing Rate P i, Di is the distributing Rate I i is the indicator function

10 Objective In the context of model To improve the food-distributing speed, namely the overall serving rate μ in part 2 so as to serve more people.

11 Constraints Three main constraints: 1. Market-style operation: standardized vs. market-style 2. Space: U-shape area with lots of limitations 3. Number of volunteers n i=1 Pi=N*pp n i=1 Di=N*pd pp: number of bags packed per unit of time pd: number of people getting food distributed per unit of time

12 Suggestions To improve ū, s.t.: 1. Arrange volunteers in a way so that Pi, Di is at the amount when ū is maximized 2. Reduce Min(Pi, D i ) 3. Model Improvement Super Station

13 1. Volunteers Arrangement Maximum achieved when: Pi=Dj, for i=1,2..,5, j=1,2..,5 D 1 = D 2 =D 3 = D 4 = D 5 Pi varied by station: how the food is packed, how easy to pack Observation: Di=10s, ppi=32s (with weighting), ppi=15s (without weighting) Pi=ppi/n Notes: Sufficient scales: # of scales = # of volunteers packing Large enough plate

14 2. Reduce Min(Pi, D i )

15 2. Reduce Min(Pi, D i ) Pack in 2 amounts instead of 4 Observations: Sensible about the amount if continuously packing the same amount 4 categories get mixed up easily Small bag Large bag

16 2. Reduce Min(Pi, D i )

17 2. Reduce Min(Pi, D i )

18 3. Model Improvement

19 Simulation - Methodology

20 Simulation: Results Original Case Probability of skipping: 0.2 Arrivals <100: Max(N(9,1.2), 6) Arrivals : Max(N(21,6), 9) Arrivals >400: Max(N(27,9), 15) Improved Case Probability of skipping: 0.2 Arrival <100: Max(N(7.5,1.2), 6) Arrivals : Max(N(15,6), 9) Arrivals >400: Max(N(21,9), 15) 2hr - 460ppl 2.5hr - 550ppl 2hr - 560ppl ( 22%) 2.5hr - 660ppl ( 21%)

21 Objectives 1. Improving serving rate of food-distributing system 2. Reducing Line-up time

22 Reducing Line-up time 1. Scanning at the designated area from the i. time Nutrient the facts market opens 1Distributing Flyer, brochure ii. Cooking recipe iii. Distribution rate 2. Time slotting based on participants preference 2Inviting musicians and artists Time 3. Providing distraction Number of people 9:00 9: people 9:30 10: people 10:00 10: people 10:30-11:00 -

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