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Transcript of 1 Transportation Network Optimization Project GPRE Inc. Group Members: Aditya Nambiar, Anuj Gandhi,...
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Transportation Network Optimization Project
GPRE Inc.
Group Members: Aditya Nambiar, Anuj Gandhi, Ashwin Mishra, Daksh Sabharwal, Graham Thomas, Sandeep Prakash
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Overview
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Overview
• Goal: Develop a tool in Gurobi to optimize transportation network for minimizing weekly freight costs
• Problem Formulation• Operational Implementation• Financial Benefits• Adding Value• Truck Premium Discussion
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Problem Formulation
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• Rates[plant][destination][rail_road] = Rates for transport from plant to destination through a particular rail road/route
• Min Cars [plant][destination][rail_road] = Min Cars in a plant
• Max Cars [plant][destination][rail_road] = Max Cars in a plant
• Demand [load_no][destination][rail_road] = Demand at a destination
• Carb_Int [plant] = Carbon Intensity for a plant
• Carb_Int [destination] = Carbon Intensity for a destination
• FOB = Flag denoting Shipment is FOB or not
Parameters:
Problem Formulation
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Problem Formulation - Model
Variable:
• Car_Quant [load_no][plant][destination][rail_road] = No. of cars from a plant to destination through a particular rail road for a load no.
Objective Function:
Minimize
Sum (over load_no, plant, destination, rail_road) { Rates[plant][destination][rail_road]* Car_Quant [load_no][plant][destination][rail_road] }
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Constraints:
For meeting the customer demand for all individual destinations…
Sum (over all plants, rail_road) { Car_Quant [load_no][plant][destination][rail_road] } = Demand [load_no][destination][rail_road]
Minimum cars out of plants requirement…
Sum (over load_no, plant, rail_road) { Car_Quant [load_no][plant][destination][rail_road] } > = Min Cars [plant][destination][rail_road]
Maximum cars out of plant requirement…
Sum (over load_no, plant, rail_road) { Car_Quant [load_no][plant][destination][rail_road] } <= Max Cars [plant][destination][rail_road]
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Problem Formulation - Constraints
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FOB constraint: Here sum of quantity going from plants of a particularFOB region should be equal to demand of the load_no for the customer…
if (FOB){ Sum (over plants, rail_road) { Car_Quant [load_no][plant][destination][rail_road] } = Demand[load_no][destination][rail_road] }
Carbon intensity constraint: Carbon intensity of the plant sending the shipment should be less than or equal carbon intensity requirement of the destination
Sum (over plant, rail_road) {Carb_Int [destination] * Car_Quant [load_no][plant][destination][rail_road] >= {Car_Quant [load_no][plant][destination][rail_road] * Carb_Int [plant] }
Problem Formulation - Constraints
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Mock Nominations Constraint: Here sum of quantity going to destinations of a particular destination region should be equal to demand of the load_no for the customer…
If (Region)
{ Sum (over plants, rail_road, destination) { Car_Quant[load_no][plant][destination][rail_road] } = Demand [load_no][destination-region][rail_road]}
Non-Negativity and Integer constraints
Car_Quant [load_no][plant][destination][rail_road] are positive integers
Problem Formulation - Constraints
1010
Optimization Tool
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• Inputs – Shipments & Origin Threshold
• Output – Optimized Shipments
Optimization Tool - Input / Output
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Operational Implementation
• To be used weekly once to optimize delivery of shipments
• Integrated with ShipXpress where user enters shipment data and min-max for plants
• Users will use the tool via ShipXpress to determine the optimum amount to be sold in Spot Market opportunity
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Destination Carbon Intensity
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Cost Comparison:
Financial Benefits
Net Weekly Savings: $40,000
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Origin Transportation Costs
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• Scalability – Feature to incorporate Carbon Intensity for All
locations
– Number of Plants/Destinations can be increased
– Provision to increase number of carriers to four
• Mock Nominations – Gives optimal destination to ship in a
region
Value Additions
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Suggestions
• Location parameters should be consistent across all tables to get best results
• Incorporating Spot Market / Truck Premium opportunity in the tool
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Current Model w/o Truck Premium
Plants
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
Min-Max
100
30
40
55
30
60
45
75-85
95-115
105-115
Rail Cars
100
30
40
55
30
60
45
75
96
105
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Transportation Cost - Premium
Plants
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
New Min-Max
94-100
30-32
40-42
55-57
30
60
45
75-85
95-115
105-115
Optimized Rail Cars
94
30
40
55
30
60
45
77
98
107
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Spot Price: 0.8Truck Rate in terms of Rail Car: 1000Truck Premium Demand: 6
PlantsP1P2P3P4P5P6P7P8P9
P10
Cost0.1
0.110.090.1
0.150.2
0.250.140.170.19
New Min-Max
94-10030-3240-4255-57
306045
75-8595-115
105-115
Spot Price - Cost
0.80.690.710.7
0.650.6
0.550.660.630.61
Premium Quantity
q1q2q3q4q5q6q7q8q9
q10
Premium Cost0.7*q1
0.69*q20.71*q30.7*q4
0.65*q50.6*q6
0.55*q70.66*q80.63*q9
0.61*q10
Comprehensive Model including Costs
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Cost per Plant0.1*Q1 + 6300*Q10.11*Q2 + 6632*Q20.09*Q3 + 5000*Q30.1*Q4 + 5200*Q40.15*Q5 + 6500*Q50.2*Q6 + 6800*Q60.25*Q7 + 5500*Q70.14*Q8 + 4900*Q80.17*Q9 + 5000*Q90.19*Q10 + 5100*Q10
Total Cost0.1*Q1 + 6300*Q1 - 0.7*q1 + q1*10000.11*Q2 + 6632*Q2 - 0.69*q2 + q2*10000.09*Q3 + 5000*Q3 - 0.71*q3 + q3*10000.1*Q4 + 5200*Q4 - 0.7*q4 + q4*10000.15*Q5 + 6500*Q5 - 0.65*q5 + q5*10000.2*Q6 + 6800*Q6 - 0.6*q6 + q6*10000.25*Q7 + 5500*Q7 - 0.55*q7 + q7*10000.14*Q8 + 4900*Q8 - 0.66*q8 + q8*10000.17*Q9 + 5000*Q9 - 0.63*q9 + q9*10000.19*Q10 + 5100*Q10 - 0.61*q10 + q10*1000
Comprehensive Model including Costs Contd.
Constraint: 1. qi <= spot-market demand near each plant2. All qi’s are Non-negative
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Thank You!
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Questions