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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

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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