Minimising a sum of costs:

- Total fixed cost of operating plants and DCs

- Total variable cost of covering the capacity of DCs at plants and the demand of retailers at DCs - Total cost of delivering products in

each route throughout the network

Constraints:

1. Each demand node on one route 2. Limits the length of each route 3. Assigns each route to one facility

4. Any route entering a node must exit the same node 5. A route can operate out of only one facility

6. Defines the flow into a facility from the supply points (in terms of demand) 7. Restricts throughput at each facility to the maximum allowed at that site and

links the flow variables and facility location variables

8. If pathkK leaves customer nodeiIand facilityjJ , then customeri must be assigned to facilityj

9. AHP-integrated constraint (green constraint), considering the DMs’ priorities Integer constraints;

Non-negativity constraints

Two phased DoE-guided solution approach

Execution platform: modeFRONTIER®

Initial population table: generated by DoE Optimisers: Multi-objective GA-based: MOGA-II,

NSGA-II; Multi-objective PS-based: MOSPSO

Final results Modelling Solution approach Analysis of Results Case of the demand side of an Irish dairy market supply chain

DoE generates the initial population of 50 for optimisers

Phase-I results:

- FL decision regarding DCs; - VR decision regarding plants,

DCs, retailers Phase-II results: - VR decision regarding retailers Analysis of results Pareto efficiency: - analyses realistic solutions - analyses Pareto efficiency TOPSIS

- used for ranking selected solutions - considers DM’s

opinions

Identical optimiser setting for Phase-I and Phase-II

Outcomes

Geographical maps

- realistic set of low - carbon low-cost vehicle routes are geographically mapped Scenario analysis - analyses effect of opening closed routes on CO2 emission and costs Phase-I considers plants, DCs, and retailers ANOVA

- compares the means of two or more groups of the optimised realistic solutions

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Part I: Modelling

5.2. Three-Layer Multi-Objective AHP-Integrated Location-Routing

The three-layer low-carbon MO-LRP is formulated integrating AHP with a 0-1 programming approach. The purpose of this model is to minimise the level of CO2 emission caused from transportation and minimise a combination of costs on the demand side of three-layer supply chain networks. This model is generic and can be extended to any three-layer supply chain network.

The proposed model is formulated based on a set of realistic assumptions (Box 5.1). The three-layer MO-LRP considers three key players on the demand side of a SC, viz., plants, DCs and retailers. Two fleets of vehicles/trucks are considered for transporting the products throughout the SC network. A fleet of trucks transport products from plants to DCs, and a different fleet of trucks transport products from DCs to retailers and then from retailers to other retailers. Each route may be a combination of different types of roads. In every country different speed limits apply to different types of roads. Speeds in different types of routes are captured in the model by the use of an appropriate variable.

Box 5.1 Assumptions for the three-layer MO-LRP

 Demand side of the SC is considered

 Multiple facilities, multiple retailers and single product are considered  Location of facilities (plants, DCs) are known

 Retailers have known geographical locations  Plants are always open

 DCs can be open or closed

 Vehicle routes have known geographical start and end points  Vehicle routes are all real and feasible

 Multi-stop routes from DCs to retailers and from retailers to retailers are considered  Routes are capacitated

 Each vehicle route is served by one or more vehicle based on the demand at the dest i- nation

 Two fleets of vehicles/trucks are considered

 Heavy duty trucks/Heavy Goods Trucks (HGVs), class 7 are used for transporting products are considered

 If the product is perishable t he vehicle is refrigerated HGV

 Fuel consumption of vehicles is dependent on the total mass of the vehicles

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95 is assumed in the model

 Consumption of the fuel is dependent on the speed of the vehicle/trucks  Truck drivers’ wage is dependent on the speed of the trucks

 The average wage of a truck driver ( €/hr) is considered for a specific period of time  A portion of variable cost is dependent on the capacity at the DC locations and de-

mand at the retailer locations.

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Table 5.1 Nomenclature

Sets and indices Parameters (cont’d)

I Set of retailer locations indexed by i

sj

d Distance from plantsSto DCjJ in km

J Set of DCs indexed by j

ji

d Distance from DC jJto retaileriIin km

S Set of processing plants indexed by s

ii

d

Distance from retaileriIto retaileriI in km

P Set of pointsS J I indexed by sS,

jJ,iI

sj

u Number of vehicles needed to transport the products; from processing plantsS to DC K Set of paths defined in set P

ji

u Number of vehicles needed to transport the products; from DC jJ to retaileriI M Set of attributes in AHP decision matrix

(CO2 emission and costs) indexed by m ii

u

Number of vehicles needed to transport the products; from retaileriIto retaileriI

N Set of alternative in AHP decision matrix

(trucks) indexed by n



k

Length of combined routes limit

Parameters _z Speed in different roads in km

s

f

Sum of fixed cost of locating at plant jJ

mn

In document Low-carbon multi-objective location-routing in supply chain network design (Page 113-116)