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A conventional two-layer Location-Routing Problem (LRP) on the demand side of a SC is found in Berger (1997) and Daskin et al. (2005). A proposed low-carbon/green two- layer Multi-Objective-Location Routing Problem (MO-LRP) improves the conventional models of Berger (1997) and Daskin et al. (2005) and contributes to the literature in the field of low-carbon capacitated two-layer LRPs.
The demand side of a two-layer SC with two facilities and multiple retailers is illustrated in Fig. 4.1. This two-layer SC network consists of plants and retailers. The flow of materials is also indicated in Fig. 4.1. The physical distribution of a two-layer SC network is the subject of analysis in this chapter.
Figure 4.1 A two-layer SC with multiple retailers (Adapted from: Schroeder et al. 2013)
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The main contribution of this chapter is three inter-linked aspects of the proposed variant of the two-layer MO-LRP, viz.:
(i) a green location-routing model is designed by integrating AHP with 0-1 mixed integer programming
(ii) a Design of Experiment (DoE) guided meta-heuristic-based robust solution approach under the modeFRONTIER® commercial solver is provided and
(iii) the decision-makers’ (DMs’) prioritisation and subsequent ranking of the realistic solutions are examined using Pareto frontiers, ‘Technique for Order Preference by Similarity to Ideal Solution’ (Hwang and Yoon 1981) (TOPSIS) and various scenarios of the green location-routing are featured.
This chapter is divided into three connected parts. Part-I presents the integrated green MO-LRP. Part-II elucidates the DoE-guided meta-heuristic-based robust solution approach under the modeFRONTIER® commercial solver followed by the deployment of a case of a two-layer supply chain. Part-III delineates the DMs’ prioritisation and subsequent ranking of the realistic solutions using Pareto frontiers and TOPSIS. In this part various scenarios of the two-layer routing events are featured by determining alternative possible outcomes. This validates the robustness of the realistic solution sets. The two-layer MO-LRP, its efficient solution approach and analysis of the realistic results contribute to the following aspects on the demand side of the SC in the following ways:
(i) a low-carbon two-layer MO-LRP optimisation model on the demand side of an SC is formulated. Green elements are embedded in an objective function and an AHP- integrated constraint.
(ii) the model allocates retailers to the facilities, i.e., plants.
(iii) the model optimally routes the vehicles to serve the demand-side of the SC.
(iv) the total carbon emission and total cost are optimised. These criteria are conflicting in nature having incommensurable units of measurements.
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(v) the optimisation model is found to be computationally NP-hard. The model is implemented using DoE-guided meta-heuristic disparate optimisers under the modeFRONTIER® commercial solver platform (ESTECO 2013).
(vi) sets of Pareto efficient realistic optimum results are found. The results are then prioritised and ranked by the DMs. TOPSIS assists in evaluating sets of selected results. An analysis reflecting the DMs’ preferences is performed. This analysis reflects the changes in the controlling parameters with respect to the changes in the decision weights of TOPSIS.
(vii) a scenario analysis of the location-routing events is performed. The scenario analysis offers possible alternatives to DMs when the closed routes are forced to open. This shows the robustness of the realistic solution sets.
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Figure 4.2 The formulation of the multi-objective two-layer location-routing model, its solution approach and analysis procedure
Multi-objective integrated two -layer location-routing model
Objective One:
Minimising the total CO2 emission during transporta-
tion of products between processing plants to retail- ers
- Demand and the number of vehicles required for transportation of the products at each node are consid- ered
Objective Two:
1. Minimising the sum of costs:
- Total fixed cost of operating processing plant - Total variable cost of covering the demand of each
retailer at each processing plant
- Total cost of delivering products in each route.
Constraint 1: Each
retailer on one route
Constraint 2: Assigns
routes only to one open facility
Constraint 3: Allots
vehicles using AHP- integrated constraint (Green constraint)
Analysis of Results
ANOVA
- compares the means of two or more groups of the optimised realistic solutions
Pareto Efficiency: - analyses realistic solutions - analyses Pareto Efficiency TOPSIS - ranks selected solutions - considers DM’s opinions Outcomes Scenario Analysis - analyses effect of opening closed routes on CO2 emission and costs Geographical Maps
- realistic set of low - carbon low-cost vehicle routes are geographically mapped AHP is integrated in the 0-1 programming framework as a green constraint. Features: - Capacitated - Multi-objective - Low-carbon - Low-cost - Multi-vehicle/trucks - Single commodity - 0-1 mixed-integer framework - Computationally NP-hard
DoE-guided meta-heuristic based solution approach
Deployment based on disparate optimisers; Number of generations: 50 Case of the demand
side of an Irish dairy market supply chain
Summary of results: - Optimal feasible
results obtained. - Identical and non-
realistic results eliminated.
- A set of feasible results selected.
- Selected realistic results are prioritised and ranked. Execution platform: modeFRONTIER® Optimisers: MOGA-II, NSGA-II, HYBRID, MOPSO, MOSA
DoE generates the initial population of 51 for optimisers
Analysis of results
Modelling
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