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Chapter One presented an introduction to the study outlining its background, scope, aims and objectives and significance. Chapter Two presented a survey of the literature in the main context of SC network design. This chapter presents and overview of the adopted methodology to meet the aims and objectives of the research.

The chapter outlines as follows. The research method is introduced in section 3.2. Section 3.3 describes the modelling approach. Section 3.4 deals with solution approach while section 3.5 describes the data analysis approach. A summary on the chapter is presented in section 3.6.

3.2. Research Method

This research is focused on ‘Integrated Location-Routing’, one of the Facility Location integrated models in Supply Chain Network design. Facility Location is a well- established subject area in Operations Research. Thus, in order to explore and enquire the aims and objectives of this study mathematical optimisation is adopted. Mathematical optimisation involves three main steps in Operations Research: i) Modelling approach, ii) Solution approach and iii) Analysis approach. In the following section these main steps of the methodology for this research are briefly introduced.

3.3. Modelling Approach

One of the main aims of this research is to improve Berger’s (1997) two-layer LRP and Perl’s (1983) three-layer LRP. The improvement is focused on inclusion of the green elements into these models. The ‘green’ element in this research is defined as ‘minimising CO2 emission from transportation within the two and three SCNs’. The focus is on developing and introducing two components to the two and three layer

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LRPs: developing a new green objective function and developing a new green constraint.

Conventionally two and three layer LRPs are single-objective primarily focused on cost. The developed models are multi-objective with two objective functions. The traditional objective function exists which focuses on ‘costs’. The green objective function aims to minimise the ‘CO2 emission from transportation’. These two objective functions work simultaneously in order to find an optimum solution space to the developed models. The green constraint leads the model to find the best transportation option considering the DMs’ priorities. In the construction of this constraint the DMs’ priority regarding the importance and weight of ‘cost’ and ‘CO2 emission’ when it comes to transportation (i.e. types of trucks) is considered. Contribution of this constraint to the model is offering a transportation option tailored based on the DMs’ priorities and within the main framework of the model. MCMD techniques are considered to construct this constraint.

3.4. Solution Approach and Solution Platform

Literature reveals that two-layer LRPs are computationally NP-hard problems. There is no unique solution to these types of models but a feasible solution area. In different attempts a variety of heuristics/meta-heuristics in one or multi-phase algorithms have been implemented to solve LRPs.

Two-layer LRPs are solvable in a one phase solution approach while multi-phase solution approaches are implemented in order to solve three-layer LRPs. Typically the multi-phase solution algorithms break the problem into its main components (facility location, allocation of customers to facilities, vehicle routing). These algorithms follow a consecutively connected multi-phase approaches to solve the three-layer LRPs. The Perl (1983) three-layer LRP has been solved by him using a three phased heuristic. In another attempt, Wu et al. (2002) solves the Perl’s (1983) three-layer LRP in two phases.

One of the main aims of this study is to find or offer an effective solution approach for both the two-layer and the three-layer MO-LRPs. The two-layer MO-LRP is an exten- sion of the Berger (1997) LRP and the three-layer MO-LRP is an extension of the Perl

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(1983) and a variation of the two-layer MO-LRP. Implementation platforms, solution approaches and different optimisers are considered to be studied in this research to find or offer the best possible implementation platform, the most effective solution approach and the most efficient optimiser.

After reviewing available software solution platforms, modeFRONTIER® is recognised as the most suitable platform for solving complex NP-hard multi-objective LRPs as are being developed in this study. This commercial solver can be described as a design en- vironment in contrast to a final stage software package. It allows significant scope and flexibility to the designer. In modeFRONTIER®, MOGA-II, NSGA-II, MOSPOS, MO- SA and HYBRID are selected to solve the two and three-layer MO-LRPs.

3.5. Supply Chain Cases and Data Analysis Approach

In order to elucidate the efficacy of the formulated generic mathematical models, a dairy supply chain network in east of Ireland is considered. Two case studies consisting of two-layer and three-layer dairy SC networks in east of Ireland are developed. The required data is collected and calculated according to their availability and their nature. The structure of these SC cases are validated by means of: (i) interviewing a consultant to few dairy companies in Ireland, (ii) interviewing experts from two major dairy companies in Ireland, (ii) using company profiles, technical reports from dairy companies, outcomes of researches on dairy SCs, and SC text books. There is a questionnaire designed to collect data from experts (Appendix B.1). Based on this validated real structure of the dairy supply chain network in Ireland, two-layer and three-layer SC cases are considered to test the models on. Carbon-emission related data is calculated based on the available recognised methodologies for calculating carbon emission from transportation. Due to unavailability of production fixed and variable cost-related data, they are assumed based on: i) interviewing a consultant to dairy SC companies in Ireland, and ii) the real available data regarding costs of dairy products in Ireland. Vehicle-routing costs are calculated using real data. After validating the structure of the SC networks, distance-related data are calculated using google map. And finally, DM’s priorities are collected by interviewing experts in the modelling phase to develop the green constraint. The process of collection and calculation of the required data is respected to the two-layer and the three-layer SC networks structures.

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In LRPs, Analysis of the obtained results is of a great importance as there is a feasible solution area not a single optimum solution to them. The analysis process consists of checking all feasible solutions, ranking them and offering the best possible solutions to the DMs. DMs’ opinions is considered in this process using MCDM tools and techniques.

3.6. Summary

This research is dealing with Integrated-Location Routing in Supply Chain (SC) network design. Two-layer and three-layer SC networks are considered in this study. The two-layer SC network consists of plants and retailers while the three-layer SC network includes plants, distribution centres and retailers. The main outcome of the research would be a generic low-cost low-carbon framework to design a network of facilities and offering a routing pattern to connect these facilities.

The main subject area of this research is an interdisciplinary field in supply chain covered by operations research. The effective method to conduct research in this subject area is mathematical optimisation. This is the approach that this PhD study has taken to pursue its aims and objectives. Multi-objective location-routing optimisation is adapted to design two and three-layer supply chain networks. The developed optimisation models are explained in details in the following chapters of this dissertation.