Implementation Platforms for LRPs

In the context of Facility Location, Tafazzoli and Mozafari (2009) have done a literature review on the ‘classification of location models and location software tools’. They first tried to review the classification of facility location problems and then presented a soft- ware survey on FLPs. They categorised the software packages used for solving FLPs into general specialised software packages for solving specific problems. A brief review of some of the main software used for solving/modelling facility location problems are presented in Table 2.5.

Table 2.5 A brief review of the main solution software tools and programmes for facility location modelling (Tafazzoli and Mozafari 2009)

Software Covering Methods/Models Source

General software packages and programs

LOLA Network, and discrete FLPs including: median,

centre, q-median, q-centre (q: the number of facilities in a multi facility problem or the num- ber of objective functions in a multi-objective problem)

Hamacher et al. 1996

SITATION p-median, set covering, maximal covering, p-

centre, UFLP FLs;

using branch & bound, Lagrangian relaxation, genetic algorithm, variable neighbourhood

Daskin, 2002

(accompanies Daskin text: Network and Discrete Location: models, algo- rithms, and applications)

S-Distance focused on location-allocation analysis:

p-median, p-centre, maximal covering, multi- objective;

using greedy and randomised algorithms, local search heuristics, meta-heuristics, Lagrangian relaxation

Sirigos and Photis, 2005

More specifically focused software programs and tools (limited) Mathematical Pro- gramming 1. LINGO 2. LINDO 3. GAMS 4. CPLEX

These software programs need a different level of programming and coding to solve the mathematical model.

Jure Mihelic (k- centre algorithms)

K-centre algorithms; a program for solving facil- ity location problems with k-centres

Mihelic 2004

RLP Solving restricted one facility location problem Nickel and Hamacher,

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Advanced Interactive Multidimensional Modelling System (AIMMS), a software sys- tem designed for modelling and solving optimisation models has been tested as an op- tion. The software is not compatible to the nature of the models and failed in reaching a feasible solution space.

For the purpose of this research a commercial solver capable of solving the two-layer and three-layer multi-objective 0-1 mixed integer AHP-integrated LRP is required. Fur- thermore, a commercial solver that offers a variety of optimisers of different natures is desirable. Conventional software packages and tools are not capable of providing a Pa- reto efficient optimum solution space for these two SC network design models using a variety of advance multi-objective heuristics/meta-heuristics. A multi-disciplinary and multi-objective software capable of handling complex optimisation problems is availa- ble for designing purposes. modeFRONTIER® is a multi-disciplinary and multi- objective optimisation and design environment developed by ESTECO SpA (ESTECO 2013). The complex algorithms within modeFRONTIER® can spot the optimal results, even conflicting with each other or belonging to different fields. modeFRONTIER® consists of Design of Experiments (DoE), optimisation algorithms, and robust design tools, capable of blending to create an efficient strategy to solve complicated multi- disciplinary problems. It is offering a wide range of evolutionary optimisers to manage continuous, discrete, and mixed variable problems.

After initial evaluation of available software solution platforms, it was concluded that modeFRONTIER® is the most suitable platform for solving complex NP-hard multi- objective LRPs as are being developed in this study based on its extended capabilities and multi optimiser availability. modeFRONTIER® is a commercial solver, which can be described as a design environment in contrast to a final stage software package. As such a development platform it allows significant scope and flexibility to the designer. In modeFRONTIER®, MOGA-II, NSGA-II, MOSPOS, MOSA and HYBRID are se- lected to solve the two and three-layer MO-LRPs. MOGT works using a combination of Game Theory and a Simplex algorithm and uses only the first entry of DoE table, there- fore this optimiser is not selected to solve the models in this study. SAnGeA is devel- oped for unconstrained models. As the MO-LRPs are both constrainted in this study, it is deemed not suitable for these models. modeFRONTIER® is explained in more details in Appendix A.4.

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Survey of literature shows that there has been very little research into the environmental impacts of SC network design. This area of research has the potential to offer a considerable contribution to the environment in terms of GHG emission. Facility location and vehicle-routing are already well established areas of study in SC network design. However, the literature review reveals that more focus should take into account green considerations on the use of facility location and vehicle-rooting techniques and methods.

The main three objectives of this study are: (a) Developing low-carbon location-routing models, (b) Finding an effective solution approach to implement the developed models, and (c) Offering targeted and tailored low-carbon low-cost scenarios to DM’s considering their priorities. In order to consider green elements in SC network design, this research is particularly focused on improvement of Berger’s (1997) two-layer LRP and Perl’s (1983) three-layer LRP. The critical survey of literature reveals the following gaps in location-routing modelling in the context of SC network design:

 From modelling perspectives of LRPs

» Prior research fails to include cost of serving routes while optimising CO2 emission in SC network. Therefore this research optimises the total CO2 emission caused from transportations throughout the SC network considering the cost of serving the routes. Existing LRPs do not include the capacity of DCs and the demand of retailers. The effect of the capaci- ty of DCs and the demand of retailers on the total cost is studied in this research by adding these components to the developed models.

» DM’s priorities are not considered in designing prior LR models. This research considered the DM’s priorities in the mathematical model by using MCDM tools and techniques. This will make the mathematical model capable of responding to the priorities of the DM with qualitative nature

 From solution perspective on LRPs

» The developed models in this research are multi-objective. Besides, MCDM techniques are used to consider the DM’s priorities. The combi-

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nation of these two characteristics makes the developed models quite dif- ferent from any prior LRPs. Therefore, an effective implementation plat- form for low-carbon multi-objective LRPs is to be identified and de- ployed.

» One of the shortfalls of evolutionary algorithms such as genetic algo- rithms is that they generate a considerable number of irrelevant solutions. By introducing DoE to the solution algorithms robust solution approach is achieved.

 From analysis of results perspective

» Prior research to LRPs doesn’t consider MCDM techniques to rank the results. This research considers MCDM techniques for ranking results obtained from evolutionary algorithms used for implementing the mod- els.

» Prior research fails to provide the decision-makers with various scenarios and analysis related to these scenarios. This research suggests multiple scenarios followed by analysis based on the scenarios and the solutions offered by each one of them.

2.6. Summary

This research is focused on low-carbon low-cost integrated location-routing and this chapter reviewed the highly inter-disciplinary relevant literature to this topic. The litera- ture on Supply Chain Design, Facility Location Problems and Integrated Location- Routing Problems are reviewed. Logistics Decisions and Green Logistics Decisions are surveyed as sub-sections to SC design. The survey of available literature in these three main sections reveals that the environmental issues have been considerably neglected in Integrated Location-Routing modelling. The next observation from reviewing the avail- able literature is that the decision-makers opinions are not considered in making LR decisions. There is possibility of considering DM’s opinion and their priorities in the modelling phase and/or in the analysis of results phase. Implementation platforms and solution approaches available to LRPs are studied in this chapter. Literature shows that there is room for improvement in the solution approaches to LRPs.

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The thorough survey of literature reveals that low-carbon low-cost LRPs have not been studied before. To the best of my knowledge there is no evidence of a multi-objective low-carbon LRP in literature. This is the exact area this PhD research is focused on. Next chapters of this dissertation explain two sets of multi-objective LRPs developed to minimise cost and carbon emissions simultaneously.

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CHAPTER THREE