Steady State Snap Shot Design

Published Date: 02 Nov 2017

CHAPTER 4

This chapter presents a model-based decision making method to determine the design and operation of a steady-state reverse supply chain. The examined reverse supply chain involves disposal markets, recycling plants and material markets connected by a transportation mode. The reverse supply chain is represented by a mathematical model which is formulated as a moMILP optimisation problem allowing the inherent trade-offs between the conflicting economic and environmental objectives to be explored. The total cost (inc. both infrastructural and operation costs) required to install and operate the supply chain network is used as the economic function. In contrast, the ecological objective function is based upon the environmental impact resulting from the operation of the entire network. This is achieved by adopting the principles of LCA, expanding the network boundaries to incorporate a set of life cycle stages and using the Korean Eco-Indicator method to assess the environmental impact of the network. This requires the characterisation of a set of impact categories/indicators.

The construction of the supply chain will be driven by end-of-life products return and secondary product demand that are assumed to be both deterministic and time-independent. This leads to a snapshot of representation of the reverse supply chain network which is revealed without deriving a migration pathway from the existing infrastructure. The main objective of this model is to explore whether centralised recycling is favoured over decentralised recycling, and analyse the economies of scale that dictate capital investment decisions associated with optimal selecting and installing different size of recycling technologies.

The proposed mathematical model is used to establish and investigate a number of strategic and operation design decisions. The strategic decisions included are (1) the geographical location, number, capacity and type of recycling plants, (2) assignment of different size of recycling technologies; (2) the transportation channels necessary, (3) the amount of end-of-life products to recycle, (4) the amount of end-of-life products to ship from disposal markets to recycling plants and (5) the amount of secondary products to ship from recycling plants to material markets. The applicability of the model is explored within a South Korea context in order to determine the optimal reverse supply chain configuration of fluorescent lamp recycling.

4.2 Model structure and components

The superstructure of the proposed reverse supply chain model is depicted in Figure 3.1. Within the figure, there are grid squares g and g’ enclosing, disposal markets, recycling plants and material markets. The grid squares represent different areas within a South Korea. Grids containing a recycling plant exist to collect end-of-life products within a grid and from other particular grids, and also satisfy demand of secondary products within a grid and other grids. The recycling plants were allowed to take different sizes. Each grid is connected with different transportation mode. The primary transportation mode is used to transport end-of-life products from disposal markets grids to recycling plant grids. The secondary transportation mode is used to transport secondary products from recycling plant grids to material market grids.

As shown in Figure 3.1, the resulting model structure contains all possible configurations of the reverse supply chains as well as the interactions between the various supply chain components. From this structure, the optimisation algorithm will search for the best reverse supply chain network design option eliminating the undesired combinations of recycling plants and transportation links. In the following subsections, each component of the model structure will be addressed in detail, starting with grid squares and ending with transportation modes.

4.2.1 Grid square

An important step in designing a reverse supply chain model is identifying the geographical location required to map out all possible configurations. In this study, the mainland of South Korea is considered as a scene for our study. The mainland is divided into 54 grid squares of equal sizes. Each grid has a length of 50 kilo-metres (km), and represented by an index g in a set of indices from g1 to gn (Appendix C).

After determining each grid’s location, the geographic density of end-of-life products is estimated. The potential end-of-life product return in South Korea is estimated based on their average life time and past domestic annual sales. The actual end-of-life products return is obtained by multiplying the potential return by a collection rate. Since returned end-of-life products have very different characteristics in terms of type and brand, it is almost impossible to consider all kinds of product types. Therefore, we consider a particular end-of-life product group designated by the index u which has similar characteristics in terms of size, component and structure.

Figure 4.1 Superstructure of the steady-state model for a reverse supply chain network

The geographic density of secondary products demand (i.e. products, components and/or materials) is also characterized. In general, the secondary products, f reclaimed from recycling plants can be fed back into a forward supply chains which produce same or different types of products, or can be disposed in landfill sites due to economic or technical reasons. Therefore, the total equivalent secondary product demand is estimated based on the capacity and demand of the material markets or final treatment sites.

4.2.2 Recycling plant

Since end-of-life products can be reprocessed by various types of recycling technologies, a set of plant types with different recycling technologies can be used at several plants at different locations. Recycling plants including different technologies are designated by the index r. Each recycling plant has a recycling capacity which is bound between minimum and maximum limits. These limits determine the size of each type of the recycling plant. Also, each plant type incurs fixed capital and unit recycling costs; and unit environmental impacts. The establishment of a plant type will be determined mainly by the end-of-life product return of the grids and the secondary product demand of the grids; and trade-offs between establishing recycling plants and transportation links. The recycling plant decisions compromise of the number, location and capacity of plant types. The total recycling rates in each grid are included within the recycling decisions.

4.2.3 Recycling plant sizes

The different types of recycling technologies are couple with the index k in order to account for different sizes. Three recycling sizes are considered, referred to as small, medium, and large. The establishment of several small plants means that recycling operation is carried out at several different locations in parallel (decentralized). A large recycling plant, on the other hand, indicated that recycling operation is installed at a few location only (centralized). Each size of a recycling plant is bound between minimum and maximum limits, and has different capital & unit operating costs and environmental impacts. The recycling decision compromises the number, location, and capacity of plant type with respect to size. The total recycling rates for each size of the recycling plants are also contained within the recycling decisions.

4.2.4 Primary and secondary transportation modes

A number of transportation means could be utilized to deliver end-of-life products from disposal markets to recycling plants; and from the recycling plants to material markets. The corresponding options are given by the index l which has a wide range of transportation options such as a truck and rail. Each transportation option has a specific capacity, known delivery distance, minimum/maximum allowable flow rates, capital & operating costs, and environmental impacts. The establishment of transportation links between various grids is determined by the cost and environmental impacts of transportation mode versus the cost and environmental impacts of establishing new recycling plants. Transportation decisions include whether to establish a link between different grids and what flow rate of end-of-life products and secondary products should be. Since the delivery distance is crucial factor in determining the type of transportation mode, a detailed assessment was carried out to estimate the average distance between grids using a Tortuosity factor calculated by dividing actual delivery distance by Euclidian distance.

4.3 Mathematical model

The mathematical formulation is composed of nomenclature, constraints and objective function terms. The nomenclature includes indices, parameters, and decision variables, which are further categorized into: continuous, integer, and binary design variables. The corresponding notation and formulation are discussed below in more detail. The model proposed for this design problem is a moMILP as described below.

4.3.1 Nomenclature

Indices

g

gird square

g’

grid square such that g’g

u

end-of-life products

f

secondary products

k

size of recycling plants

l

type of transportation modes

r

potential plant type with different recycling technologies

b

emissions and waste substances (burdens)

e

environmental impact indicator categories

n

normalised impact categories

p

life cycle assessment stage

λen

classification of impact e under normalised category n

Parameters

capital charge factor

potential return of end-of-life product u in grid g (kg/d)

total demand for secondary materials f in grid g (kg/d)

minimum capacity of a recycling plant r and size k for end-of-life product u (kg/d)

maximum capacity of a recycling plant r and size k for end-of-life product u (kg/d)

capacity of transportation mode l transporting end-of-life product u between grids (kg/trip)

capacity of transportation mode l transporting secondary products f between grids (kg/trip)

minimum flow rate of end-of-life products u by transportation l (kg/d)

maximum flow rate of end-of-life products u by transportation l (kg/d)

minimum flow rate of secondary products f by transportation l (kg/d)

maximum flow rate of secondary products f by transportation l (kg/d)

capital cost of establishing a recycling plant s size k for end-of-life product u (won)

unit recycling cost of end-of-life u by plant type s and size k (won/kg)

availability of transportation mode l for end-of-life products u (hr/d)

availability of transportation mode l for secondary products f (hr/d)

average speed of transportation mode l transporting end-of-life products u between grids (km/hr)

average speed of transportation mode l transporting secondary products f between grids (km/hr)

capital cost of installing transportation mode l transporting end-of-life products u (won)

capital cost of installing transportation mode l transporting secondary products f (won)

fuel economy of transportation mode l transporting end-of-life products u between grids(km/L)

fuel economy of transportation mode l transporting secondary products f between grids (km/L)

fuel price of transportation mode l (won/L)

driver wage of transportation mode l for end-of-life products u (won/hr)

driver wage of transportation mode l for secondary products f (won/hr)

general expenses of transportation mode l for end-of-life products u (won/d)

general expenses of transportation mode l for secondary products f (won/d)

maintenance expenses of transportation mode l for end-of-life products u (won/km)

maintenance expenses of transportation mode l for secondary products f (won/d)

delivery distance between grid g and g’ (km/trip)

load/unload time for transportation mode l (hr/trip)

collection rate

network operating period (d/yr)

tortuosity factor for solid road

weight of material f

weight percentage of materials f in end-of-life products u

emission inventory entry of burden b resulting from the unit reference flow of life cycle stage p

characterisation factor used to convert burden b into impact of category e

normalisation factor for impact categories belonging to group n

weighting factor for each normalised impact category n

Continuous variables

return of end-of-life product u in grid g collected by a local recycling plant r and size k (kg/d)

imported return of end-of-life product u to grid g (kg/d)

demand for secondary product f in grid g satisfied by a local recycling plant r and size k (kg/d)

imported demand for secondary product f to grid g (kg/d)

recycling rate of end-of-life products u by plants type s and size k at grid g (kg/d)

total recycling rate of end-of-life products u in grid g (kg/d)

flow rate of end-of-life products u transported from g to g’ per day (kg/d)

flow rate of secondary products f transported from g’ to g per day (kg/d)

fuel cost (won/day)

total capital cost (won)

total operating cost (won/d)

general cost (won/d)

labour cost (won/d)

maintenance cost (won/d)

transportation capital cost (won)

total daily cost of the network (won/d)

transportation operating cost (won/d)

characterised environmental impact in terms of category e resulting from life cycle stage p (impact/d)

normalised environmental impact in terms of category e resulting from life cycle stage p in grid g (point/d)

single weighted Korean eco-indicator (point/d)

Integer variable

number of recycling plant of type r and size k for end-of-life products u in grid g

number of transport units for end-of-life products u

number of transport units for secondary products f

Binary variables

1 if end-of-life product form u is to be transported from grid g to g’; by transportation model l, 0 otherwise.

1 if end-of-life product form u is to be exported from grid g, 0 otherwise

1 if end-of-life product form u is to be imported into grid g, 0 otherwise

1 if secondary product form f is to be transported from grid g to g’; by transportation model l, 0 otherwise.

1 if secondary product form f is to be exported from grid g, 0 otherwise

1 if secondary product form f is to be imported into grid g, 0 otherwise

4.3.2 Constraints

Return constraints

As previously indicated, each grid has its potential daily return of end-of-life product form u in a grid g (). This return must be collected by a recycling plant within a grid or exported to other neighbouring grids. The presence of recycling plants within a particular grid will ensure this return collection. Therefore, the end-of-life product return collected by a local recycling plant in grid g () must be stipulated by the following constraints:

On the other hand, the return of an end-of-life product form u in a grid g exported to neighbouring grids () is equal to the total flow exported from that grid by the all types of transportation mode:

Total grid return () must equal to the demand satisfied by the local recycling plus the demand exported to other grids, as follows:

Demand constraints

As previously indicated, each grid has its own deterministic demand of secondary products. This demand must be fulfilled by local recycling plants or importing the products from other neighbouring grids. The presence of recycling plants within a particular grid will ensure this demand satisfaction. Therefore, the secondary product demand satisfied by a local recycling plant in grid g () must be stipulated by the following constraints:

On the other hand, if the demand for a secondary product form f in a grid g is imported from neighbouring grids (), the flow rate of secondary product transported by all transportation modes must be equal to the corresponding demand:

Total grid demand () must equal to the demand satisfied by the local recycling plus the demand imported from other grids, as follows:

Recycling plant constraints

The total mass balance on a grid must be written to determine the total daily recycling rate in a particular grid. Since steady-state operation is assumed, the sum of the total flow rate of each end-of-life product entering grid g () plus the total recycling rate of that same grid () must equal to the total flow rate leaving this grid () plus the total end-of-life product return grid g itself ():

The total mass balance on a grid must be written to determine the total daily recycling rate in a particular grid. Since steady-state operation is assumed, the sum of the total flow rate of each secondary product entering grid g () plus the total recycling rate of that same grid () must equal to the total flow rate leaving this grid () plus the total secondary product demand required by grid g itself ():

The total daily recycling rate of an end-of-life product u in a grid g is g is equal to the recycling rate of all plants of type r size k established in that same grid:

The recycling rate of an end-of-life product u recycled by any plant type r and size k in grid g () cannot exceed certain limits. Thus, there is always a maximum recycling capacity for any product (); moreover, there is often a minimum recycling rate () that must be maintained while the plant is operating:

This means that the maximum daily recycling rate of an end-of-life product u recycled by plant of type r and size k is constrained by the number of recycling plants (.

Likewise, the total recycling rate of each product form u in each grid g ( ) cannot exceed certain limits. Therefore, is bound between the minimum and maximum recycling capacities of all recycling plants that are established in this particular grid:

Primary transportation constraints

There must be a continuous flow of end-of-life products between grids in order to move them to recycling plants. The flow of end-of-life product form u from a grid g to a different grid g’ will exist only if the transportation mode has been established. Therefore, there is always a minimum and maximum flow rate of end-of-life products ( and ) needed to justify the establishment of a transportation mode between two grids in the network:

(4.12)

Flow of an end-of-life product u between grids can occur in one direction. This is because if a grid can only satisfy its needs by importing from other grids it would not make sense for the grid to export to other grids. Therefore, a particular grid can only import product neighbouring grids or export product to other grids, or neither but not both:

(4.13)

(4.14)

(4.15)

Secondary transportation constraints

Similarly, there has to be a continuous flow of secondary products between different grids in order to satisfy the required demand. The flow of secondary product form f from a grid g’ to a different g will exist only if the transportation mode has been established. Therefore, there is always a minimum and maximum flow rate of secondary products ( and ) needed to justify the establishment of a transportation mode between two grids in the network:

(4.16)

Flow of a secondary product form f between grids can occur in one direction. This is because if a grid can only satisfy its needs by importing from other grids it would not make sense for the grid to export to other grids. Therefore, a particular grid can only import product neighbouring grids or export product to other grids, or neither but not both:

(4.17)

(4.18)

(4.19)

Non-negativity constraints

All decision variables must be non-negatives:

(4.20)

(4.21)

(4.22)

(4.23)

(4.24)

(4.25)

(4.26)

(4.27)

(4.28)

4.3.3 Economic assessment

One of the objectives of the proposed model is to minimise the average total daily cost of possible reverse supply chain networks for end-of-life products. The cost includes both capital and operating expenditure. The former are one-time costs associated with the establishment of recycling plants and transportation links. Operating costs, however, are incurred on a daily basis and are associated with recycling and transportation cost through the network. In the subsequent sections, the cost terms used to estimate the overall cost of the reverse supply chain network are addressed in detail.

Facility capital cost

In this model, the facility capital cost is related to the establishment of recycling plants at candidate locations. It is calculated by multiplying the number of recycling plants by their capital costs as follows:

Transportation capital cost

The capital cost of different types of transportation modes takes into account the number of transport unit such as trucks, required to satisfy return and demand and cost of each unit. The number of transport units ( and ) depends significantly on on the average distance travelled between different grids (). Long delivery distances mean more trucks are required to deliver a given quantity of end-of-life and secondary products, which can result in a higher transportation capital costs. The capacity of a transport container (and ) is also an important factor, especially for long distances, since it determines the number of trips that must be made between the disposal markets and the recycling plants; and between the plants and material markets. It is clear that large capacity of a recycling plant will reduce the cost of transportation as fewer trucks are required. In addition, the flow rate of end-of-life and secondary products between various grids ( and ), transportation mode availability ( and ), average speed ( and), and loading/unloading time () are other main factors that affect the capital and operating costs of transportation. On the other hand, the cost of the transport unit (and ) includes the cost of the transport container, the cost of the undercarriage and the cost of the cab.

The number of trucks required satisfying a certain flow between disposal markets and recycling plants are given by the following relationship:

The number of trucks required satisfying a certain flow between recycling plants and material markets are given by the following relationship:

It can be noted from Equation (4.31) that LLgg’ is multiplied by two to account for the return journey. Therefore, the transportation capital cost is given by the following equation:

Facility operating cost

The facility operating cost is related to the cost required to operate the recycling plants efficiently. The recycling plant operating cost is calculated by multiplying the unit recycling cost () by the recycling rate (). Thus, the corresponding cost terms in the objective function are of the form:

In Equation (4.33) the unit recycling costs are directly proportional to the size of recycling units. As presented in Figure 3.2, these unit costs benefit from economies of scale. Therefore, as the capacity of recycling increase the unit cost decrease.

Figure 4.2 Unit cost versus size

Transportation operating cost

The transportation operating cost consists of fuel, labour, maintenance, and general costs. The daily fuel cost contributes significantly to the total operating cost. It is a function of daily fuel usage and fuel price:

where the first and second terms of the multiplication in Equation 4.34 represent fuel price and daily fuel usage, respectively.

The daily labour cost associated with transporting product forms between different grids is given as a function of the total delivery time and driver wage:

Again, the first and second terms of the multiplication in Equation 3.35 represent driver wage and total delivery time, respectively.

The maintenance cost includes general maintenance of the transportation systems. It is a function of the total daily distance driven and the cost per unit distance travelled:

The last operating cost is the general cost. It consists of transportation insurance, license and registration, and outstanding finances. It depends on the number of transport units required to deliver products to the storage facilities and the corresponding general expenses:

Finally, the total transportation operating cost is equal to the sum of fuel, labour, maintenance, and general costs as follows:

Economic model summary

To total daily cost of the reverse supply chain network is obtained by combining the cost terms derived in Section 4.3.2 as follows:

The first term of the right-hand-side of Equation 4.39 is divided by the network operating period () in days and the annual capital charge factor (CCF) in order to find the cost per day.

4.3.4 Environmental impact assessment

The ecological objective function is based on the environmental impact resulting from the operation of the entire network. This is achieved by adopting the principles of LCA, expanding the network boundaries to incorporate a set of life cycle stages and using Korean Eco-Indicator method to assess the environmental impact of the reverse supply chain. The first step in the LCA procedure is the goal and scope definition whereby the functional unit and systems boundaries of the study are defined. For the model developed here, the boundary around the supply chain superstructure depicted in Figure 3.1 is expanded to include the following set of life cycle stages:

where (1) is a recycling process for end-of-life product u using technology r and size k; (2) is the transportation of end-of-life products u from disposal markets to recycling plants; and (3) ) is the transportation of secondary products f from recycling plants to material markets. The functional unit for the overall system is defined as the operation of reverse supply chain network to recover end-of-life products u and deliver reclaimed secondary products f to material markets. The assessment of the impacts resulting from the operations of each of these life cycle stages is performed with reference to the site to which it is linked. This allows the environmental performance of the different grids to be compared during the interpretation stage, which can then for the basis for improvement recommendations.

Once the goal and scope defined, the next phase is to quantify the materials, energy inputs and emissions (i.e. environmental burdens) per functional unit crossing the systems boundary; and compile these data in a life cycle inventory table [1] . These inputs and emissions constitute the environmental burdens which includes direct burden and indirect burdens. Direct burdens are inputs and environmental emissions from the foreground activity, and these are described by process specific data. Indirect burdens are environmental burdens associated with supplying both energy and ancillary materials (i.e. materials such as fuels and lubricants), which are consumed in the foreground activity, but do not become part of the material flow.

However, environmental burdens summarised in the life cycle inventory table are recognised as environmental problems only when they pose problems to the environment and society. Thus, there is an intrinsic value-bound aspect to the definition of an environmental problem (Heijungs, 1997). To deal with this it is necessary to establish scientific relationships between pollutants and a set of environmental impact categories, such as global warming, acidification or ozone layer depletion. Similarly, there is a relationship resource extraction and various depletion problems. Hence, the impact categories can be defined in terms of damage to the environment by pollutant in air, water or soil and by depletion of available natural resources. In this context, the burdens are aggregated in terms of their contributions to a set of recognised environmental impacts.

For the environmental impact assessment, we utilise a Korean Eco-Indicator method (Lee, 1999) which is developed to model the potential environmental impacts on a Korean scale according to 8 impact categories, e (Appendix D):

where, correspond to the resource depletion, global warming, ozone layer depletion, acidification, eutrophication, photochemical oxidant creation, human toxicity and eco toxicity, respectively. More specifically, three steps are followed to arrive at the single performance score (i.e. Korean Eco-Indicator) of a particular process (see Figure 4.3). The first step calculates characterised environmental impacts by multiplying environmental burdens (i.e. life cycle inventory table) by its potency factor which represents the relative contribution of burden to impacts. In step 2, individual indicators in the set of impacts categories, are put on a common dimensionless basis in terms of the set of normalised impact categories. Using the normalisation factors of each category for the particular perspective, the set of impact indicator for the various life cycle stages are normalised. Finally, the single Korean Eco-Indicator score can be obtained by attaching weights [2] of relative importance to the normalised categories and aggregating them.

Figure 4.3 Representation of the Korean Eco-Indicator method

If one considers the set of p life cycle stages, each of which relate to a reverse supply chain in grid g through their reference flows, the value of indicator e resulting from the operation of life cycle stage p, characterised impacts) an be calculated as the general expression:

where (i) is the amount of reference flow required of life cycle stage p in grid g such as ton of crude oil extracted, load and distance of goods transported; (ii) is the set of environmental burdens; (iii) is the emissions inventory entry per 1 unit of reference flow of life cycle stage p, and (iv) is the potency factor of substance b contributing to impact indicator e such as global warming and resource depletion. In this approach (the ‘problem oriented’ method), for example, GWP factor, for other greenhouse gases are relative to the GWP of CO2, which is therefore defined to be unity. If a different impact assessment approach is used, then Equation 4.40 may be redefined accordingly. Note that at the present LCA approach assumes that environmental burdens and impacts function are linear, i.e. they are directly proportional to the output of functional unit(s) and there are no synergistic or antagonistic effects.

Although the general relationship for calculating the various impact categories is consistent for all the life cycle stages, it is necessary to determine the reference flow for each individual stage uniquely. Starting with the recycling plants ), an isolated boundary is drawn around each grid with the reference flow being the unit recycling of end-of-life product u.

Next, the environmental impact resulting from both the transportation of end-of-life products from disposal markets to recycling plants, and the transportation of secondary products from the recycling plants to material makers have to be assessed. Typically functional units used to report the emission data for transportation are based upon both distance and mass being carried. Therefore knowing the distance between the location of the disposal markets and the location of each recycling plants r, and using the transportation emissions inventory, then the impact associated with the primary transportation of end-of-life products are:

Similarly, the environmental impact resulting from the transportation of secondary products f reclaimed by recycling plants r to material markets over a distance, can be obtained from:

In normalisation step, the individual indicators in the set of impacts are put on a common dimensionless basis in terms of the same set of 8 impact categories:

where correspond to the resource depletion, global warming, ozone layer depletion, acidification, eutrophication, photochemical oxidant creation, human toxicity and eco toxicity, respectively. Using the normalization factors, of each category for the particular perspective, the set of impact indicators for the various life cycle stages are normalized and aggregated as follows:

Finally, the single Korean Eco-Indicator can be obtained by attaching weights of relative importance to the normalised categories and aggregating them. As for the normalisation step, this is performed using the weighting factors, according to the chosen perspective:

In order to obtain more reliable the relative importance (i.e. weight) of each impact category, the Korean Eco-Indicator methodology systematically adopts a systematic way which combines a reduction factor in the distance to target method with a relative significance factor based on the precautionary principle (Lee, 1999). However, the calculation procedure can be interrupted at any step according to the particular needs of the impact assessment. If it is desired to represent the environmental impact caused by a process without normalisation, the calculations are simply terminated prior to normalisation. In other word, environmental optimisation can be performed either at the inventory or impact assessment levels, in which case the environmental objectives are defined as either burdens or impacts, respectively (Azapagic & Clift, 1999a,b).

4.4 Multi-objective optimisation

Two objective functions enter the multi-objective formulation: (1) the total cost and (2) the potential environmental impact. The problem is, therefore, to simultaneously minimise the total cost and environmental impact:

Plant location and capacity constraints

Network structural constraints

Return and demand constraints

Recycling plant constraints

Capital and operating costs

Emission inventory

Life cycle input output balance

Environmental impact assessment

where U is the utility function and x and y represent the vectors of continuous and discrete variables, respectively, belonging to the feasible region of equality and inequality constraints as defined in Section 3.3.2. Based on this multi-objective mixed integer linear programming, reverse & closed-loop supply chain network is then optimised simultaneously on a number of environmental and economic objective functions to locate the multi-dimensional non-inferior or Pareto surface which maps the optimal solutions. Each optimal solution is the set of non-inferior or Pareto optimal solution (also referred to non-efficient or non-dominant set) which represents alternative supply chain configuration with a unique capacity and combination of environmental and economic performance. The Pareto optimal solutions can be defined as:

Definition 4.1: A decision vector x’, y’ is non-inferior if there does not exist another x’, y’ such that for at least one objective q. Otherwise, x’, y’ is not non-inferior. In other words, a solution is non-inferior if it is not possible to find another feasible solution so as to improve one objective without necessarily worsening at least one of the others.

Considering now the general case when q objective functions need to be simultaneously optimized, the set of non-inferior solutions can be obtained using a generation method. Although the generation methods are less popular due to their computational effort (the calculation of efficient solution is usually a time consuming process and the lack of widely available software). However, they have some significant advantages. One of the main advantages of the generation method is that it does not require a priori articulation of preferences, so that the whole non-inferior set of solutions can be explored. The emphasis is then on the range of choices from the set of non-inferior solutions, rather than explicit definition of preferences before analysing all the trade-offs among objectives. Trade-offs between the non-inferior solutions show explicitly what can be gained and what lost by choosing each alternative. Where there are multiple decision-makers with conflicting interests, this technique can help to resolve disputes by generating different alternative solutions. Decision makers who understand the trade-offs and the alternatives are more likely to understand the interests of other parties and, therefore, to compromise. Although the evaluation of trade-offs between the objectives to choose the best compromise solution will still imply certain preferences and value judgments, at least the choice will be made from all possible non-inferior solutions.

There are several approaches to produce the entire non-inferior set. In general, the most widely used, generation methods are the weighting method and the ε-constraint method. These methods can provide a representative subset of the Pareto set which in most cases is adequate. An essential step towards further penetration of the generation methods in multi-objective optimisation application is to provide appropriate code for mathematical programming solvers such as XPRESS-MP (Dash associates, 1993) and GAMS (1998) and that widely used in engineering, economics and so on.

Figure 4.4 Graphical interpretation of non-inferiority in generating methods

In this study we have used the ε-constraint method because it has several advantages over the weighting method. Firstly, for linear problems, the weighting method is applied to the original feasible region and results to a cornet solution (i.e. extreme solution), thus generating only extreme non-inferior solutions (see Figure 4.4). On the contrary, the ε-constraint method alters the original feasible region and is able to produce non-extreme efficient solutions. As a consequence, with the weighting method we can spend a lot of runs that are redundant in the sense that there can be a lot of combination of weights that result in the same extreme non-inferior solution. On the other hand, with the ε-constraint we can exploit almost every run to produce a different non-inferior solution, thus obtaining a more rich representation of the non-inferior set. Secondly, the weighting method cannot produce unsupported non-inferior solutions in multi-objective integer and mixed integer programming problems, while the ε-constraint method does not suffer from this inadequacy (Steuer 1986, Miettinen 1999). Thirdly, in the weighting method the scaling of the objective functions has strong influence in the obtained results. Therefore, we need to scale the objective functions to a common scale before forming the weighted sum. In the ε-constraint method this is not necessary. Finally, an additional advantage of the ε-constraint method is that we can control the number of the generated efficient solutions by properly adjusting the number of grid points in each one of the objective function ranges.

In this context, the set of non-inferior solutions is obtained by firstly reformulating the multi-objective optimisation problem as a multi-parametric mixed integer programming problem (Papalexandri and Dimkou, 1998):

st:

…

,

where

st:

,

(4.48)

While at each solution the value of each objective function i is recorded.

(4.49)

such that the maximum bound on each objective function is given by its greatest value over all the solutions:

In principle, the reformulated problem then be solved using recently algorithms for parametric optimisation. However, in order to address large number of variables more systematically, discretizing the parameter space into sufficiently small intervals and applying the e-constraint method at each parameter interval realisation:

st:

…

,

where

4.5 Multi criteria decision making

The non-inferior solutions, obtained in the previous step, provide input into the decision-making process. To choose the best compromise solution out of a number of optimum alternatives, some articulation of preferences is necessary. However, these preferences are at least articulated by decision-makers in the post-optimal analysis of all non-inferior solutions and their trade-offs, as distinct from expressing preferences and aggregating the objectives prior to identifying all non-inferior solutions. One of the possible ways to choose the ‘best’ solution is to consider a graphical representation of the non-inferior set and then choose the best compromise solution on the basis of the trade-offs. However, this approach is limited to two or three objective functions at most; beyond that, graphical representation becomes too complex. Alternatively, the non-inferior values of the objectives may be expressed in terms of the difference from the value at their individual optima. If all objectives are considered to be of the same importance, than the best compromise solution might be that which equalises the percentage by which all objectives differ from their optimum values. However, should any of the objectives be considered more important than the others, then other methods that allow ordering and quantifying of preferences, usually referred to as multi-criteria decision-making (MCDM) techniques, can be used to identify the best compromise solution.

MCDM techniques provide a structured approach to a decision making process. They enable systematic analysis and modelling of preferences with the aim of providing help and guidance to decision-makers in identifying their most desired solution. The major advantages of these techniques are that they are transparent, non-ambiguous and easy to use by non-experts. Furthermore, the quantitative nature of these numerical methods may particularly be appealing to quantitatively oriented managers and engineers. A number of methods for ordering and quantifying preferences have been developed over the past years and some of them include simple additive weighting, weighted product, median ranking method (Hwang, Paidy & Yoon, 1980), the analytic hierarchy process (Saaty, 1980), multi-attribute utility theory (Keeney & Raiffa, 1976), simple multi-attribute rating technique (von Winterfeldt & Edwards, 1987). Extensive reviews of MCDM techniques can be found in Stewart (1992) and Yoon and Ching (1995). User friendly software with various MCDM methods to aid the decision making process are also available (Ha¨ma¨la¨inen & Lauri, 1995).

The choice of a suitable MCDM technique will depend on a given decision-making situation and the sophistication of the decision-makers. Most of these techniques are based on a definition of a multi-attribute or utility function, which associates a number with each alternative to reflect the importance of the attribute in the opinion of the decision-maker, so that all alternatives may be ordered. For example, if there are five non-inferior solutions identified in the previous step, each with different values for the three objectives (attributes), i.e. GWP, OD and costs, the decision-makers are then asked to articulate their preferences for each of the attributes on scale 1–10. The mathematical analysis or ordering of the preferences, for instance by a pair-wise comparison of attributes (Saaty, 1980), returns the best compromise solution for this particular example. It is important to note that the attributes and the preferences are always identified on a case by case basis within a bounded decision space, and that they only apply in that particular decision-making context. The developed model is now applied to optimize the reverse supply chain network of fluorescent lamps in Korea.

4.6 Illustrative example: fluorescent lamps recycling in Korea

4.6.1 Network structure

The model developed will be used to optimise the reverse supply chains of florescent lamps in South Korea. The supply chain encompasses disposal markets, recycling plants and material markets. In South Korea relatively small amount of end-of-life florescent lamps from households are collected by using drop-off collection boxes. Large amount of end-of-life lamps are collected from big building, sign makers by private collection companies. Once the returned end-of-life florescent lamps reach the lamp recycling plant which located in Whasung (, Chilgok ( and Jangsung (, they then go through the recycling processes which consist of three steps: cut & blow, tube crushing and mercury distillation. Once end-of-life fluorescent lamps are fed into the recycling plants, the metal caps and other components at the end of the lamps are cut and separated from the lamps. Then, the residues (i.e. fluorescent powder, mercury) in the stem glass are blown out and sent to a distillation process for mercury recovery. The stem glass released from the cut and blow step is crushed as cullet. This cullet is transported to a glass fiber manufacturing plants at Dang-zin ( and Incheon ( and Yang-zu (; and used as a raw material to produce new glass fibers. Metal caps are stored in plastic bags and delivered to aluminum recycling companies at Kwang ju ( and Masan ( and used as raw materials to produce aluminum ingot. Plastics are transported to Qe-san ( and dusts are finally moved to Pyungtaek ( and Jechun (.

4.6.2 Input data

Return and demand

The daily returns of end-of-life fluorescent lamps and the daily demand of secondary products in the 54 grid square are summarised in Appendix E. The reverse supply chain network obtained from satisfying these supply and demand values is assumed to operate at 100% utilisation rate, i.e. 365d/yr, in order to cover daily and seasonal variation of return and demand. The capital charge factor associated with this investment is assumed to be 8 years.

Economic and technical data

The minimum and maximum recycling capacities ( and ) of each plant type with respect to size are given Table 4.1. The capacity range assumed for the different sizes of recycling plants is based on actual database obtained from the plants currently in operation in South Korea. In particular, the maximum recycling capacity of large plants was assumed to be double that of the large batch type recycling equipment. This was based on the assumption that EPR legislation will lead to the construction of larger recycling plants. The table also shows the capital and unit operating costs for the different sizes of recycling plants. These values were also obtained from the field.

Table 4.1 Capital and unit recycling costs of end-of-life fluorescent lamp

Recycling plant type, r

Fluorescent lamp recycling plant

Recycling size, k

Small

Medium

Large

Recycling

Tech. 1

Minimum recycling capacity (kg/d)

900

1,800

3,600

Maximum recycling capacity(kg/d)

9,000

18,000

36,000

Capital cost (won x 106)

1010

2600

5200

Operating cost (won/kg)

350

180

110

Recycling

Tech 2

Minimum recycling capacity (kg/d)

900

1,800

3,600

Maximum recycling capacity(kg/d)

9,000

18,000

36,000

Capital cost (won x 106)

1975

3950

7900

Operating cost (won/kg)

465

234

135

The maximum flow rate (of end-of-life product via trucks was assumed to be 36,000kg/d, while the minimum flow rate (is assumed to be equal to the capacity of each transport mode (see Table 3.3). This means that the minimum allowable quantity of end-of-life products between grids is equal to a fully-loaded transport unit. Similarly, the maximum flow rate (of secondary products via trucks was assumed to be 32,000kg/d, while the minimum flow rate (is assumed to be equal to the capacity of each transport mode. The parameters used to calculate the capital and operating costs for the different type of transportation mode are listed in Table 4.2.

Table 4.2 Capital and unit disassembly/recycling costs of end-of-life fluorescent lamp

Transportation model, l

PT

ST

Fuel economy (km/L)

7

6

Average speed (km/hr)

80

80

Mode availability (hr/d)

18

18

Load/unload time (hr/trip)

2

2

Driver wage (won/hr)

12,404

12,404

Fuel price (won/L)

1322

1322

Maintenance expenses (won/km)

77

95

Transport unit capacity (kg/trip)

1300

2184

Transport mode cost (won)

21

39

Environmental impact data

LCA was performed to calculate the environmental impacts of recycling plants. The life cycle inventory analysis (LCI) was conducted in accordance with the methods stipulated in ISO 14040 (1997) and 14041 (1998). First of all, total inputs including energy used and total outputs data were collected from the recycling facilities. Energy was allocated to processes, materials and components according to the physical relationships between inputs and output. LCI results were calculated using TOTAL LCA software. The life cycle impact assessment (LCIA) was conducted following ISO 14042 (2000) and the Korean eco-indicator method developed by Lee (1999). The results of two recycling technologies are presented in Figure 4.5 and 4.6.

Impact categories

Korean eco-indicator

ADP

1.77E-05

AP

8.41E-07

EP

5.02E-07

GWP

2.87E-05

HTP

8.72E-09

ODP

9.09E-11

POCP

2.40E-06

TETP

2.95E-12

Korean eco-indicator

5.02E-05

Figure 4.5 Eco-indicator for recycling plants (Technology 1)

Impact categories

Korean eco-indicator

ADP

3.48E-03

AP

7.09E-04

EP

1.36E-04

GWP

2.43E-03

HTP

1.37E-03

ODP

9.62E-05

POCP

4.74E-04

TETP

5.63E-05

Korean eco-indicator

8.75E-03

Figure 4.6 Eco-indicator for recycling plants (Technology 2)

We also estimated Korean eco-indicator for transporting 1 kg of end-of-life products (i.e. end-of-life FLs) and secondary materials (i.e. glass, plastic, aluminium and mercury) per 1 kilometre (km). The results are presented in Figure 4.7 and 4.8

Impact categories

Korean eco-indicator

ADP

1.15E-08

AP

5.18E-10

EP

2.65E-10

GWP

7.73E-09

HTP

4.55E-09

ODP

3.28E-10

POCP

1.52E-09

TETP

1.92E-10

Korean eco-indicator

2.663E-08

Figure 4.7 Eco-indicator for 2.5 tonne truck (PT)

Impact categories

Korean eco-indicator

ADP

8.03E-09

AP

2.31E-09

EP

1.34E-09

GWP

5.39E-09

HTP

3.20E-09

ODP

2.29E-10

POCP

2.06E-09

TETP

1.34E-10

Korean eco-indicator

2.270E-08

Figure 4.8 Eco-indicator for 3.5 tonne truck (ST)

4.6.3 Results

Solving the two objective function problem results in the efficient set of solutions, it is clear that a conflict exists between a reverse supply chain design that achieves minimum environmental damage and total cost. It shows that an improvement in the environmental performance is only possible if the decision-maker is willing to compromise cost reduction. It is worth highlighting that a huge drop A to B points in the efficient set of solutions (Figure 4.9) originates from the strategic decisions included in the model and correspond to the optimal solution switching from one recycling technology to another. This provides the opportunity to achieve a significant improvement in cost reduction at a marginal increase in environmental impact by adopting a different technology. For example, at the circle region in Figure 3.9 with an f2 value of approximately 1.7x102, a compromise in the environmental impact of only a few percents can reduce huge amount total cost.

Figure 4.9 Efficient set of trade-off solutions to the illustrative example

Upon analysis of the results, we studied two different configurations (i.e. current network and optimal network) concerned with establishment of the optimal reverse supply chain for fluorescent lamps recycling. Compared to the current network presented in Figure 4.10 (a) the cost and environmental impacts of the network presented in Figure 4.10 (b) (i.e. centralized network) is nearly two times lower. Although relocation and capacity expansion of a recycling plant can be quite expensive at the current stage due to high capital cost. However, as EPR regulation is becoming more strict and end-of-life returns will be increasing in the near future, this option will be much more competitive because of low recycling cost and environmental impacts. It should be noted that the main reason behind the centralisation in grid 33 could be explained by the high population density surrounding regions and a distance to material markets.

Figure 4.10 Optimal reverse supply chain structures

Based upon the steady-state reverse supply chain model, the eco-efficient reverse supply chain design problems have been addressed in this work. Combining the classical features of the capacitated reverse supply chain network problem with the concept of life cycle assessment, a mixed integer linear programming model for the strategic design and planning of a reverse supply chain has been developed. This model supports the strategic planning decisions of selecting the optimum combinations of recycling technologies, allocating these selected technologies to potential sites and determining the scale of the selected technologies. In addition, the strategic design of the transportation links required to satisfy the return and demand at the disposal and material markets is also established. At the operational level, optimal recycling profiles and the flows of end-of-life and secondary products between the different grids within the supply chain are determined.

At this stage, the preliminary computational results of the models are promising. However, there are major tasks that still need further investigation to improve our model. The following tasks will be addressed in next reverse supply chain models (i.e. extended RSC & multi-period RSC model):

At the present stage, the reverse supply chain network is optimised without taking into account the collection facilities of end-of-life products. The model will be improved to consider the establishment of collection facilities with different sizes.

The model considers only regional distribution of end-of-life and secondary products between grids. The model will be improved to also accounts for distribution of the products within the grid (i.e. local distribution, together with regional distribution).

The model developed considers only one reprocessing options (i.e. material recycling). The model will be improved to consider the various types of reprocessing options such as remanufacturing and reuse.

Consider the evolution of the reverse supply chain network over time, rather than a snapshot of the supply chain network at one point in time. This will require building ‘pathway’ model within a robust optimisation framework. Also, we will consider an unsteady-state form of the problem according to which return and demand are time-variant.

In order to assess the consequence of return uncertainty for the supply chain network design, it is necessary to analyse the impact of (deterministic) return variations. In other words, how robust are reverse supply chain network with respect return variations? An answer to this question at the same time concerns modelling appropriateness. Hence, we will see more clearly whether a deterministic model appears adequate for reverse supply chain design or whether more advanced approaches are required, such as stochastic or robust optimisation technique.