Minimising transportation in manufacturing supply chains

Abstract

The movement of raw material, work-parts and bought-out components is an essential aspect of modern-day global manufacturing systems. It is also an expensive, non-value adding and pollution-generating activity with many undesirable consequences. These manifest themselves not only in terms of the immediate cost of transportation between suppliers, manufacturers and customers but also in the consequential effect this movement has on human health and the environment. Accordingly, modern manufacturing supply chains should be designed with great care to minimise the amount of movement required both internally within a manufacturing facility's production system and externally between the supplier, manufacturer and customer. In so doing, a good supply chain design minimises the costs associated with the transportation of goods along with the effect this has on the environment. In complex supply chains, however, minimising overall transportation movement for large sets of components is no easy task. Consequently, the contribution contained in this paper seeks to outline a technique whereby an initial supply chain design solution which does so can be identified. The method is explained in the first instance via a straightforward material movement example. The resulting solution is subsequently modified to indicate its application in the context of temporal supply chain design. By utilising this approach, the article emphasises the importance of obtaining a solution that minimises transportation movement within the supply chain together with the practical effects of doing so on flexibility, cost and environmental pollution. In addition, the work required for further development of this technique is outlined and finally suitable conclusions are drawn.

Keywords::

• supply chain design
• minimisation of movement
• cost and environmental impact

1. Introduction

The minimisation of work-part movement has long been recognised in the design of manufacturing systems as a desirable goal (Tompkins et al. 2002, 5), principally because it not only lowers the cost of transportation between processing stations but also results in a shorter product throughput time. Reducing the transit time in production, processing or supply cycle yields major competitive advantages that include a smaller unit cost flow, quicker delivery of the required product volumes to the market and on sale, a faster and increased overall cash flow for the company concerned. In recent years, many research activities have taken place in the area of manufacturing supply chain design and management (Sachan and Datta 2005). This has been consequent upon the adoption by industrial organisations of the Japanese philosophy of manufacturing and, in particular, one aspect of this approach known as Just-In-Time (JIT) production. A key premise on which this methodology is based is that of demand-linked production and minimal work in progress inventory. Accordingly, much of the research undertaken in this area has concentrated on the inventory control aspect of supply chain design. This has been done in the context of a JIT environment and the performance of any given solution should be evaluated under the stress of unstable demand plus minimum inventory holding (Towill, Childerhouse, and Disney 2002).

For many companies in a global marketplace, downsizing the direct manufacturing labour force, alliances with overseas partners or moving manufacturing operations to countries where labour rates are low have allowed them to remain competitive and profitable. In the short term, this may have been a strategically correct decision for a company that is unable or incapable of reducing its manufacturing costs in any other way. In the longer term, however, it may prove to be a strategic mistake as orders become more difficult to obtain, fuel for transporting goods becomes more expensive, and insurance, regulation and security plus product transportation costs rise along with lengthening or uncertain delivery times. This is all as a consequence of the distance between suppliers, the manufacturing facility and the customer (Companies Bring Production Back Home 2010). The last two elements of cost and delivery time have long been recognised as key competitive factors in the marketplace together with both direct and indirect production costs (Hill 1993, 38). Hence the emphasis that has been placed in recent years on the design of company supply chains to achieve, if possible, very high operational flexibility consistent with minimum delivery times and transportation costs (Chopra and Meindel 2001).

To achieve this desirable objective, outsourcing has become a major strategic approach for many manufacturing firms, thereby establishing what has been apparent over the last decade or so, a switching of costs between the categories of labour and that of overheads, or direct to indirect costs, as a simple way of achieving a substantial cost reduction in the area of manufacturing operations. The strategic error, if it turns out that one has been made by companies who have moved all or part of their manufacturing operations overseas and away from their customers, is the relinquishing of an important aspect of cost control by company managers. This aspect being that market-driven and regulatory items, such as fluctuating interest and exchange rates, fuel, emission limits and other transportation costs, are external factors over which company managers have little or no control and even less influence. Unfortunately, this is an unpleasant and perhaps previously overlooked fact which for many firms has now been exacerbated by an on-going financial crisis together with the current world economic recession. In part, this may have led to the collapse of transportation-linked companies including some low-cost airlines [Robinson, D. 2008. ‘Zoom Airline Collapses and Halts Flights’ (The Times Online, August 29)] and many independent hauliers [Strange H., and F. Yeoman. 2008. ‘Angry Hauliers Descend on Capital in Fuel Price Protest’ (The Times Online, July 2)].

Shipping and airline companies, in particular, have high operational, maintenance and personnel costs to cope with, in addition to fuel and other commodity price variations. It should therefore be recognised by manufacturers of consumer products that operating and maintaining rail, maritime, aviation and other transportation systems require highly skilled and knowledgeable personnel, with all the attendant labour rate values that this implies. It should also be noted that such firms are subject, possibly sensitive, to many problems in a global economy not the least of which are strikes, piracy, terrorism, natural disasters and adverse weather conditions, all of which may result in loss, delay, ransom or damage to manufactured consumer products. In addition, many other factors are becoming increasingly relevant to the cost of extended supply chains and thus the competitiveness of companies. These are pollution, emission limits, global warming, sustainability and the potential impact of reverse logistics on the environment. Such concerns raise serious questions regarding the viability of a product's environmental sustainability and its carbon footprint with the extent of CO₂ emissions linked to transportation of products now giving rise to high levels of concern worldwide [Crooks, E., and V. Romei. 2009. ‘The G2: The Key to CO₂’ (The Financial Times, December 9, 13)].

Thus, the need for a full understanding of the health and environmental problems linked to work-part transport within the supply chain is only now being realised (Bates 2012), although considerable research and implementation in the area of ‘greening’ supply chains has been undertaken by the research and manufacturing community over many years (Rao and Holt 2005). For the most part, it appears that attempts to green the supply chain have concentrated on elements linked to both internal- and supplier-based production systems such as the introduction of waste and pollution management, environmentally friendly material usage and processing efficiency. The inbound, outbound and reverse logistic areas contribute to this initiative through the waste and pollution management programme by adopting environmentally friendly packaging design, transportation and control, plus product/packaging recovery and other recycling activities (Rao and Holt 2005). As previously indicated, a further possibility in this area of activity is the minimisation of transportation movement within the internal and external supply chains. This has the potential of reducing directly both the cost and the generation/release of combustible emissions, thereby improving company competitiveness, human health and environmental conditions. Accordingly, the following sections of this article outline a technique that provides an initial design solution for minimum transportation movement within both internal and external manufacturing supply chains.

2. The flow direction weighting scheme (FDWS)

The FDWS technique is an adaptation of a methodology originally proposed by Mukhopadhyay, Ramish Babu, and Vijai Sai (2000), wherein the authors have initially formulated a diagram known as the facility–edge flow graph in which facilities or machinery are represented as nodes or vertices and component flow paths as undirected edges. The component or work-part process routes are shown on this diagram to identify the number of items that require each of the created edges. Using these data, Mukhopadhyay, Ramish Babu, and Vijai Sai (2000) and his co-authors then tabulated each of the created edge connections and the total number of components that require a given edge. Although useful, the facility–edge flow graph can be confusing particularly when examining large problems and somewhat deficient in respect of the information it displays. As a consequence, it can perhaps be better presented as a cascade flow diagram similar to that shown in Figure 1.

Figure 1 Cascade diagram illustrating the goods/inter-stage flow direction and edge linkages. Note: Unused edge linkages are 1–4, 1–5, 1–6, 1–7, 2–6, 2–7, 3–5, 3–6, 3–7, 4–6 and 5–7.

The figure relates to a simple illustrative example of the original method as discussed by John, Davies, and Thomas (2009) and is presented here in the context of a supply chain rather than that of a facility layout. As may be seen in John, Davies, and Thomas (2009), when used in the context of a facility layout, the component flow path directions are indicated in the diagram along with the components that use them and those edges or linkages that are not used. In this contribution, the generic terminology of ‘supply routes’ replaces that of flow paths and the word ‘goods’ used in place of components. The revised form of representation shown in Figure 1 provides more information than that of the original graph, as the type of ‘good’ flow is shown and this allows the development of a solution procedure based on a FDWS (Davies, John, and Thomas 2013).

In the original Mukhopadhyay, Ramish Babu, and Vijai Sai (2000) method, a tabulated list of edge connections and components is generated from the machine/component edge flow direction and usage graph. These are then ranked in descending order by the number of work-parts that use a given edge and starting with the highest ranked edge, this is used to construct a modified Hamiltonian chain for the facility set. As explained in John, Davies, and Thomas (2009), the means by which this ranking is achieved materially affects the quality of the resulting solution. The requirement to improve solution quality has led to the development of the FDWS and its application to both internal and external supply chain designs.

3. A simple illustrative example

The dataset shown in Table 1 and the inter-stage goods incidence matrix (ISGIM) shown in Table 2 are used in this contribution to illustrate the effectiveness of the FDWS in the context of supply chain design and management. In this article, the simplicity of the initial example is appropriate, to demonstrate the methodology proposed and to evaluate the resulting solution in the context of supply chains. The sample data consist of four items or ‘goods’ (G1–4) that are processed through seven inter-stages (IS1–IS7). The initial section of the procedure creates the goods/inter-stage flow direction and edge linkage diagram as shown in Figure 1. This diagram was developed from the data contained in Table 1 and the corresponding ISGIM shown in Table 2. The supply route and path direction are indicated in the diagram by the solid lines and arrows. Once the goods/inter-stage edge flows have been established and depicted as in Figure 1, it is then possible to generate the inter-stage edge pair ranking list as shown in Table 3. This tabulates the edge connections required by each of the ‘goods’ supply routes: the ‘goods’ involved and the number of ‘goods’ that use a given edge connection.

Table 1 Goods/supplier routing data. After John, Davies, and Thomas (2009).

Goods	Supplier routing	No. of inter-stages visited
G1	IS2>IS4>IS7	3
G2	IS1>IS2>IS5>IS6	4
G3	IS1>IS3>IS2>IS4>IS7	5
G4	IS2>IS3>IS4>IS5>IS6>IS7	6

Table 2 ISGIM for Table 1. After John, Davies, and Thomas (2009).

	Goods
Inter-stages	G1	G2	G3	G4
IS1		x	x
IS2	x	x	x	x
IS3			x	x
IS4	x		x	x
IS5		x		x
IS6		x		x
IS7	x		x	x

Table 3 Inter-stage edge connection and total usage list.

Edge pair	Goods	Total usage
IS2–IS4	G1, G3	2
IS4–IS7	G1, G3	2
(IS7–IS2)^a	G1, G4	2
IS1–IS2	G2	1
IS2–IS5	G2	1
IS5–IS6	G2, G4	2
(IS6–IS1)^a	G2	1
IS1–IS3	G3	1
IS3–IS2	G3, G4	2
(IS7–IS1)^a	G3	1
IS3–IS4	G4	1
IS4–IS5	G4	1
IS6–IS7	G4	1

a These are return routes.

In the FDWS technique, and in the context of supply chains, the edge connections identified in Table 3, column 1 are ranked by giving the ‘good’ flow direction at each edge a weight and multiplying this by a total usage number of the ‘goods’ using that edge. That is, the number of times that edge is used by a ‘good’ during a supply cycle or a single processing iteration of the complete set of goods. This overcomes the implication that longer supply routes are somehow more important than shorter ones as suggested by John, Davies, and Thomas (2009) and takes into account complex backtracking within supply routings as indicated in a later example (Vandor 2010). It also defers to the fact that some types of movement in supply chains as with manufacturing systems are more desirable than others, a point previously recognised by Smith (1955) and Hollier (1963).

If the FDWS is adopted, then Table 3 can be expanded to that shown in Table 4. In the revised table, the following suffix notation is included to explain how the flow weight values are assigned to each edge:

	1Edge connection is sequential forward flow in raw data (accordingly, flow weight = 2). Table 4 Edge weighting and subsequent ranking. After Davies, John, and Thomas (2013). Edge pair Goods Total usage Flow weight Total and rank (IS2–IS4)^2 G1, G3 2 3 6 (1) (IS4–IS7)^2 G1, G3 2 3 6 (2) (IS7–IS2)^4 G1, G4 2 0 0 (x) (IS1–IS2)^1 G2 1 2 2 (10) (IS2–IS5)^2 G2 1 3 3 (5) (IS5–IS6)^1 G2, G4 2 2 4 (3) (IS6–IS1)^4 G2 1 0 0 (x) (IS1–IS3)^2 G3 1 3 3 (4) (IS3–IS2)^3 G3, G4 2 1 2 (6) (IS7–IS1)^4 G3 1 0 0 (x) (IS3–IS4)^1 G4 1 2 2 (7) (IS4–IS5)^1 G4 1 2 2 (8) (IS6–IS7)^1 G4 1 2 2 (9)
	2Edge connection is non-sequential forward flow in raw data (accordingly, flow weight = 3).
	3Edge connection is sequential forward and backward flows in raw data (accordingly, flow weight = 2 − 1 = 1).
	4Edge connection is not existent in raw data (accordingly, flow weight = 0).

The edge connection weighting scheme outlined above thus recognises the importance of a non-sequential forward movement in supply chains and reflects the fact that this type of flow in a routing sequence, as with manufacturing systems, implies a faster completion of the supply/processing cycle than does a sequential forward flow through each facility or inter-stage. Although the scheme penalises a backward flow in the routing sequence, it does so in the knowledge that this may be an unavoidable, though undesirable, manufacturing or supply chain requirement. A zero in the total column and ‘x’ in the rank column indicate that the edge does not appear in the raw dataset. In the context of supply chains, this would indicate that the return transportation routes are not considered in the analysis.

If the rankings generated and shown in Table 4 are now utilised using the procedure set out by Mukhopadhyay, Ramish Babu, and Vijai Sai (2000) for formulating in this case the supply routing as a Hamiltonian chain, the inter-stage sequences shown in Figure 2 can be formulated. From Figure 2(d), it is possible to observe that two couplets and one triplet are generated by the FDWS technique. If these are placed in the order of ‘good’ flow as shown in Figure 2(e), then the final inter-stage sequence is determined as:

Figure 2 Hamiltonian chain for the example data given in Table 4. (a) Rank 1 edge pair in Table 4, (b) rank 2 edge pair in Table 4 added to form initial chain, (c) rank 3 edge pair in Table 4 unconnected to chain, (d) rank 3 and 4 edge pairs in Table 4 unconnected to chain, (e) Hamiltonian chain with edge pair ranks 3 and 4 placed in the order of ‘good’ flow. After Davies, John, and Thomas (2013).

The inter-stage movement requirements to process the ‘goods’ contained in Table 1 are then as shown in Figure 3. By utilising the above sequence, it can be determined that the number of inter-stage moves to process the set of goods (G1–4) in one supply cycle is therefore 20. This is the minimum possible for the example (see Acknowledgement). In this simple problem, the distance between the stages is in all cases unity and this provides a measure of goodness when comparing competing solutions. Note that in the context of supply chains, this value can refer to a unit of time replacing physical distance between stages, and consequently, the total time required to complete a supply cycle now provides the measure of solution goodness.

Figure 3 FDWS supply routes for (a) ‘good’ G1 (two inter-stage moves), (b) ‘good’ G2 (six inter-stage moves), (c) ‘good’ G3 (four inter-stage moves) and (d) ‘good’ G4 (eight inter-stage moves). Total number of inter-stage moves = 20. After Davies, John, and Thomas (2013).

4. Application to supply chains

At this point, it is important to note that the FDWS technique solution provides a transport design that gives a minimum inter-stage movement for a given pre-determined set of supply route sequences and the precedence constraints they contain. It does not try to answer the travelling salesman problem, in which the solution given is the visitation sequence that minimises the travel distance between the locations of a known set of facilities within given precedence constraints (Applegate et al. 2006). Nor does it attempt to solve the transportation problem, wherein a product is transported from a number of sources to a number of destinations at the minimum possible cost, given that each source is able to supply a fixed number of units of the product, together with each destination having a fixed demand for it (Russell and Taylor 2000, 424–444). This is an important albeit subtle point to note as it affects the principles upon which a supply chain is designed.

In an academic sense, it is traditional to advocate that new manufacturing facilities are positioned in accordance with the location of existing suppliers and/or customers. Several techniques are available to identify the optimal location of the new facility based on the existing geographical coordinates of the suppliers or customers and the weight or number of deliveries required to or from them in a given period of time (Waters 2003, 104–136). In practice, however, supply chains tend to develop organically in relation to the locations of existing processing facilities and will alter over time as products change, suppliers are displaced and customers are won or lost. The reality is therefore that the supply chain design is at best a transient arrangement of such facilities, valid at a particular point in time and optimal only in relation to a given set of supply route sequences and the precedence constraints contained within them. With this understanding, we can now see how the FDWS technique can be utilised repeatedly in the context of both internal and external supply chains. It is applicable because the design criterion for the positioning of facilities or stages has changed, from minimising distance to minimising movement itself within a continually changing supply chain.

By adopting this approach, a degree of synchronicity of movement within the supply chain is also now possible by modifying the assessment criterion in the FDWS technique from a unit step in movement to a unit step in time. In addition, undertaking this modification, JIT principles and sustainability considerations can also be accommodated as movement time directly relates to the cost which in turn is influenced by distance, terrain and traffic conditions, all of which affect fuel consumption and hence combustible emissions. If we assume that in the above example, road transportation is envisaged using heavy goods vehicles to move the ‘goods’ between stages, then unit movement time provides the inter-stage measurement value. Hence, the minimum layout sequence given above that results in 20 transportation steps can be replaced by 20 h where the unit movement time between stages is designed to be 1 h. This concept of the temporal separation of facilities or stages raises all sorts of interesting implications and possibilities in respect of sustainable internal and external supply chain designs.

For instance, although it is obvious that the unit movement time can vary in value on a case-by-case basis, for the FDWS technique to be applicable, it must remain a constant at whatever value is set as the inter-stage movement time in a particular supply chain design. It is this which in theory would permit the degree of synchronicity to movement within the supply chain alluded to above and although intra-stage processing times can vary, it is now not inconceivable to apply line balancing techniques in the design of the logistic system. Certainly, overall supply cycle times for the set of ‘goods’ and individual ‘good’ throughput times can then be determined quite easily as shown in Table 5 as a modification to the example given above, if we assume that the sequential processing times of ‘goods’ through the inter-stage set are identical with one ‘good’ being completely processed prior to the commencement of processing the next ‘good’ and a unit movement time of 1 h. Clearly in this case and ignoring the ‘good’ in-stage processing times and transport mechanism return times, the FDWS technique would provide a solution that minimises overall supply cycle time, cost and combustible emissions.

Table 5 Comparison of the results of four evaluation techniques for the example presented, the inter-stage sequence solutions, the ‘good’ transportation times and the total supply cycle times.

Techniques
Mukhopadhyay, Ramish Babu, and Vijai Sai (2000) solution	Ho, Lee, and Moodie (1993) solution	John, Davies, and Thomas (2009) solution	Davies, John, and Thomas (2013) solution
IS3>IS2>IS4>IS7>IS1>IS6>IS5	IS1>IS3>IS2>IS4>IS5>IS6>IS7	IS1>IS3>IS2>IS4>IS7>IS6>IS5	IS1>IS3>IS2>IS4>IS7>IS5>IS6
G1 = 2 h	G1 = 4 h	G1 = 2 h	G1 = 2 h
G2 = 9 h	G2 = 5 h	G2 = 7 h	G2 = 6 h
G3 = 7 h	G3 = 6 h	G3 = 4 h	G3 = 4 h
G4 = 10 h	G4 = 6 h	G4 = 8 h	G4 = 8 h
Total = 28 h	Total = 21 h	Total = 21 h	Total = 20 h

The main implication of the above temporal separation concept in respect of minimising supply chain movement and the consequent CO₂ emissions is that processing stages should be designed according to a given movement time or temporal separation from each other rather than to a particular physical distance. In many supply chains, this amounts to the same thing, although the design originators using the criterion of cost minimisation may not have clearly understood this point at the time the design was conceived. It should be noted that movement time can account for the physical distance between facilities, the type of terrain involved, the transportation method and the conditions encountered during movement. In order to fully understand how the FDWS technique can be applied in practice, the example used above is now modified as outlined in the first of the examples below to be more representative of a practical albeit simple supply chain.

5. Illustrative examples

To distinguish between the original technique application area in a facility layout design and its proposed cross-over use in an external supply chain design, the following examples are expressed in italics.

5.1 Example

Assume that the four components or ‘goods’ of the previous example are now produced by a manufacturing company using the simple external supply chain elements or inter-stages outlined below.

	IS1 = Steelworks-metal foundry
	IS2 = Material supply stockist
	IS3 = Casting and forging facility
	IS4 = Machining facility
	IS5 = Forming facility
	IS6 = Metal finishing facility
	IS7 = Warehouse–distribution centre

The components or ‘goods’ are processed through the seven inter-stages in the supply chain as outlined inTables 1 and 2. As already indicated, each element in the supply chain is interconnected with its neighbours and travel, if required, is possible in both directions. Element separation is characterised by an average one-hour travel time in either direction, a temporal factor value that accounts for mode of transport, distance, terrain and transportation conditions between the elements. The problem is to determine the following aspects:

• The individual and overall supply chain processing times for the four goods using the comparative solution techniques of Mukhopadhyay, Ramish Babu, and Vijai Sai (2000), Ho, Lee, and Moodie (1993), John, Davies, and Thomas (2009) and Davies, John, and Thomas (2013). The in-stage processing period and the return of transport system times may be ignored.

• The amount of CO₂ emitted during the supply cycle transport for the four ‘good’ sets on the basis of an average transportation speed of 40 miles per hour and 2 kg of CO₂ being emitted per mile.

• The supply chain transportation flexibility index for the four ‘good’ sets outlined above and the implications of this value in respect of the supply chain design.

5.2 Solution

• Since the intra-stage processing period and the return transportation times can be ignored, the solution is given by converting the previous result for unit step minimisation into that of unit time as shown inTable5. In this case, transportation time between stages is one hour; therefore, the results mirror that for a unit step but in the time rather than movement domain.

• Fairly obviously, given the solution values for the four alternative techniques presented above, it is easy to understand that the CO₂ emitted values for each of these solutions follow the same pattern. This is shown below and it should be noted that the minimum time solution provides considerable savings in both transport mileage and CO₂ emitted. It should be further noted that although no figures are provided in the example, by implication, fuel consumption, transport infrastructure and vehicle deterioration and hence the cost of transport for this set of ‘goods’ are also reduced by adopting the minimum time solution.

• In this example, there are seven inter-stages and if these were arranged in a straight line, there would be six links between them. If movement between the inter-stages was restricted such that only one-way forward transfer was allowed, the transport flexibility in the supply chain would be in effect zero and the system regarded as ‘rigid’. This can be expressed mathematically as Dapiran and Manieri (1983), 555–568:

  where I_ft = transport flexibility index, n = number of inter-stages, n_e = number of utilised links or (n–1) in a ‘rigid’ system, N = maximum number of two-way connections between the inter-stages.

By substitution intoEquation (1), the transport flexibility is given by:

For the given example, and removing the straight-line layout restriction, seven inter-stages and six links would provide a maximum of 42 two-way connections, which would reduce to 21 one-way connections if bi-directional travel is disallowed.

By substitution intoEquation (1), transport flexibilities are given by:

For the given ‘goods’ set in this example, the transport flexibility by substitution intoEquation1 is given by:

It can easily be observed that the transport flexibility value for the four ‘good’ sets implies poor flexibility in the supply chain. If we accept the validity ofEquation1 as providing a suitable description of supply chain flexibility, then to improve flexibility it is necessary to either increase the number of connections used and/or reduce the number of inter-stages required to process the ‘good’ set. This can be illustrated in the first case by allowing the transport mechanism to return from the finish to the start of each ‘good’ processing cycle as would be required in a practical supply chain. By relaxing the original return restriction, three additional connections are then activated. That is, IS7>IS1, IS6>IS1 and IS7>IS2, the last of which is duplicated in the four ‘good’ processing sets. By substitution intoEquation1, the transport flexibility now becomes:

The effect of the second alternative can be gauged by combining, say, IS4 (the machining operation) with IS5 (the forming process) to create a single inter-stage with the capability of performing both functions. Re-evaluating the transport flexibility index by substitution of the new parameter values inEquation (1) now gives:

Note that the effect of combining the two elements IS4 and IS5 in the supply chain reduces the number of inter-stages required to 5 and the active connections by 1 in the ‘good’ G4 processing cycle. In addition, the maximum number of two-way connections between the inter-stages is reduced from 42 to 30.

The practicality of undertaking such a redesign of the supply chain as that proposed above would obviously require further investigation as would its effect on the inter-stage layout solution. However, it is possible to speculate that by activating more usable connections between the inter-stages, the expectation would be to see a rise in transportation flexibility along with additional transport movement, leading to increases in both cost and CO₂ emissions. Conversely, a reduction in the number of inter-stages required in the supply chain appears to provide increasing transportation flexibility while reducing transportation movement, cost and CO₂ emissions.

5.3 Example

The FDWS technique has been applied to a more complicated example of an internal supply chain as documented by Vandor (2010). In this case, an eight facility-by-sixteen component problem was addressed, which involved considerable backtracking.Table6 illustrates the problem as a facility/component incidence matrix.

Table 6 Vandor's (2010) 8 × 16 problem.

	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16
F1		x		x	x					x		x	x		x
F2	x	x	x	x	x			x	x	x		x	x		x	x
F3		x	x		x	x	x	x	x		x		x	x	x	x
F4	x	x	x	x	x		x		x	x	x		x	x	x	x
F5	x	x	x		x	x	x	x					x		x	x
F6	x		x		x	x		x	x	x	x	x	x	x	x	x
F7		x		x	x	x	x	x	x			x	x	x	x	x
F8	x	x	x	x	x		x	x	x	x	x	x			x

5.4 Solution

Vandor (2010)initially used the method ofJohn, Davies, and Thomas (2009)to solve the problem by producing a 188-movement solution for the component set. Subsequently, the FDWS technique was applied to the same problem by the current authors and with minor additions to the weighting scheme, which produced a movement answer of 181. The additions to the weighting scheme given above are as follows:

	5Edge connection is non-sequential backward flow in raw data (accordingly, flow weight = 3).
	6Edge connection is non-sequential forward and backward flows in raw data (accordingly, flow weight = 2).
	7Edge connection is sequential backward flow in raw data (accordingly, flow weight = 4).

The processing sequence is shown to progress vertically in the columns ofTable7.

Table 7 Vertical processing sequences for Vandor's (8 × 16) problem.

C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16
F2	F1	F2	F8	F5	F7	F3	F8	F2	F4	F4	F6	F3	F6	F1	F5
F4	F8	F5	F1	F7	F6	F4	F2	F8	F6	F8	F7	F1	F4	F2	F4
F6	F5	F4	F7	F4	F5	F8	F5	F7	F1	F3	F8	F7	F7	F3	F6
F8	F2	F3	F2	F6	F3	F7	F3	F3	F2	F6	F1	F4	F3	F4	F3
F5	F4	F6	F4	F8		F5	F7	F4	F8		F2	F5		F7	F7
	F7	F8		F1			F6	F6				F2		F8	F2
	F3			F2								F6		F6
				F3										F5

Further examination of the problem via a total enumerationexercise (see Acknowledgement) confirmed that the FDWS solution string F1, F2, F8, F5, F6, F4, F7, F3 provided the minimum movement answer of 181.

6. Conclusions

It would appear based on the composition outlined above that, as with the FDWS method, techniques in the design of facility layouts may be directly transferable and utilised in the area of the design of internal and external manufacturing supply chains. In addition, the concepts of temporal separation and minimum movement between supply chain elements would seem to be appropriate criteria to adopt when contemplating competing supply chain designs and evaluating them for flexibility, cost-effectiveness and environmental impact. Although speculative, the work outlined in this article does appear to raise some interesting questions regarding the possibility of techniques hitherto traditionally confined to manufacturing system design, such as those for facility layout and line balancing, being applied in the context of JIT supply chains. Obviously, much further research is required in these areas to indicate the validity or otherwise of such speculation via both case and simulation studies of real-life supply chain system designs. However, the single-site manufacturing policy recently adopted by some leading manufacturing companies, wherein qualified suppliers are encouraged via single sourcing contracts to site their production facilities in close proximity to the main product manufacturer, would appear to support the minimum time and movement concepts espoused above. Although the economics of any particular supply chain design will without doubt decide its relevance for adoption, there is some irony involved here, as the policy of single-site vertical integration manufacturing was first advocated and implemented in the early twentieth century by Henry Ford (1922) at his River Rouge plant in Detroit (Ford 1922).

Acknowledgements

The authors wish to acknowledge the contribution made by Dr R.I. Grosvenor in confirming, via a suitable MATLAB program, that the minimum numbers of inter-stage moves, quoted for the example problems used in this article, are in fact 20 and 181 as recorded in the text.

Notes

^1. Email: [email protected]

^2. Email: [email protected]