Exploitation of material consolidation trade-offs in multi-tier complex supply networks Vinod Kumar Chauhan12 Muhannad Alomari3 James Arney3 Ajith Kumar Parlikad1

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Exploitation of material consolidation trade-oﬀs in multi-tier

complex supply networks

Vinod Kumar Chauhan∗1,2, Muhannad Alomari3, James Arney3, Ajith Kumar Parlikad1,

and Alexandra Brintrup1

1Institute for Manufacturing, University of Cambridge, UK

2Department of Engineering Science, University of Oxford, UK

3Data Labs, Rolls-Royce, UK

November 21, 2023

Abstract

While consolidation strategies form the backbone of many supply chain optimisation problems, ex-

ploitation of multi-tier material relationships through consolidation remains an understudied area, despite

being a prominent feature of industries that produce complex made-to-order products. In this paper, we

propose an optimisation framework for exploiting multi-to-multi relationship between tiers of a supply

chain. The resulting formulation is ﬂexible such that quantity discounts, inventory holding, and transport

costs can be included. The framework introduces a new trade-oﬀ between tiers, leading to cost reductions

in one tier but increased costs in the other, which helps to reduce the overall procurement cost in the

supply chain. A mixed integer linear programming model is developed and tested with a range of small

to large-scale test problems from aerospace manufacturing. Our comparison to benchmark results shows

that there is indeed a cost trade-oﬀ between two tiers, and that its reduction can be achieved using a

holistic approach to reconﬁguration. Costs are decreased when second tier ﬁxed ordering costs and the

number of machining options increase. Consolidation results in reduced inventory holding costs in all

scenarios. Several secondary eﬀects such as simpliﬁed supplier selection may also be observed.

Keywords: Supply chain management; multi-tier; supply network complexity; conﬁguration; procure-

ment cost optimisation; mixed integer programming; consolidation.Analytics, Artiﬁcial Intelligence

1 Introduction

Procurement of parts from suppliers is a key task in the supply chain management, greatly impacting its

competitiveness and performance (Amid et al. (2006)). In many industries, procurement cost often forms

the highest proportion of total cost of a product (Willard (2012)).

Consolidation has been a key underlying strategy in the context of procurement decisions. Consolidation,

as the name suggests, is a process of combining related activities or materials to improve performance of

a supply chain resulting from cooperation and coordination (Schulz and Blecken (2010); Chadha et al.

(2022)) and can help in reduction of costs, increase eﬃciency and improve performance (Vaillancourt (2016);

Giampoldaki et al. (2023)). Material consolidation consists of purchasing, transportation and inventory

activities (Brauner and Gebman (1993)), where a buyer or a set of buyers may choose to group items or

orders to obtain quantity discounts (Monczka et al. (1993); Hagberg and Hulth´en (2022)). While this helps

in increased eﬃciency and reduction of costs it can reduce ﬂexibility of sourcing options, thus reducing supply

chain resilience. Inventory consolidation considers relocation of warehouses to increase inventories in order to

∗Corresponding author (This work was done at University of Cambridge UK.)

arXiv:2210.11479v3 [cs.CE] 19 Nov 2023

make use of reduced operational costs but may introduce increased transport cost (Wanke and Saliby (2009);

Ralfs and Kiesm¨uller (2022)). Transportation consolidation merges small deliveries into single dispatch of

economical load but increase uncertainty in delivery times (Trent and Monczka (1998); C¸ etinkaya (2005);

Torbali and Alpan (2023)).

Consolidation activities to date have been overwhelmingly studied within the span of single supply eche-

lons (Stenius et al. (2018)). This is not surprising, as buyers often have control of their dyadic connections,

gradually losing both visibility and inﬂuence beyond their immediate connections, making consolidation de-

cisions not applicable beyond their immediate connections. There are, however, an increasing number of

industrial contexts where a buyer may inﬂuence its wider supply chain, and there is willingness for coop-

erative decision making for collective performance (Chauhan et al. (2023)). Examples include production

of complex, made-to-order products, such as heavy machinery, turbines, aerospace products, and medical

devices. Due to long-term supply relations involved in these sectors, a manufacturer may be involved in

conﬁguration of whole supply chain. In addition to whole supply chain conﬁgurability, longevity of relation-

ships necessitates de-risking through multi-sourcing activities. This increased span of control, coupled with

multi-sourcing oﬀers a unique multi-to-multi relationship structure whereby products may be consolidated

further upstream, aﬀecting cost structures at diﬀerent tiers.

In this paper, we highlight this understudied multi-tier consolidation problem presented by the above

context and formulate it through a case study. We term this new consolidation opportunity as “multi-tier

material consolidation problem”.

To contextualise the multi-tier consolidation problem, we consider following example from an aerospace

industry (Fig. 1). Here, aircraft engines are produced, requiring diﬀerent types of parts, which manufacturer

outsources from a set of certiﬁed machining suppliers. These Tier 1 suppliers need diﬀerent types of forged

metal to manufacture ﬁnal ﬁnished parts, which are themselves outsourced to Tier 2 forging suppliers. The

forgings that could be used for manufacturing diﬀerent parts is predetermined by the company.

Figure 1: Two-tier supply chain of a manufacturing company

The forging process involves manufacturing roughly shaped parts from melted alloys and machining

reﬁnes those into ﬁnal parts. The supply chain has N diﬀerent forgings to manufacture M diﬀerent parts,

and creates a multi-to-multi relationship between forgings and parts. That is, one forging can be used

to manufacture many parts, and similarly, one part can be manufactured in multiple ways from diﬀerent

forgings. The total procurement cost of parts from Tier 1 and forgings from Tier 2 depend on ordering

cost, unit cost and consequent transportation costs. Since parts can be manufactured in multiple ways

from diﬀerent forgings, requiring diﬀerent machining costs, forgings can be consolidated into a smaller set,

thereby, reducing the cost of forgings at the expense of increased machining time to manufacture parts from

a limited set of forgings, and hence increased machining cost. Thus, there is a trade-oﬀ between the reduced

cost of forgings at Tier 2 and increased machining cost at Tier 1. Additionally, since forging process takes

longer compared to machining, the company also maintains a speciﬁc inventory of forgings. This leads the

company to order additional forgings resulting in extra purchasing cost and cost of holding inventories.

Hence, objective of the multi-tier material consolidation problem in this example is to minimise overall

procurement cost across the supply chain by consolidating forgings and striking an optimal balance between

cost of forgings at second tier and machining cost at ﬁrst tier. This problem can be visualised as a clustering

problem, as presented in Fig. 2. Here, each forging is represented as a point in some space depicted as a

circle (as shown in left panel). The problem is to ﬁnd clusters whereby all forging in a cluster can be replaced

with a single forging from the group. That is, the selected forging is used to manufacture all machined parts

that were manufactured using diﬀerent forgings in the cluster (as shown in middle-panel). Thus, we need to

ﬁnd minimum number of clusters, and hence minimum number of forgings in the consolidated set (as shown

in right-panel), which balances the trade-oﬀ between cost of forgings and machining cost. Since ordering

items in diﬀerent quantities aﬀects the suppliers so quantity discounts also need to be considered.

Figure 2: Illustration of the multi-tier consolidation problem: Diﬀerent colours represent clusters where a

square-enclosed forging is used to replace all other forgings in its cluster.

The rest of this paper is structured as follows. In Section 2, we present related work on supply chain

consolidation to situate context of our contribution. In Section 3, we characterise the multi-tier material

consolidation problem, formulate it using an aerospace supply chain as a case study, discuss our solution

approach and choices of modelling languages as well as solver libraries, and present our analysis. We then

present concluding remarks, limitations and future scope of the study in Section 4.

2 Related work

Scholars in supply chain management have proposed several consolidation strategies to improve cost against

operational decision criteria. These can be broadly categorised as purchasing, shipment, inventory and part

consolidation (Brauner and Gebman (1993)), as discussed below.

2.1 Purchasing consolidation

Purchasing consolidation considers regrouping of items for purchase, which may involve grouping of multiple,

related types of products to be purchased from same supplier in order to obtain contractual and logistics

discounts (Monczka et al. (1993); Chauhan et al. (2023)), or pooling items to be purchased with other buyers

(group buying) to increase economies-of-scale and obtain a reduction on unit cost of production and delivery

(Vaillancourt (2017); Hu et al. (2022)). Both of these strategies may result in a loss of ﬂexibility, due to

the need to align production and deliveries with other product lines (in case of product grouping), or other

buyers (in case of group buying) (Vaillancourt (2016)). Early deliveries may result in increased inventory

costs (Guiﬀrida and Nagi (2006)), and over-reliance on a single supplier may increase risk and opportunism

(Chopra and Sodhi (2014)).

A related but separate strand of consolidation literature considers multi-sourcing decisions determining

number of suppliers supplying an item. It is generally presumed that single-sourcing, i.e., procurement from

a single supplier, results in the cheapest unit cost (Silbermayr and Minner (2016)) while dual-sourcing and

multi-sourcing avoid supplier monopoly of items and help reduce the risk of disruptions in a supply chain

(Tomlin (2006)).

Researchers have proposed a number of analytical models to characterise these trade-oﬀs. For example,

Gaur et al. (2020) considered a real-world case study of an automotive-parts manufacturer to study impact of

disruption on a closed-loop supply chain using sourcing policies. They developed a mixed-integer non-linear

programming model for the problem and found that, under the risk of supply chain disruption, multi-sourcing

generates more proﬁt as compared to single sourcing.

2.2 Shipment, volume and order consolidation

Shipment consolidation, also known as freight consolidation, transportation consolidation and terminal con-

solidation, is a logistics strategy which refers to merging of small deliveries into a single dispatch of economical

load (¨

Ulk¨u (2012); Wagner et al. (2023)). This helps in increased eﬃciency and reduction of CO2emissions,

and delivery costs, e.g., Mu˜noz-Villamizar et al. (2021) investigated shipment consolidation by pooling and

developed a mixed integer linear programming (MILP) model to study its eﬀect on CO2emission, distance

and transport costs. However, the practice can cause uncertainty in delivery times leading to poor service

for customers (Masters (1980)).

Volume consolidation, i.e., a strategy where a buyer purchases most of its supply from one supplier,

results in shipment consolidation and helps to reduce shipping costs. For example, Cai et al. (2010) studied

volume consolidation and its eﬀect on supply chain outcomes. Through an empirical study, they found that

volume consolidation enhances buyer’s ability to learn from the supplier, and supplier performance. However,

coordination costs negatively aﬀect buyer satisfaction and supplier performance.

Order consolidation refers to consolidation of a customer’s orders at a delivery station so as to organise

delivery in fewer trips. For example, Zhang et al. (2019) studied order consolidation for last-mile split-

delivery in online retailing and developed an integer programming model to study the trade-oﬀ between

splitting orders and consolidating shipments.

2.3 Inventory consolidation

Inventory consolidation, also called facility location problem, is identiﬁcation of optimal warehousing and

distribution centre locations and capacities to stock up inventories with aim of meeting customer demand

(Wanke and Saliby (2009); Seyedan et al. (2023)). Minimisation of inventory holding locations in a supply

chain helps to reduce operational costs, however, leads to increased distance travelled to customers and thus

increased CO2and transport costs (Gabler and Meindl (2007)).

A classical and widely studied strategy is postponement, which refers to late diﬀerentiation of products

to cater to fast changing demand (Zinn (2019)), resulting in cost savings (Geetha and Prabha (2021)). For

a systematic review on postponement strategy refer to Ferreira et al. (2018); Zinn (2019) and for a review

on consolidation eﬀect and inventory portfolio analyses refer to Wanke (2009).

2.4 Part consolidation through product redesign

Part consolidation is an activity that aims to drive supply chain costs down through part redesign (?Kunov-

janek et al. (2022)). Here, the assembled unit may be redesigned to contain fewer but more complex parts

leading to a trade-oﬀ between increased manufacturing cost and reduced supply chain cost (Knoﬁus et al.

(2019)), whilst manufacturing lead time may depend on process technology used. For example, Knoﬁus et al.

(2019) observed that part consolidation through Additive Manufacturing reduced lead times but resulted in

increased total costs due to loss of ﬂexibility.

Part consolidation is widely studied with diﬀerent objectives. For example, Johnson and Kirchain (2009)

applied a process-based cost model to quantify eﬀects of parts consolidation and costs on material selection

choices, and Crispo and Kim (2021) studied a multi-layered topology-based optimisation approach for part

consolidation in Additive Manufacturing. Gan et al. (2021) explored concurrent design of product and supply

chain and presented a trade-oﬀ between modularity of product and sourcing ﬂexibility in supply chain. For

a detailed review on part consolidation, refer to Sigmund and Maute (2013); Liu (2016); Gan and Grunow

(2016).

From this brief literature review, it is clear that consolidation has been studied widely in supply chains

at diﬀerent levels and with diﬀerent perspectives.

Our work presents a unique perspective, diﬀerent from the existing research, in its focus on the trade-

oﬀ between two supply tiers. We consider the problem of minimising procurement cost by consolidating

material through exploitation of multi-to-multi relationships in complex made-to-order products and show

that consolidation in one tier results in cost savings at that tier but increased manufacturing and inventory

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Exploitationofmaterialconsolidationtrade-offsinmulti-tiercomplexsupplynetworksVinodKumarChauhan∗1,2,MuhannadAlomari3,JamesArney3,AjithKumarParlikad1,andAlexandraBrintrup11InstituteforManufacturing,UniversityofCambridge,UK2DepartmentofEngineeringScience,UniversityofOxford,UK3DataLabs,Rolls-Royce,UKNo...

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Exploitation of material consolidation trade-offs in multi-tier complex supply networks Vinod Kumar Chauhan12 Muhannad Alomari3 James Arney3 Ajith Kumar Parlikad1

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