Real-time large-scale supplier order assignments across two-tiers of a supply chain with penalty and dual-sourcing Vinod Kumar Chauhan12 Stephen Mak1 Ajith Kumar Parlikad1 Muhannad Alomari3

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Real-time large-scale supplier order assignments across two-tiers of

a supply chain with penalty and dual-sourcing

Vinod Kumar Chauhan∗1,2, Stephen Mak†1, Ajith Kumar Parlikad‡1, Muhannad Alomari§3,

Linus Casassa¶3and Alexandra Brintrup‖1

1Institute for Manufacturing, Department of Engineering, University of Cambridge UK

2Institute of Biomedical Engineering, Department of Engineering Science, University of

Oxford UK

3R2Data Labs, Rolls-Royce

January 3, 2023

Abstract

Supplier selection and order allocation (SSOA) are key strategic decisions in supply chain manage-

ment which greatly impact the performance of the supply chain. Although, the SSOA problem has been

studied extensively but less attention paid to scalability presents a signiﬁcant gap preventing adoption

of SSOA algorithms by industrial practitioners. This paper presents a novel multi-item, multi-supplier

double order allocations with dual-sourcing and penalty constraints across two-tiers of a supply chain,

resulting in cooperation and in facilitating supplier preferences to work with other suppliers through

bidding. We propose Mixed-Integer Programming models for allocations at individual-tiers as well as an

integrated allocations. An application to a real-time large-scale case study of a manufacturing company

is presented, which is the largest scale studied in terms of supply chain size and number of variables so

far in literature. The use case allows us to highlight how problem formulation and implementation can

help reduce computational complexity using Mathematical Programming (MP) and Genetic Algorithm

(GA) approaches. The results show an interesting observation that MP outperforms GA to solve SSOA.

Sensitivity analysis is presented for sourcing strategy, penalty threshold and penalty factor. The devel-

oped model was successfully deployed in a large international sourcing conference with multiple bidding

rounds, which helped in more than 10% procurement cost reductions to the manufacturing company.

Keywords: Supply chain management; supplier order allocation; mixed-integer programming; ge-

netic algorithms; large-scale problems.

1 Introduction

Supplier selection and order allocation (SSOA) is the procurement problem of determining which item/material

should be procured from which suppliers in what quantities, that has been widely studied (Chakravarty

(1979); Pan (1989)). SSOA constitutes a fundamental part of supply chain management which greatly im-

pact the performance and competitiveness of the supply chain (Amid et al. (2006)). In many industries, the

procurement of materials and services can cost up to 80% of the total cost of a product (Willard (2012)).

∗vinod.kumar@eng.ox.ac.uk (This work was done at University of Cambridge UK.)

†sm2410@cam.ac.uk

‡aknp2@cam.ac.uk

§Muhannad.Alomari@Rolls-Royce.com

¶Linus.Casassa@Rolls-Royce.com

‖ab702@cam.ac.uk (corresponding author)

arXiv:2210.11953v3 [cs.CE] 30 Dec 2022

Having been studied for few decades, research streams on SSOA have focused on the creation of optimiza-

tion algorithms and mathematical models for various problem types, including single, dual, multi-sourcing,

the incorporation of discounting and inﬂation, and how closed-loop supply chain and sustainable conﬁgura-

tions could be embedded (Aouadni et al. (2019); Pasquale et al. (2020); Naqvi and Amin (2021)).

However, according to a recent review, only 34% of the studies in the sample were conducted based on

real industrial cases or real collected data (Pasquale et al. (2020)). The literature consists mainly of supply

chains of limited sizes - our review shows that for real cased studies, the maximum scale of supply chain

studied under the SSOA literature consists of 15 suppliers and 90,000 variables (See Table 1).

In light of the above, the industrial trend shows an interesting conundrum. Companies with large scale

complex supply chains would be more likely to be in need of automated algorithms to conﬁgure their supply

chains, as the problem space becomes too complex to tackle manually. Recent studies show an increasing

trend in the complexity of supply chains (e.g. Christopher (2021)), add to the urgency of need for algorithms

that can handle high numbers of products and suppliers in SSOA optimization.

Large-scale SSOA across multiple-tiers brings about unique advantages as well as challenges. Current

little to no attention paid to the multi-tier and large-scale nature of the problem presents a gap between

theory and practice, as extant algorithms are not adopted to serve the needs of industries with complex

supply networks including aerospace engineering, industrial machinery and medical devices. Taking a multi-

tier perspective, where suppliers’ preferences to work with one another are incorporated is realistic and helps

improve cooperation. Large-scales of complex supply networks are another reality that have not yet been

tackled. Several industries have to select and assign hundreds, if not thousands of products/items during

procurement due to the complexity of engineered products being built. However, as our literature review

shows, scalability of existing approaches are hitherto unknown. On the other hand, the solution approach we

present that tackles these issues do increase the complexity of the problem due to the inherent dependency

of the tiers on each other. Moreover, the collection of data for multiple tiers is diﬃcult and the OEM needs

to be in a position to be able to do so, for our approach to be applicable.

In this paper, we present a set of techniques for researchers to consider solving the SSOA at scale and

discuss how it can be extended to SSOA variants. We test our proposed approach using a real-life case

study involving 2 tiers, 7,200,020 decision variables and 70 suppliers, constituting the largest SSOA use case

to date. The case study includes a time constraint, in that the SSOA allocation needs to be done under

a reasonable time limit that would allow procurement oﬃcers to negotiate with suppliers proposing bids

during a multi-round bidding process taking place during a sourcing conference. Our work presents a novel

SSOA problem which considers allocations on two-tiers allowing suppliers to bid to work with each other and

penalize non-preferred allocations through the penalty constraints. The problem characteristics additionally

include NP-hardness and dual-sourcing constraints.

Our results show that there exists few methods in literature that can handle a real-time constraint.

Problem formulation, as well as modelling language and solver engine all play a role in the success of the

algorithm, whereas extant literature typically treats these solution components in isolation from one another.

We go on to argue that all three components need to be considered as they impact one another.

Thus, the research question of the study is given as: How to automate a dynamic/real-time real-life large-

scale double supplier allocations at two-tiers of a multi-item supply chain with dual-sourcing and penalty

constraints? The contributions of the study, while solving the research questions are summarized below.

•A novel multi-item multi-supplier order allocation problem with penalty constraints and dual-sourcing

is presented.

•The problem involves double allocations at two diﬀerent tiers of the supply chain which result in

cooperation between tiers and facilitate supplier preferences to work with each other.

•Mixed-Integer Linear Programming models are developed for supplier order allocations at individual-

tiers as well as integrated allocation.

•A generic approach to solve large-scale problems using mathematical programming is presented.

•A dynamic large-scale real-life case study of a manufacturing is presented which helps the company to

automate the manual allocations and negotiate better prices.

The rest of the paper is organized as follows:

Section 2 gives the relevant background of the SSOA problem highlighting a signiﬁcant gap on real-life

studies that consider problem scale. Section 3 introduces the case study which sets out the industrial context

in which large scale SSOA issues arise. Section 4 proposes a threefold method to handle large scale SSOA

problems. Section 5 applies the aforementioned method to the case study presenting experimental results.

Section 6 concludes the paper.

2 Literature review

Here, a brief literature review on supplier selection and order allocation (SSOA), discounts on order allocation

and scale of the problem are presented.

2.1 SSOA

SSOA problem has attracted the interests of academicians as well as practitioners for a long time with

the earliest known works starting in 1979 (Chakravarty (1979)). Here, we brieﬂy summarize the main

categorisations of the SSOA problem to give the reader a background, before moving onto discounting and

industrial practicability, which form the main constituencies of our inquiry. For detailed reviews on the

SSOA problem, please refer to Aouadni et al. (2019); Pasquale et al. (2020), and Naqvi and Amin (2021).

The problem has been studied extensively in diﬀerent industrial settings including automotive (Hadi and

Robert (2019)), manufacturing (Guo et al. (2013)) and food supply chain (Mohammed et al. (2018)) etc.,

and with diﬀerent supply chain conﬁgurations, e.g., traditional SC (Chakravarty (1979)), green/sustainable

SC (Hosseini et al. (2022)), collaborative/Integrated SC (Renna and Perrone (2015)) and closed-loop supply

chains SC (Nasr et al. (2021)).

Diﬀerent settings included supply chain conﬁguration under disruption risks (PrasannaVenkatesan and

Goh (2016)), supply chains with single and multiple products, single, dual and multi-sourcing strategies

(Sawik (2014b)), with discounts (Alegoz and Yapicioglu (2019)), inﬂation (Khoshfetrat et al. (2020)) and

order splitting (Sun et al. (2022)) etc.

SSOA can also be classiﬁed into three categories, according to the solution approach (Pasquale et al.

(2020)): conﬁguration problems involve those where (i) Suppliers are selected from a predeﬁned certiﬁed

list, according to some measure such as reliability (Meena and Sarmah (2013)) (ii) Bi-phase SSOA where

suppliers are selected using a multi-criteria decision making (MCDM) method such as analytic hierarchy

process (AHP), analytical network process (ANP) and technique for order preference by similarity to ideal

solution (TOPSIS) or artiﬁcial intelligence (AI) based techniques (C¸ ebi and Otay (2016)), after which orders

are allocated. (iii) An integrated model is used for supplier selection and order allocation (Gupta et al.

(2016)).

SSOA problems have been solved mainly by four types of methods: (i) Mathematical Programming

methods such as linear, non-linear integer programming, single and multi-objective optimization problems

etc. (Sawik (2014a)), (ii) MCDM methods such as AHP, ANP, VIKOR (which stands for ‘VlseKriterijumska

Optimizacija I Kompromisno Resenje’) and TOPSIS etc. (Alegoz and Yapicioglu (2019)), (iii) AI methods

such as neural networks, fuzzy inferencing, GAs and particle swarm optimization (PSO) etc. (Meena and

Sarmah (2013)), and (iv) Simulation based methods (Moghaddam (2015)).

2.2 Penalties and discounts

Discounts in SSOA have been studied by many researchers, such as Alegoz and Yapicioglu (2019); Alfares

and Turnadi (2018); Ayhan and Kilic (2015); Cheraghalipour and Farsad (2018); Hadian et al. (2018); Meena

and Sarmah (2013); Hadi and Robert (2019); Safaeian et al. (2019); Shalke et al. (2018).

Some notable works include:

Vital Soto et al. (2017) addressed multi-period lot sizing problem with supplier selection and considered

both all-units and incremental quantity discounts. A mixed-integer non-linear programming (MINLP) model

is developed and solved using a hybridized search evolutionary LP-driven local search method.

Ghaniabadi and Mazinani (2017) considered dynamic lot sizing with supplier selection, backlogging and

both all-units and incremental quantity discounts. They proposed mixed-integer linear programming (MILP)

models and solved using Gurobi 6.5.2.

Shalke et al. (2018) studied all-unit and incremental quantity discounts in a sustainable supply chain.

They proposed a multi-objective model for SSOA and solved it using a multi-choice goal programming

approach.

Cheraghalipour and Farsad (2018) studied a case study of SSOA in plastic industry with disruption

risks and considered quantity discounts of all-unit, incremental and no-discounts. Here, supplier selection is

performed using a multiple criteria decision making (MCDM) approach called best-worst method (BWM)

and for order allocation a MILP model is proposed to minimize the total costs and maximize the total

sustainability score of all suppliers. The proposed model is solved using a Revised Multi-Choice Goal

Programming (RMCGP) method.

Most recently, Alegoz and Yapicioglu (2019) posed an SSOA problem with fast service options and

considered incremental quantity discount and no-discounts. They developed a hybrid approach based on

fuzzy TOPSIS (FTOPSIS), trapezoidal type-2 fuzzy AHP and goal programming.

A challenge in multi-tier SSOA that has not yet been handled is price dependencies resulting from relations

between suppliers. When a certain Tier1 supplier is selected to supply a certain product, that supplier itself

will have preferences on whom it wants to work with on Tier2. However, if Tier2 suppliers are also suggested

by the OEM, such as in the use case presented here, then the Tier1 supplier will assert its preferences by

applying diﬀerent bids. Another interesting point to note is that when a certain amount of orders is given to

a Tier1 supplier, unit price of obtaining parts from Tier2 may increase or decrease, which will be passed onto

the OEM. While most SSOA problems to date either assumed no control by the OEM over the second tier,

or full control, where the suppliers choices to work with one another are not considered. Our study presents

an approach where such dependencies are considered through the incorporation of penalties from suppliers.

The penalties are opposite of discounts provided by suppliers and not discussed for SSOA. Moreover, these

penalty constraints are based on certain type of items and orders received by suppliers, unlike quantity

discounts studied in the literature.

2.3 Scale and industrial practicability

Although the SSOA problem has been studied extensively in diﬀerent settings, according to a recent sys-

tematic review by Pasquale et al. (2020), only 34% of the studies in the sample were conducted based on

real industrial cases or real collected data. Even in recent studies, supply chains of limited sizes were stud-

ied. Typically, the studies consider 5–10 suppliers and 5–20 products/parts, e.g., automotive studies (see

Table 1). But in reality, these industries have thousands of parts and large number of suppliers.

Some recent example studies are summarized here.

Sawik (2014a) considered a customer driven supply chain where diﬀerent parts supplied by diﬀerent

suppliers are assembled into a variety of products by a producer to meet customer orders. The problem

considered a numerical study with 10 suppliers and 25 products, each of which could have up to 3 parts.

Both single and dual-sourcing under disruption risks were considered. The authors formulated a mixed-

integer programming model and solved using AMPL (A Mathematical Programming Language) modelling

language and CPLEX solver. This work was further extended using multiple sourcing in Sawik (2014b)

which was solved using CPLEX and Gurobi solvers.

Hadi and Robert (2019) solved Sustainable SSOA problem for multiple products, multiple periods in a

multimodal transportation supply chain with shortage and discount conditions. They formulated a multi-

objective MILP (MOMILP) model which was solved using a hybrid solution approach based on Benders

decomposition. They studied a use case from the automotive industry with 4 suppliers and 2 raw materials

for 2 years with 172 variables. But they studied a large test problem with 50 suppliers, 30 materials and 18

products with 6,929,314 variables. This is the largest study to date with respect to number of variables.

Youseﬁ et al. (2019) considered a two-stage hybrid supply chain with single-buyer and multi-vendor

coordination. They used a novel, game theoretic, pricing strategy. The problem was formulated as multi-

objective MINLP (MOMINLP) model to minimize costs and evaluate suppliers simultaneously, which was

solved using LINGO 14 software. It was a numerical study and the problem had 1 buyer and 10 suppliers

with less than 100 variables.

Alegoz and Yapicioglu (2019) considered fast service options and discount factors in SSOA problem and

developed a hybrid approach based on FTOPSIS, trapezoidal type-2 fuzzy AHP and goal programming.

They considered a case study of 6 suppliers and 13 products with 325 variables.

Hosseini et al. (2019) considered SSOA problem for building resilient SC considering supplier restoration

under disruption risks. They used a probabilistic graphical model for supplier selection and stochastic multi-

objective model for order allocation is solved using a fuzzy c-mean clustering algorithm and using augmented

-constraint method. They studied numerical problems with 10-19 suppliers and 397-861 variables.

Mohammed et al. (2019) studied the sustainable supply chain of a metal factory with 3 suppliers in Saudi

Arabia, and having only 3 variables. For supplier evaluation and ranking, they considered economic, envi-

ronmental and social aspects using an integrated Fuzzy AHP (FAHP)–FTOPSIS method, and for selecting

supplier and assigning optimal quantities, using a fuzzy multi-objective optimization model.

Esmaeili-Najafabadi et al. (2019) considered a centralized supply chain with disruption risks and for-

mulated the SSOA problem as a MINLP model. Their use case had 1 buyer, 10 suppliers and 2 types of

parts.

Almasi et al. (2019) studied a sustainable supply chain of an automotive manufacturing company under

disruption risk and inﬂation. They formulated the SSOA problem as a multi-objective and multi-period

mathematical model, and solved using weighted sum approach (WSA) and augmented -constraint (AEC)

method. The supply chain had 1 manufacturer, 5 products, 3 suppliers and 3 periods, and 750 variables in

the model.

Rezaei et al. (2020b) discussed SSOA problem in closed-loop supply chain conﬁguration with various

sourcing strategies and under disruption risk. They used the sample average approximation (SAA) method

to solve the problem which considered a numerical example having 30 suppliers, 20 products and 5 parts

with 78,152 variables.

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Real-timelarge-scalesupplierorderassignmentsacrosstwo-tiersofasupplychainwithpenaltyanddual-sourcingVinodKumarChauhan*1,2,StephenMak1,AjithKumarParlikad1,MuhannadAlomari§3,LinusCasassa¶3andAlexandraBrintrup11InstituteforManufacturing,DepartmentofEngineering,UniversityofCambridgeUK2InstituteofBiom...

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Real-time large-scale supplier order assignments across two-tiers of a supply chain with penalty and dual-sourcing Vinod Kumar Chauhan12 Stephen Mak1 Ajith Kumar Parlikad1 Muhannad Alomari3

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