An economic production model with imperfect quality components and probabilistic lead times

• Date: 03 November 2020
• Published date: 03 November 2020
• Pages: 320-336
• DOI: https://doi.org/10.1108/IJLM-02-2020-0074
• Subject Matter: Management science & operations,Logistics
• Author: Abdul-Nasser El-Kassar,Alessio Ishizaka,Yama Temouri,Abdullah Al Sagheer,Daicy Vaz

An economic production model

with imperfect quality components

and probabilistic lead times

Abdul-Nasser El-Kassar

Information Technology and Operations Management,

Lebanese American University, Beirut, Lebanon

Alessio Ishizaka

NEOMA Business School, Mont-Saint-Aignan, France

Yama Temouri

Khalifa University, Abu Dhabi, UAE and

Aston University, Birmingham, UK

Abdullah Al Sagheer

Advisor for the Minster of Public Works, Minister’s Office Department, Kuwait, and

Daicy Vaz

Humanities and Social Sciences, Khalifa University of Science and Technology,

Abu Dhabi, United Arab Emirates

Abstract

Purpose –This study investigates a production process that requires Nkinds of components for the

production of a finished product. The producer orders the various kinds of components from different suppliers

and receives the orders in lots at the beginning of each production cycle. Similar to situationsoften encountered

in real life, the lead times are random variables with known probability distributions so that a production cycle

starts whenever all Nkinds of components become available. Each of the lots received at the start of a

production run contains both perfect and imperfect quality components. Once all Nkinds of components

become available, the producer initiates a screening process to detect the imperfect components. The

production of the finished product uses only perfect quality components. The imperfect components are

removed from inventory whenever the screening process is completed. The percentage of components of

perfect quality present in each lot is a random variable with a known probability distribution.

Design/methodology/approach –This production process is described and modeled mathematically and

the optimal production/ordering policy is derived based on the mathematical model.

Findings –The formulated mathematical model resulted in the determination of the optimal policy consisting

of the optimal number of finished items ordered to be produce during each production run, the number of

components ordered from each supplier, and the reorder point. The derived closed form expression for the

optimal lot size depends on the minimum of the number of perfect quality components in a lot, whereas the

reorder point is determined based on the maximum lead time.

Practical implications –The modeling approach and results of this study provide practical implications

that may be beneficial to both production and supply chain managers as well as researchers.

Originality/value –This modeling approach that incorporates decision-making related to the logistics of

acquiring the componentsand accounts for the probabilistic nature of the leadtimes and quality of components

addresses a gap in the logistics/production literature.

Keywords Economic production quantity, Probabilistic lead time, Imperfect quality components,

Reorder point

Paper type Research paper

IJLM

32,2

320

This paper forms part of a special section “Decision Making in Logistics Management in the Era of

Disruptive Technologies”, guest edited by Vijay Pereira, Gopalakrishnan Narayanamurthy, Alessio

Ishizaka and Noura Yassine.

The current issue and full text archive of this journal is available on Emerald Insight at:

https://www.emerald.com/insight/0957-4093.htm

Received 1 February 2020

Revised 12 September 2020

Accepted 13 September 2020

The International Journal of

Logistics Management

Vol. 32 No. 2, 2021

pp. 320-336

© Emerald Publishing Limited

0957-4093

DOI 10.1108/IJLM-02-2020-0074

1. Introduction

The classical production/inventory models, introduced at the turn of the last century, make

use of certain assumptions that ignore factors found in real life. Over the past decades,

numerous research studies have extended, modified and generalized these models by

including real life factors into the classical production/inventory models. Examples of factors

incorporated into these models include monetary factors (Salameh et al., 2003), deterioration

(Bandaly and Hassan, 2019), quality of items (Salameh and Jaber, 2000) and cost of

components required in the production process (Salameh and El-Kassar, 2007). Other recent

studies considered decision-making at the supply chain level (Pereira et al., 2019;Khan and

Jaber, 2011;Bandaly et al., 2014), learning and imperfect inspection processes (Khan et al.,

2014) and sustainable practices (Lamba et al., 2019;Yassine, 2018). Decision-making in

logistics management has been incorporated in the classical production/inventory models

(Bandaly et al., 2016;Khan and Jaber, 2011;Yassine, 2018;Yassine and El-Rabih, 2019).

A recent modeling approach (Salameh and Jaber, 2000) incorporating the quality of items

acquired by suppliers or produced by manufacturers has generated a stream of research

studies extending the classical production/inventory models (Khan et al., 2011). A number of

studies have examined the quality of components and/or raw material items used to produce

a finished product (Yassine, 2016;Yassine and AlSagheer, 2017). Khan and Jaber (2011)

proposed an extension of the model of Salameh and Jaber (2000) that considers the quality of

components/raw material items in a two-stage supply chain. However, they used a very

restricted assumption that ignores the excess good quality components. Yassine (2016)

investigated the minimum of a set of random variables and pointed out how the results can be

used to rectify the modeling approach of Khan and Jaber (2011).

Recentstudies in logistics andproduction managementindicate that supply chainmembers

are compelledto obtain components/raw materialitems of higher quality at competitive costs.

Hence, manufacturers and producers are inclined to look for suppliers who meet the

environmentaland quality requirements at affordable prices. Yassine(2018) incorporated into

the classicalproductionmodel the effect of transportationemissionstax as well as quality of the

various kindsof components used in the productionof the finished product anddemonstrated

how the excess perfect quality components are properly accounted for. Lamba et al. (2019)

determined the optimal lot sizes and supplierselection that reduce the total supply chaincost

that include the logistics carbon emissions cost. Yassine and Singh (2020) investigated the

selection of suppliers for a production model that uses one kind of components for the

production of the finished product. Their production model examined the effects of emission

taxes, the component’s quality, and inspection errors within a collaborative supply chain.

Limited by scarce resources and strict environmental requirements, corporations must

function in efficient, effective (El-Khalil and El-Kassar, 2016), and responsible manner (Song

et al., 2019a). Engagement in sustainable activities improves performance (Pereira et al.,

2020a,b;El-Khalil and El-Kassar, 2018;Singh et al., 2019;El-Kassar and Singh, 2019) and

results in favorable employees and customers related outcomes (El-Kassar et al., 2017). Higher

levels of competitiveness can be achieved by making optimal use of strategic resources that

include innovation (El-Kassar and Singh, 2019;Singh et al., 2020;Pereira et al., 2020a,b), ICT

technologies (Yunis et al., 2017,2018), big data analytics (Song et al., 2019a;Singh and El-

Kassar, 2019), and human resources (Yassine and Singh, 2020;Larsado and Pereira, 2017).

Due to environmental concerns, stakeholders put pressure on supplychain members to

ease the impact of their logistics and operational functions on the environment (Song et al.,

2018a). This drives members of the supply chain to revise and adopt strategies directed

toward the engagement in responsible and environmentally friendly operational activities.

Making careful decisions related to procurement and production can decrease cost, improve

quality, and ease the harmful impact of the activities of a supply chain on theenvironment

(Lamba et al., 2019). In the era of disruptive technologies and in the increasing volume,

An economic

production

model

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