Li, Xiaodong

Mohammed, Ahmed

Wang, Qian

Ahmed Mohammed

Qian Wang

Xiaodong Li

Crossref

A cost-effective decision-making algorithm for integrity of HMSCs: A multi-objective approach

In recent years, there has been a growing concern about safety and quality of food in the public society. This requires food suppliers or retailers who can monitor their food supply chains providing adequate information that can be easily accessed by customers who purchase food products in supermarkets. This can be achieved partially by implementing fast-growing IT techniques such as an integrated RFID (radio frequency identification)-based management system into an entire network of food supply chains. Nevertheless, this may lead to additional costs that need to be addressed when designing and implementing such an RFID-based food supply chain network. This paper presents a development of a multi-objective mathematical model that was used for quantifying a proposed design of a three-echelon Halal meat supply chain (HMSC) network, which is monitored by an integrated RFID-based management system. The study was aimed at maximizing the integrity of Halal meats, return of capital investment and minimizing costs in implementation of such a system into the HMSC network. A case study was also used for examining the validation and applicability of the developed HMSC model.</p

University of Birmingham Research Portal

A cost-effective decision-making algorithm for integrity of HMSCs:A multi-objective approach

Portsmouth University Research Portal (Pure)

A COST-EFFECTIVE DECISION-MAKING 
ALGORITHM FOR INTEGRITY OF HMSCs: A 
MULTI-OBJECTIVE APPROACH
Ahmed Mohammed, Qian Wang 
School of Engineering. University of Portsmouth 
Portsmouth, UK 
Ahmed.mohammed@port.ac.uk 
Xiaodong Li 
Department of Mathematics. University of Portsmouth 
Portsmouth, UK
 
 
Abstract—In recent years, there has been a growing concern 
about safety and quality of food in the public society. This 
requires food suppliers or retailers who can monitor their food 
supply chains providing adequate information that can be easily 
accessed by customers who purchase food products in 
supermarkets. This can be achieved partially by implementing 
fast-growing IT techniques such as an integrated RFID (radio 
frequency identification)-based management system into an 
entire network of food supply chains. Nevertheless, this may lead 
to additional costs that need to be addressed when designing and 
implementing such an RFID-based food supply chain network. 
This paper presents a development of a multi-objective 
mathematical model that was used for quantifying a proposed 
design of a three-echelon Halal meat supply chain (HMSC) 
network, which is monitored by an integrated RFID-based 
management system. The study was aimed at maximizing the 
integrity of Halal meats, return of capital investment and 
minimizing costs in implementation of such a system into the 
HMSC network. A case study was also used for examining the 
validation and applicability of the developed HMSC model.  
 Keywords—RFID, Halal, supply chains, modeling, multi-
objective optimization 
I. INTRODUCTION 
Today, it is essential for designing and implementing a cost-
effective food supply chain in order to gain a profitable share 
in the competitive market. Meantime, the issue in safety and 
quality for food is one of major concerns and consumers 
increasingly demand more transparent information on food 
they purchase in supermarkets. For many Muslim 
communities who live in countries like the UK, integrity of 
Halal food is also important. Thus, these consumers also 
demand more transparent information in terms of integrity of 
Halal food they purchase in local supermarkets.  
 
The Islamic term of Halal means allowed or permitted in 
English translation and it is often used in association with food 
products, i.e., food products that are permissible for Muslims 
to eat or drink under the Islamic Shari’ah (laws). For instance, 
production of Halal meats needs to comply with the Islamic 
Shari’ah in each process of livestock feeding, slaughtering, 
packing, storing and transporting before being sold as Halal 
meats in supermarkets. If a specific process is not handled 
properly in a Halal way, retailers and consumers may regard 
these meat products as non-Halal. Today, consumption of 
Halal meats is a well-known diet among not merely Muslim 
but also many non-Muslim people and it is one of fast-
growing businesses in the world. Nevertheless, there is a little 
amount of research work relating HMSC-related design and 
implementation in an aspect of both customer satisfactions (of 
Halal meat integrity) and economic costs. Apparently, this 
area is overlooked by researchers [1], [2]. 
 
Gen [3] and Deb [4] proposed a multi-objective 
mathematical model in solving a practical supply chain design 
problem. Wheras other researchers applied this approach into a 
design of supply chains with different objectives as in [5], [6], 
[7].  Kannan [8] developed a mathematical model to examine a 
supply chain management in battery recycling. Amin [9] 
developed a mixed integer linear programming model that 
minimizes a total cost for multiple locations in a closed-loop 
supply chain network. Duffuaa [10] developed a multi-
objective model with three objectives, which were aimed to 
maximize profit, income and product uniformity based on a 
ranking system that rates quality for those inspected products to 
determine different selling prices in the market. Amin [11] 
developed a multi-objective fuzzy programming model that 
was used for configuring a closed-loop supply chain network, 
which consists of disassembly, refurbishing and disposal sites. 
Three objectives were considered in optimizing profit, 
suppliers’ selections and defect rates. Lee [12] proposed a non-
linear multi-objective programming model for managing a coal 
supply chain with three objectives: costs of facility location, 
path selection and transportation. Wu [13] developed a 
mathematical model for a closed loop supply chain with two 
objectives using a scenario-based programming. Similar 
studies were published by Vahdani [14] in designing a closed 
loop supply chain using a fuzzy multi-objective optimization 
model. Samanlioglu [15] developed a multi-objective location 
routing model in configuring a supply chain management of 
hazmat recycling. Cakravastia [16] provided a mixed integer 
multi-objective model for determining a selection of suppliers 
in designing a supply chain. Tzeng [17] developed a production 
and distribution model using a multi-objective programming in 
order to maximize the total profit by improving the service 
level.  
The authors wish to thank the Higher Committee for Education 
Development (HCED) in Iraq for the financial support in this study. 
II. THE MATHEMATICAL MODEL 
 
Fig. 1 illustrates a three-echelon HMSC network which 
consists of farms, abattoirs and retailers. To ensure the integrity 
of Halal meat products, an RFID (radio frequency 
identification) based monitoring system was proposed to 
monitor every process during production (at farms and 
abattoirs) and transportation. Obviously, implementation of the 
proposed RFID-based monitoring system requires capital 
investments or additional costs, which are one of key measures 
in designing and implementing a cost-effective HMSC. Thus, a 
mathematical model with the multi-objective approach was 
developed as an aid for determining investment costs, return on 
investments and integrity in numbers of Halal meat products. 
The three objectives include the objective (equation 5) to 
minimize the total cost of investments, the objective (equation 
6) to maximize the integrity halal meats and the objective 
(equation 7) to maximize the return of investment (profit). 
 
 
 
 
 
 
 
 
 
 
 
Fig. 1. The three-echelon HMSC 
Sets, parameters and decision variables are as follows: 
Parame
ters: 
 
,αE
iC  equipment (E) cost (GBP) required for farm i  
E,β
iC  equipment (E) cost (GBP) required for abattoir j   
I,α
iC  implementation (I) cost (GBP) required for farm i   
,βI
jC     implementation (I) cost (GBP) required for abattoir j   
T,u
ijC  unit transportation (T) cost (GBP) per mile from farm i  
to abattoir j   
T,v
jkC  unit transportation (T) cost (GBP) per mile from abattoir j  
to retailer k   
u
ijd  travel distance (mile) from farm i to abattoir j  
v
jkd  travel distance (mile) from abattoir j to retailer k  
W transportation capacity (units) per vehicle 
α
iS   maximum supply capacity (units) of farm i  
β
jS   maximum supply capacity (units) of abattoir j  
β
jD   minimum demand (in units) of abattoir j  
kD   minimum demand (in units) of retailer k  
u
ijP   integrity percentage through first transportation link u  
from farm i to abattoir j  
v
jkP   integrity percentage through second transportation 
 link v from abattoir j to retailer k  
α
iR   return of investment (GBP) for farm i  
β
jR   return of investment (GBP) per item for abattoir j  
1G   goal of the objective 1  
2G   goal of the objective 2 
3G   goal of the objective 3 
 
Variables: 
 
u
ijx   quantity of units transported through first  
transportation link u from farm i to abattoir j  
v
jkx   quantity of units transported through second  
transportation link v from abattoir j to retailer k  
α
iy   1: if farm i is open 
0: otherwise   
β
jy   1: if abattoir j is open 
0: otherwise   
1n   negative deviation variable of the objective 1  
2n   negative deviation variable of the objective 2  
3n   negative deviation variable of the objective 3 
1p   positive deviation variable of the objective 1 
2p   positive deviation variable of the objective 2 
3p   positive deviation variable of the objective 3 
The goal programming approach was employed, i.e., each 
objective was given a goal value to be approached by 
minimizing the undesired deviation towards to the goal value 
to be achieved. To this aim, each objective was solved 
individually and its value was given as a target for the 
approaching function. Equations 1-4 show the solution 
functions for tackling the problem of the developed multi-
objective model. 
 
min  Z  (1) 
1
1
n Z
G
≤  (2) 
Sets:  
I   set of farms i I∈  
J  set of abattoirs j J∈  
K  set of retailers k K∈  
u
ijd
v
jkd  
1 
2 
3 
K 
      Farm sites iα   
1 
2 
3 
I 
 
1 
2 
3 
J 
Abattoir sites jβ  Retailer sites ky   
 1jβ =  u
ijx  xvjk  
1ky =   1iα =   
2p Z
2G
≤  
(2) 
3
3
p Z
G
≤  (3) 
Objective function 1:  
( ) ( )E,α I,α α E,β I,β βi i i j j j
i I j J
u v
ij jkT,u u T,v v 1 1 1
ij ij jk jk
i I j J j J k K
C C   y C C   y
x x
C  ] d C  ] d n p
W
[ G
W
[
∈ ∈
∈ ∈ ∈ ∈
+ + +
+ + − =+
∑
∑∑ ∑∑
∑
 
 (4) 
 
Objective function 2: 
u u v v 2 2 2
ij ij jk jk
i I j J j J k K
P  x P x n p G 
∈ ∈ ∈ ∈
+ + − =∑∑ ∑∑   (5) 
 
Objective function 3:  
α u β v 3 3 3
i ij j jk
i I j J j J k K
R  x R x n p G 
∈ ∈ ∈ ∈
+ + − =∑∑ ∑∑   (6) 
 
Constraints: 
α αS y xu i
i
ij i
I∈
≤∑        j J∀ ∈   (7) 
v β β
jk j jx S y          k
j J
K
∈
≤ ∀ ∈∑  (8) 
u β
ij j
i I
x D
∈
≥∑             j J∀ ∈  (9) 
v
jk k
j J
x D
∈
≥∑            k K∀ ∈  (10) 
β v
j jk
k K
D x
∈
≥∑            j J∀ ∈  (11) 
u
ijx integer  
(12) 
v
jkx integer  (13) 
α
iy binary  (14) 
β
jy  binary  (15) 
Where, equations 8 and 9 are supply capacity constraints in 
quantity; and equation 10-12 are demand constraints in 
quantity. 
III. APPLICATION AND VALIDATION 
In order to examine applicability and validation of the 
developed mathematical model, a case study was applied. 
Table I shows data collected and provided from farms, 
abattoirs and retailers by the Halal Meat Committee (HMC) in 
the UK [18]. The Google map was used to estimate travel 
distances between farms and abattoirs, and between abattoirs 
and retailers. In case study A, London-South West area was 
considered, it includes 5 farms, 6 abattoirs and 11 retailers. In 
case study B, London-South East area was considered, it 
includes 5 farms, 6 abattoirs and 3 retailers. 
TABLE I.  DATA FOR CASE A AND B 
Case A / London – South West  
I = 5 E,β
jC = 4K-7.5K  
J = 6 I,β
jC = 700-1.2K  
K = 11 α
iS  = 1.2K-2.5K 
E,α
iC = 4K-8K 
β
jS  = 1K-1.8K 
I,α
iC  = 400-800 
β
jD  = 300-1.5K 
γ
kD  = 50-100 
u
ijd  = 23- 410 
u
ijP  = 0.85-0.98 
v
jkd = 110 -174 
v
jkP  = 0.85-100 W  = 100 
α
iR  = 30-100 
β
jR  = 15-100 
Case B / London – South East  
I   = 5 E,β
jC = 4K-7.5K  
J   = 6 I,β
jC = 700-1.2K  
K  = 3 α
iS = 1.2K-2.5K 
E,α
iC = 4K-8K 
β
jS = 1K-1.8K 
I,α
iC = 400-800 
β
jD = 600-1.5K 
γ
kD  = 100-200 
u
ijd = 23- 400 
u
ijP = 0.90-0.98 
v
jkd = 110 – 162 
v
jkP = 0.85-100 W = 100 
α
iR = 60 
β
jR = 40 
 
Table II shows computed results when each objective 
function (OF) was optimized individually for cases A and B, 
respectively.  
TABLE II.  COMPUTED RESULTS FOR CASES A AND B 
 min OF1 max OF2 max OF3 
  Case A  
OF1 279922 550358 559646 
OF2 10289 14093 13913 
OF3 559000 793600 793630 
  Case B  
 min OF1 max OF2 max OF3 
OF1 90480 502860 507945 
OF2 93151 258777 258615 
OF3 210000 654000 654000 
 
By analyzing these results, the objective functions are 
conflicted when optimizing one objective value that leads to an 
increase of the undesired values for the two others. For 
instance, by obtaining a minimum value for OF1, it yields worst 
values for both OF2 and OF3. To gain a trade-off solution, the 
goal programing method was utilized with the three objective 
values shown in Table II as targets for the goal programming 
solution function. Table III illustrates the obtained results for 
cases A and B. 
TABLE III.  COMPUTED RESULTS FOR CASES A AND B USING THE GOAL 
PROGRAMMING APPROACH 
Solution 
number 
min 
OF1 
max 
OF2 
max 
OF3 
Open 
farms 
Open 
abattoirs 
   Case A   
1 293411 10575 577060 1, 3, 4, 5 1, 2, 4, 5, 6 
2 542592 13899 793600 1, 2, 3, 4, 5 1, 2, 3, 4, 5, 6 
3 554487 13843 793600 1, 2, 3, 4, 5 1, 2, 3, 4, 6 
   Case B   
1 549558 13803 793600 1, 2, 3, 4, 5 1, 2, 3, 4, 6 
2 497660 258589 654000 1, 2, 3, 4, 5 1, 2, 3, 4, 5, 6 
3 477947 258615 654000 1, 2, 3, 4, 5 1, 3, 5 
 
As shown in Table III, these solutions are associated with 
allocations of supply chain sites of farms and abattoirs that 
need to be opened. In a real life, one of these solutions can be 
selected based on preferences of decision makers. For this case 
study, solution one for case A was determined by having four 
farms and five abattoirs using OF1 (293411), OF2 (10575) and 
OF3 (577060). Solution three for case B was decided with five 
farms and three abattoirs using OF1 (477947), OF2 (258615) 
and OF3 (654000).  
Finally, based on the chosen solutions, the optimized 
quantity product flow between the HMSCs sites is given in 
Table IV. For instance, farm one should supply livestock to 
abattoir one, five and six with the following livestock quantity: 
1200 items are sent to abattoir four, 800 items are sent to 
abattoir five and 340 items are sent to abattoir six. Abattoir one 
should supply Halal meat products to retailer one, three and six 
with the following meat quantity: 850 items are sent to retailer 
one, 210 items are sent to retailer three and 690 items are sent 
to retailer six. 
TABLE IV.  QUANTITY PRODUCT FLOW FOR CASES A AND B 
Sites 
(Link u) 
Quantity 
(Items) 
Sites 
(Link v) 
Quantity 
(Items) 
Sites 
(Link v) 
Quantity 
(Items) 
  Case A    
u1, 4 
u1, 5 
u1, 6 
1200 
800 
340 
v1 ,1 
v1 ,3 
v1 ,6 
850 
210 
690 
v6, 10 
v4, 6 
 
180 
270 
u3, 1 800 v2 ,5 290   
u3, 4 1200  v2 ,10 100   
u3, 5 1000 v2 ,8 160   
u3, 6 290 v2, 11 700   
u4, 1 
u4, 4 
u4, 6 
u4, 5 
u5, 2 
u5, 4 
u5, 6 
100 
110 
550 
130 
1100 
230 
170 
v4, 6 
v4, 7 
v5, 9 
v5, 2 
v5, 5 
v6, 6 
v6, 8 
850 
450 
110 
220 
359 
100 
330 
  
  Case B    
u1, 1 
u1, 5 
u2, 3 
u3, 3 
u3, 5 
1200 
800 
800 
1000 
290 
v1 ,3 
v1 ,7 
    v1 ,8 
 v1 ,10 
 v1 ,11 
850 
210 
690 
690 
120 
v5, 2 
v5, 3 
v5, 5 
v5, 7 
v5, 8 
180 
270 
330 
810 
1100 
u4, 1 1200     v3 ,5 290  v5, 10 100 
u4, 3 1000 v3 ,8 160 v3 ,1 160 
u4, 5 290  v3, 10 700 v3, 6 700 
u5, 1 610 v3 ,11 100 V5, 11 560 
IV. SUMMARY 
This paper presents a development of a three-objective 
mathematical model based on an RFID-based three-echelon 
HMSC. The developed multi-objective mathematical model 
can be used as a reference for HMSC designers in finding a 
trade-off solution in minimizing the total investment cost, 
maximizing the integrity of Halal meats and maximizing the 
return of investment. A case study was carried out in order to 
validate the developed mathematical model. The initial results 
indicate that this is a useful and effective way as an aid for 
designing and implementing a cost-effective RFID-enabled 
monitoring mechanism to enhance the integrity of the proposed 
HMSC.  
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A cost-effective decision-making algorithm for integrity of HMSCs:a multi-objective approach

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