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Int. J. Logistics Systems and Management, Vol.

Copyright © 2011 Inderscience Enterprises Ltd.

A design of distribution network and development

of efficient distribution policy

M. Mathirajan*

Operations Research Group,

Anna University Tiruchirappalli,

Tiruchirappalli 620 024, Tamil Nadu, India

E-mail: msdmathi@mgmt.iisc.ernet.in

E-mail: mathirajan@tau.edu.in

*Corresponding author

K. Manoj

Department of Management Studies,

Indian Institute of Science,

Bangalore 560 012, Karnataka, India

E-mail: Manoj.K@unilever.com

V. Ramachandran

Operations Research Group,

Anna University Tiruchirappalli,

Tiruchirappalli 620 024,

Tamil Nadu, India

E-mail: rama@annauniv.edu

Abstract: The distribution system design considered in this paper is derived

from current operations of a major consumer product company in India who

manages products for nationwide distribution. The company is charged with

Central Sales Tax (CST) along with local tax VAT for the trade that happens

across the state borders while distributing the products from the factories.

To avoid CST, company could consider opening warehouses in each state.

This will have an extra cost of opening and operating warehouse in each state.

So, this needs a cost tread-off between the option of continuing with the

existing system or opening a new warehouse. Accordingly, a two-stage

integrated solution framework is proposed in this study. In the first stage, a

mathematical model is proposed to solve the facility location and production

distribution policy for the company by minimising the cost comprising

production costs at factory, fixed and labour cost of new warehouses and

shipment cost from factories to warehouses and warehouses to distributors. In

the second stage, a breakeven analysis is proposed to compare the new

proposed network with the existing network based on the distribution cost. The

workability of the proposed framework is demonstrated using a pseudocase

developed based on the observation of the company, particularly for nationwide

existing distribution.

Keywords: design of the distribution system; CST and VAT; mathematical

model; facility location; breakeven analysis; case study.

A design of distribution network and development 109

Reference to this paper should be made as follows: Mathirajan, M., Manoj, K.

and Ramachandran, V. (2011) ‘A design of distribution network and

development of efficient distribution policy’, Int. J. Logistics Systems and

Management, Vol.

Biographical notes: M. Mathirajan is with Anna University Tiruchirappalli

(AU-T), Tiruchirappalli, and since May 2008, he is on lien for two years from

Indian Institute of Science (IISc), Bangalore. He is currently the Professor and

Head of the Department of Management Studies of AU-T. He received both

MSc (Engineering) by research and PhD in Operations Management from IISc.

He was a Postdoctoral Fellow at Singapore MIT Alliance of Nanyang

Technological University, Singapore. His research interests are in the areas of

mathematical modelling and development of heuristic methods for Operations

Management, Logistics/Supply Chain Management problems. He has been

guiding doctoral research students at IISc and AU-T.

Manoj Kumar received an MBA (2006–2008) from the Indian Institute of

Science (IISc) Bangalore. He had an interest in operations area and hence he

took a role of a Subject Matter Expert in the area of Customer Development

and Sales. He is currently working in the area of Information Management in

Unilever where he looks at the business needs of information in the space of

sales and distribution and how these information needs can be met. He obtained

a Mechanical Engineering Degree from Visveswaraya National Institute of

Technology (VNIT) in 2003.

V. Ramachandran received both PhD in Computer Applications in Power

Systems and ME in Power Systems Engineering from Anna University,

Tamil Nadu. He obtained his BE in Electrical and Electronics Engineering from

Madras University. Since 1980s, he has been with Anna University as Faculty

in various capacities, including Secretary for Tamil Nadu Engineering

Admissions. He was on sabbatical with Faculty of Information Technology,

Multimedia University, Malaysia. His current areas of research include media

streaming, service-oriented architecture, evolutionary programming in power

system applications and distributed models in power system analysis. He is

currently the Vice Chancellor of Anna University Tiruchirappalli,

Tiruchirappalli.

1 Introduction

The distribution network is an important part in the supply chain management and the

distribution network design problem is a very important strategic decision in supply

planning and management. Distribution network design problems involve both (a) the

optimisation of the flows of goods and (b) the improvement of the existing distribution

network (Ambrosino and Scutella, 2005). A good distribution network design can be used

to achieve a variety of supply chain objectives ranging from low cost to high

responsiveness (Chopra, 2003; Gunasekaran and Ngai, 2004; Liu and Hao, 2006).

In today’s rapidly changing economic and political conditions, it is a big challenge

for companies to constantly evaluate and optimally configure their distribution network.

An important strategic issue related to the design/re-design and operation of a physical

distribution network in a supply chain system is the determination of the best

sites/facilities for intermediate stocking points or warehouses (Melo et al., 2009). The use

110 M. Mathirajan et al.

of warehouse (facility) provides a company with flexibility to respond changes in the

marketplace and can result in significant cost savings owing to economies of scale in

transportation or shipping costs, inventory costs, tax structure while moving the product

from factory to warehouses located across the states within the country. Also,

the combined facility location/network design problems are useful for modelling a

number of situations in which trade-offs between facility costs, network design costs and

operating costs must be made (Melkote and Daskin, 2001).

During the configuration/reconfiguration of the distribution network design, operation

managers and planners need to address questions such as where to produce, where to

open the warehouses, and how it should be distributed through the distribution network.

The complexity of this problem increases for these operations managers when the selling

model of the company is multi-echelon, in which the products are shipped from

the factories to warehouses and from there distributed to the customers through the

distributors. In addition, the decision-makers need to consider the effects of taxes during

the design of distribution network because taxes add to their bottom-line cost of

distribution. Sometimes, it is possible for managers to avoid these taxes by a suitable

network design for their supply chain.

In this study, we are studying the distribution network of a multi-echelon supply

chain for a single product as observed in large consumer product company. The main

objective of the study is developing a mathematical model for the selection of warehouse

locations and distribution of product in the network. We have also considered the effect

of the sales tax in comparing the new proposed distribution network with the existing

network and proposed a breakeven analysis to make the decision.

2 Closely related review

The literature review is divided into two broad categories namely, (i) studies related to

facility location and distribution policy design issues, and (ii) studies related to

implementation of breakeven analysis methods in the area of supply chain management

issues.

Some researchers have looked at facility location problems as independent decision

issues (e.g., Aikens, 1985; Owen and Daskin, 1998; Bhutta, 2004; Wu et al., 2006;

Sahin and Sural, 2007; Rentizelas and Tatsiopoulos, 2010). There have been

many attempts to solve facility location problem along with other decision issues

such as allocation (e.g., Ohlemuller, 1997; Murat et al., 2010), allocation and routing

(e.g., Wu et al., 2002; Lashine et al., 2006; Nagy and Salhi, 2007), transportation and

inventory (e.g., Jayaraman, 1998; Perl and Sirisoponslip, 1988; Shen and Qi, 2007),

inventory control (e.g., Ballou, 1984; Miranda and Garrido, 2006; Wang et al., 2007;

Gebgennini et al., 2009), storage capacity calculation (e.g., Levén et al., 2004) and supply

chain management (e.g., Tsiakisa and Papageorgiou, 2008; Melo et al., 2009).

Furthermore, in the last decade, the facility location problem as an integral problem

while designing a distribution network has attracted the attention of researchers and these

types of researchers are closely related to the problem addressed in this paper. Chopra

(2003) described a framework for designing the distribution network in a supply chain by

considering various factors such as response time, product variety, product availability,

A design of distribution network and development 111

customer experience, order visibility and returnability influencing the choice of

distribution network. Klose and Drexl (2005) classified the facility location models for

distribution systems design. They also reviewed some of the contributions and

summarised the continuous locations models, network location models, mixed-integer

programming models and applications in an effective way.

Avittathur et al. (2003) studied the effect of CST rates and product variety

on Distribution Centre (DC) locations and concluded that CST has an effect. They

developed a non-linear mixed-integer programming model with an objective function of

minimising total cost to determine DC locations considering the impact of CST. They

have validated the proposed mathematical model using a real-life numerical problem

and for the simplicity of the analysis, they considered only the northern India for the

numerical problem. Their findings are based on the effects of DC fixed cost, product

variety, service levels, transportation cost and CST in deciding on number of DC

locations. Finally, their analysis concluded that CST rate is an important factor to

determine the optimal number of distribution locations.

Amiri (2006) studied the problem of designing a distribution network in a supply

chain system that involves determining simultaneously the best locations of both plants

and warehouses and best policy for distributing the product from the plants to warehouses

and from the warehouses to the customers. The researcher proposed mathematical model

by considering the traditional costs associated with facility location and distribution

problems such as variable cost due to supplying the products from plant to warehouses

as well as from warehouses to customers and fixed cost due to opening and operating

warehouse with specific capacity level. Also, proposed heuristic solution procedure based

on Lagrangian relaxation of the problem and demonstrated the quality of the proposed

heuristic algorithms by conducting suitable computational experiments.

Bidhandi et al. (2009) proposed a new approach for determining supply chain

network design considering simultaneously the strategic decisions concerning facilities

selection with the tactical decisions concerning supplier, production, warehouse and

customer allocation, the facility location and allocation problem. They proposed

Mixed-Integer Linear Programming (MILP) model with (0–1) variables. Because of the

computational difficulties, they proposed a modified version of Benders’ decomposition

to solve MILP model with (0–1) variables and following this they developed a new

algorithm based on the surrogate constraints. Finally, they discussed the quality of the

new algorithm.

While making decisions for facility locations and distribution networks

simultaneously, many factors have been considered in the literature including the tax

structure of the country as an important factor. However, the literature review indicates

that even though the effects of CST on distribution costs have been studied, particularly

in India, there are no instances observed where the CST is modelled in the solution

framework to make decisions on facility locations and distribution network design.

In addition to the literature gap mentioned earlier, to the best of our knowledge,

not many researchers are seen using breakeven analysis in making decisions in the areas

of distribution network design. However, Hanna et al. (1993) used breakeven analysis to

modern production economics while modelling economies of scale and economies of

scope. They found traditional cost benefit analysis inadequate in their context of study

and suggested a modified cost-volume-flexibility breakeven analysis for their study.

112 M. Mathirajan et al.

Norton et al. (2006) used breakeven analysis in their study to compare costs of upgrading

centralised treatment facility and an alternative distributed treatment facility.

3 Problem descriptions

The problem considered in this study is observed in a large consumer product company

in India, which is involved in manufacturing of electronic consumer products. This

company felt the need to reconfigure the existing supply chain because of the current

practice of CST. The CST is a tariff that is levied on all the inter-state trade transactions.

It is payable when there is any trading goods transaction, between any two parties

(e.g., manufacturer and distributor), does not happen in the same state. In other words,

when a manufacturer located in state ‘A’ ships goods to a distributor located in state ‘B’,

the transaction will be levied upon CST as well as local sales tax (=VAT – Value Added

Tax) of state ‘B’.

Let us consider a traditional supply chain network operating in India (comprising of

28 states), which is selling electronic consumer products through distributors. There are

one or few production houses (Factories) shipping goods to distributors. Generally, there

are few distributors in each state of the country. These distributors meet the demand of

stockiest, which are more in numbers for a particular state, generally one or two per

district. Finally, the product will reach to the customer through these stockiest and the

retailers. An example of a complete chain is shown in Figure 1.

Figure 1 Traditional supply chain in India selling through distributors

Now, suppose the Factory is in state ‘A’ and the Distributor is located in state ‘B’

(Figure 2). In such case, the CST is levied on goods traded between them, in addition to

VAT. To avoid this CST, the company can open a Warehouse in state ‘B’ and transaction

is shown from warehouse to distributor, thus avoiding interstate selling and hence CST.

But, the introduction of the warehouse incurs extra fixed cost of opening a warehouse in

each state and also the operating cost of warehouses add up to the distribution cost.

Hence, this part of the supply chain (as shown in dashed box in Figure 2) is of interest to

operations manager. They have to develop a model to select the location for new

warehouse, compare the extra cost of opening and operating new warehouse with existing

network design and reconfigure the distribution network.

A design of distribution network and development 113

Figure 2 Tax structure for interstate selling and introduction of state-owned depot

3.1 Objectives of the study

Though the problem described in this section is related to a particular consumer product

company observed in Bangalore, similar problem is applicable to other companies having

supply chain across the states of India. The following objectives are emerged based on

the observation made in the industry:

1 designing new distribution network and developing optimal distribution plan

2 finding the breakeven point at which the selected potential warehouse(s)

should be operational

3 demonstrating the workability of proposed solution framework by solving

a pseudocase study.

To obtain the objectives stated in this study, the following assumptions are made in the

problem to develop the solution methodologies:

• each state should have at least one warehouse

• factory locations are known

• locations of potential warehouses are known

• only one product is considered

• warehouse located in state ‘j’ can ship goods to distributors located in state ‘j’ only

• inventory costs are not considered

• transportation costs are assumed to be unit transportation cost.

4 Solution framework

In this section, we propose the solution framework for the problem discussed.

The decision problem addressed in this study is viewed as the two-stage integrated

decision problem, namely (1) decision on warehouse location, and (2) decision on

finalising the warehouse location in comparison with the existing distribution design

114 M. Mathirajan et al.

network. The modelling and the algorithm details of this solution framework are

discussed in the following subsections.

4.1 Stage 1: Development of mathematical model

In the first stage of the proposed solution framework, the optimal decision on location of

the potential warehouse is to be decided out of various possible locations while the

distribution policy is formulated. To get the optimal decision on warehouse location

along with optimal distribution policy, an Integer Linear Programming (ILP) is developed

to solve Facility Location and Production–Distribution Policy (FLPDP) issues

simultaneously. The assumptions made and notations used for formulating the FLPDP

model are:

Assumptions

1 Single product is considered

2 There is no breakage considered in goods shipment

3 No inventory issues are considered

4 The warehouse in state j will ship goods to distributors in state j only

5 Unit transportation costs are considered in the problem.

Notations

Sets

F: (1 … I) factories and i denotes ith factory

S: (1 … J) states and j denotes jth state

W: (1 … K) potential warehouses and k denotes kth potential warehouse

D: (1 … M) distributors and m denotes mth distributor.

Parameters

R_WH: Required no. of warehouses in state S

P_WH: No. of potential warehouses in state S

K: Maximum number of potential warehouse in state S

DBUTOR: No. of distributors in state S

M: Maximum number of distributors in state S

C_F: Capacity of factory F

Capacity: Max capacity allowed for the potential warehouse

PC_F: Production cost at factory F

FC_SW: Fixed cost of opening a warehouse W in state S

LC_SW: Labour cost/operating cost per unit of warehouse W in state S

A design of distribution network and development 115

N_SD: Demand at distributor D in state S

TC_SWF: Unit transportation cost of shipping goods from factory F to warehouse W

in state S

TC_SWD: Unit transportation cost of shipping goods from warehouse W to distributor

D (both in state S).

Decision variables

Y_SW: 1, if warehouse W is opened in state S

0, otherwise

X_SWF: Quantity of goods shipped from factory F to warehouse W in state S

X_SWD: Quantity of goods shipped from warehouse W to distributor D (both

in state S).

The proposed ILP model

Objective function

_

11 1

_

11

(_() _ ())*_ ()

_()*_()

PWH

IJ

ij k

PWH

J

jk

PC F i TC FSW ijk X FSW ijk

FC SW jk Y SW jk

== =

==

+

++

∑∑ ∑

∑∑

_DBUTOR

11 1

(_ () _ ( ))*_ ( )

PWH

J

jk m

LC SW jk TC SWD jkm X SWD jkm

== =

+

∑∑ ∑ (1)

_

11

_()_()

PWH

J

jk

X

FSW ijk C F i i I

==

≤∀∈

∑∑ (2)

DBUTOR

1

_ ( ) Capacity * _ ( ) ,

m

X

SWD jkm Y SW jk j J k K

=

≤∀∈∈

∑ (3)

DBUTOR

11

_() _() ,

I

im

X

FSW ijk X SWD jkm j J k K

==

=∀∈∈

∑∑ (4)

_

1

_()_() ,

PWH

k

X

SWD jkm N SD jm j J m M

=

≤∀∈∈

∑ (5)

_

1

_()_()

PWH

k

YSWjk RWHj j J

=

≤∀∈

∑ (6)

_()PWHj K j J≤∀∈ (7)

DBUTOR( )jM jJ≤∀∈ (8)

116 M. Mathirajan et al.

_(){0,1} ,YSWjk j Jk K∈∀∈∈ (9)

_()0 ,,

X

FSW ijk i I j J k K≥∀∈∈ ∈ (10)

_

()0 , , .

X

SWD jkm j J k K m M≥∀∈ ∈ ∈ (11)

The objective is to minimise total cost, which includes: Production Cost, opening and

operating cost of warehouse, and transportation costs. Constraint set (2) is the Capacity

Constraint of factories. It ensures that the total quantity of goods shipped from each

factory is less than the capacity of the factory. Constraint set (3) is the Capacity

Constraint of the potential warehouses. Although in our problem the capacity constraint

of the warehouse is not considered but it is important because apart from capacity

constraint of the warehouses it also ensures the relation between quantity shipped and

binary variable Y_SW (whether the potential warehouse is selected or not). In our

problem, the value for capacity is given a large number so that this constraint set only

acts as the relation between quantity shipped and binary variable Y_SW. Constraint set (4)

is the Demand Constraint of the distributors. It ensures that the quantity of goods shipped

to a distributor is equal to the demand of that distributor. Constraint set (5) is the Flow

Balance Constraint at each potential warehouse. It ensures that the quantity of goods

shipped to the warehouse is equal to the quantity of goods shipped out of the warehouse.

It also ensures that the warehouse in state j will ship goods to distributors in state j only.

Constraint set (6) ensures that the number of warehouses selected for a state is equal

to the required number of warehouses in that state. Constraint set (7) ensures that the

number of potential warehouse locations does not exceed the maximum number of

potential warehouse in a state. Constraint (8) ensures that the number of distributors does

not exceed the maximum number of distributor in a state. Constraint set (9) ensures that

the variable Y_SW takes the binary values. Constraint sets (10) and (11) are non-

negativity constraint for the respective decision variables.

A LINGO set code, which generates the ILP model proposed in this section for any

given data, was developed and presented in Appendix 1. Both the proposed ILP model

and the LINGO set code were verified appropriately by solving a small-scale numerical

problem and by interpreting the optimal solution. Owing to the brevity of the paper,

the verification details are not presented here. As the proposed ILP model has minimum

number of binary decision variables, the computational difficulties of the proposed model

do not arise.

The ILP model proposed in this study does not involve routing decisions for serving

the warehouses from the plants and from the warehouses to distributors. These additional

decisions can be achieved using Travelling Salesman Problem’s modelling approach

by introducing a third phase in the existing solution methodologies.

4.2 Stage 2: Development of breakeven analysis procedure to determine

optimal distribution design

Once location of potential warehouse is decided, breakeven analysis is carried out,

as second stage of the problem, to find out whether it is beneficial to go with proposed

distribution design compared with the existing design partly or totally. Accordingly, a

procedure for carrying out breakeven analysis is developed here to find out that is it

A design of distribution network and development 117

beneficial for the company to open the warehouse in the state as suggested by the FLPDP

model or should it stick to the existing distribution design in that state.

The procedure developed for breakeven analysis involves comparison of the cost of

existing distribution and new proposed distribution for each state. Total cost of existing

distribution will include: Transportation cost from the factories to the distributors and the

CST for interstate selling. Total distribution cost for new proposed distribution system

will include: Transportation cost from factories to warehouses, opening and operating

cost (labour cost) at warehouses, transportation cost from warehouses to distributors.

In the end of the comparison of the cost of existing distribution and new proposed

distribution for each state, the optimal Breakeven Period is computed to decide whether

to go for new proposed distribution system and open the warehouses. This detail of the

proposed breakeven analysis is shown in Figure 3 with the following terminology used

in the proposed procedure for the breakeven analysis:

Figure 3 Flow chart for breakeven analysis

Net Gain: For state ‘j’, if the proposed distribution system is implemented, the Net Gain

in distribution cost can be found out by:

= (Transportation Cost from the factories to the distributors+ the CST

for interstate selling) (Transportation Cost fromfactories to

warehouses + Operating Cost (Labour Cost) at warehouses+

Tr

Net Gain

−

ansportation Cost from warehouses to distributors).

Breakeven Period: is defined as the time period in which the cost of new proposed

distribution will be equal to the cost of existing distribution. In this study, the Breakeven

118 M. Mathirajan et al.

Period is computed in two ways, namely (a) Breakeven Period without time vale of

money (denoted as N), and (b) Breakeven Period with time value of money (denoted as

Nr). If the rate of interest is known, the time value of money can be incorporated

in the computation of Breakeven Period. With this, the computation details of N and Nr

are as follows:

_

N

etGain

F

CSW

N= (12)

where

N: Breakeven Period without time value of money

FC_SW: Fixed Cost of opening a warehouse W in state S

_*

ln 1 NetGain

ln(1 )

F

CSWR

Nr R

−

=

+ (13)

where

Nr: Breakeven Period with time value of money

FC_SW: Fixed cost of opening a warehouse W in state S

R: Rate of interest for the company.

5 A pseudocase study

In this section, a pseudocase based on the observation from a consumer electronics

company in South India was developed and the same was used to demonstrate the

workability of the proposed solution framework presented in the previous section.

5.1 Problem description for the case study

The case study organisation is a marketing company (hereafter called as EFL) involved

in the sales and service of water purifiers and vacuum cleaners. The products marketed

by EFL come from five production facilities, which are located across the country. These

production facilities along with the product are located at the places mentioned here.

• Bangalore (BLR), Karnataka State: Water purifier

• Dehradun (DUN), Uttaranchal State: Water purifier

• Shillong (SLG), Meghalaya State: Water purifier

• Baddi (BDD), Himachal Pradesh State: Water purifier

• Bhimtal (BHM), Uttaranchal State: Water purifier and vacuum cleaner.

Some of these production facilities are located in small states because of the tax benefits

given by the state governments to promote industrial growth in the above-mentioned

states. For example, Uttaranchal gives tax benefits to any company on the products

A design of distribution network and development 119

produced in their state. It brings down the cost of production in those factories and hence

an incentive to increase the production capacity in those factories.

The products marketed by EFL reaches the ultimate customer through various

distribution channels. Figure 4 shows the business distribution of the company. Around

35% goes through direct sales, Industrial division caters to 15% of sales, 25% reaches the

customers through distributors and rest 25% is through services and other sales.

Currently, 25% business through distributors (shown in a shaded box: Figure 4) is

growing at a Compounded Annual Growth Rate (CAGR) of 40%, which makes it an

important part of their business. There are around 100 of such distributors across the

country.

Figure 4 Business distribution of EFL (see online version for colours)

Considering the business through distributor channel only, the distribution network for

EFL is shown in Figure 5. The products are manufactured by the production facility units

and passed on to warehouse. From these warehouses, the products are distributed to

various EFLs’ Distributors (EFLDs). Suppose the warehouse is located in state S1 and it

is distributing goods to EFLDs located in states S1, S2, S3, …, Sn, (transit points), then

the goods traded with EFLD(S1) will not attract CST because the transaction is

happening in same state. But for the goods trades with EFLDs (S2, S3,…, Sn) will attract

CST (as shown in shaded box in Figure 5) because of the interstate selling. If the

company wants to avoid this CST levied on interstate selling, it has to open their own

warehouse in each state where goods can be shipped from production facilities and then

goods can be traded from these warehouses to the EFLDs in that state, thereby avoiding

any interstate selling. But, there will be extra cost of opening and operating warehouse in

each state, so EFL has to trade off between the two options.

As some of the real data related to the research problem addressed here was not

available, it is randomly generated to demonstrate the solution framework proposed in the

study on real-life size problems and the same is discussed in the next section.

120 M. Mathirajan et al.

Figure 5 Distribution network of EFL (see online version for colours)

5.2 Data generation for the case study

Only one product: water purifier is considered because it is manufactured in all five

production facilities while vacuum cleaner was produced only in one plant. The required

data for these five production facilities such as PC_F (Production Cost), C_F

(Capacity of the production facility/factory) are assumed to be known and these are

shown in Table 1.

Table 1 Production Cost (PC_F) and Capacity (C_F) of Factories

Factory PC_F (in Rs.) C_F (in Units)

BLR 6200 22,000

DUN 6350 27,500

SLG 6500 35,000

BDD 6300 12,000

BHM 5800 15,000

State-wise, the data on required no. of warehouses (R_WH), the number of potential

warehouses (P_WH) and the number of distributors (DBUTOR) are generated randomly

considering the size (in terms of area) of the state. These data are shown in Table 2.

Unit transportation cost of shipping goods from factory F to warehouse W (TC_SWF)

and unit transportation cost of shipping goods from warehouse W to distributor D

(TC_SWD) are generated based on the physical distance between the cities where

these warehouses and distributors are located. Cost is assumed to be proportional to

the distance between two cities.

Data for other parameters such as demand at distributor D in State S (N_SD), fixed

cost of opening a warehouse W in State S (FC_SW), and labour-cost/operating-cost per

unit of warehouse W in State S (LC_SW) are generated randomly by assuming uniform

distribution functions U (50, 1050), U (30,000, 90,000) and U (25, 75), respectively.

These data is shown in Appendix 2.

A design of distribution network and development 121

Table 2 Required no. of warehouses, number of potential warehouses and number

of distributors for each state

S. No. State

State

code

Required No. of

warehouses

(R_WH)

No. of potential

warehouses

(P_WH)

No. of

distributors

(DBUTOR)

1 Andhra Pradesh APR 2 5 8

2 Arunachal Pradesh ARP 1 2 2

3 Assam ASM 1 3 3

4 Bihar BIH 2 5 8

5 Chhattisgarh CHT 1 2 3

6 Goa GOA 1 2 2

7 Gujarat GUJ 2 5 9

8 Haryana HAR 1 4 5

9 Himachal Pradesh HPR 1 2 3

10 Jammu and Kashmir JNK 1 2 2

11 Jharkhand JKD 1 2 4

12 Karnataka KAR 2 5 10

13 Kerala KER 1 2 5

14 Madhya Pradesh MPR 1 4 6

15 Maharashtra MAH 2 5 10

16 Meghalaya MEG 1 1 2

17 Mizoram MIZ 1 1 2

18 Nagaland NAG 1 2 2

19 Orissa ORI 1 4 6

20 Punjab PUN 1 3 5

21 Rajasthan RAJ 2 5 8

22 Sikkim SKM 1 1 2

23 Tamil Nadu TND 2 5 9

24 Tripura TRI 1 2 2

25 Uttar Pradesh UPR 2 5 10

26 Uttaranchal UTT 2 2 3

27 West Bengal WBN 2 5 7

28 Delhi DEL 2 5 10

5.3 Results and discussion for the pseudocase

Using the proposed solution framework, presented in Section 4, the pseudocase study

problem presented in the previous section is solved. The details of the implementation

process of the solution framework for the pseudocase study are discussed in the following

sections.

122 M. Mathirajan et al.

5.3.1 Development of ILP model for case study problem

All the relevant data on the case study is given as an input to the LINGO set code

(presented in Appendix 1) for generating the proposed ILP model for the case study data.

The generated ILP model for the case study data is solved using LINGO, an optimisation

package. Only the optimal non-zero solution is extracted from the detailed optimal

solution obtained for the case study data and the same is given to a Report Generator

Programme, developed using C++, to generate the following three managerial and

operational reports for its easy implementation of the optimal solution.

‘Report 1’ provides a strategic decision on state-wise the optimal number of

warehouses required and their optimal locations. This complete report for the case study

data is shown in Table 3.

Table 3 Optimal warehouse locations selected for each state

State No. of Warehouses selected Warehouse locations

APR 2 W03, W05

ARP 1 W01

ASM 1 W01

BIH 2 W02, W04

CHT 1 W01

GOA 1 W01

GUJ 2 W03, W04

HAR 1 W03

HPR 1 W02

JNK 1 W01

JKD 1 W02

KAR 2 W01, W02

KER 1 W02

MPR 1 W04

MAH 2 W02, W04

MEG 1 W01

MIZ 1 W01

NAG 1 W02

ORI 1 W04

PUN 1 W03

RAJ 2 W01, W02

SKM 1 W01

TND 2 W01, W05

TRI 1 W01

UPR 2 W03, W04

UTT 2 W01, W02

WBN 2 W04, W05

DEL 2 W02, W05

A design of distribution network and development 123

‘Report 2’ gives an operational decision on the factory-wise the optimal distribution

policy for each state. That is, Report 2 gives the optimal quantity of goods to be shipped

from each factory to warehouses, which are optimally decided for each state. A sample

part of ‘Report 2’ related to the factory located at Bangalore is shown in Table 4.

Table 4 Optimal distribution policy for the factory located at Bangalore

Factory State Warehouse Optimal quantity Optimal FSsum Optimal Fsum

W03 2287

APR W05 2548 4835

GOA W01 647 647

JKD W02 67 67

KAR W01 5471 5471

KER W02 1902 1902

MAH W04 5248 5248

BLR

TND W01 3830 3830

22,000

FSsum: Total quantity shipped from factory ‘F’ to state ‘S’;

Fsum: Total quantity to be produced at factory ‘F’.

‘Report 3’ indicates another operational decision on state-wise the optimal distribution

policy between each of the warehouses to a set of distributors. That is, Report 3 gives the

quantity of goods to be shipped from each of the warehouses from each of the states to a

set of distributors. A sample part of ‘Report 3’ related to the state: Andhra Pradesh is

shown in Table 5.

Table 5 Optimal distribution policy for the warehouse located at the state: Andhra Pradesh

State Warehouse Distributor Optimal quantity Optimal Ssum

D01 388

D02 370

D03 688

W03

D04 841

D05 120

D06 965

D07 525

APR

W05

D08 938

4835

Ssum: Total quantity distributed from state ‘S’.

5.3.2 Breakeven analysis

As the existing cost of distribution for each state is not available, a new LINGO set code

is developed to generate data for the existing cost of distribution. It is assumed that the

products are shipped to distributors directly from the factory, without any warehouse in

between. CST was added appropriately for the trade. The existing cost of distribution

for each state thus obtained is shown in Appendix 3.

124 M. Mathirajan et al.

The existing cost of distribution and new proposed cost of distribution as obtained

from FLPDP model is compared and breakeven period is calculated using both the

formula discussed in Section 4.2 and the result has been summarised in Table 6. The rate

of interest for formula (13) is assumed to be 7%, which is cost of borrowing for most of

the big companies.

Table 6 Breakeven Period and optimal decision (to opt for new warehouse in the state)

for accepting the new proposed warehouse

Without time value of money With time value of money

State code

Breakeven

Period N

(months)

Open

warehouse?

(Yes/No)

Breakeven

Period Nr

(months)

Open

warehouse?

(Yes/No)

APR 1.5 Yes 1.6 Yes

ARP 117.4 204.9

ASM 4.5 Yes 4.7 Yes

BIH 2.7 Yes 2.8 Yes

CHT 3.5 Yes 3.7 Yes

GOA 3.8 Yes 3.9 Yes

GUJ 2.8 Yes 2.9 Yes

HAR 2.2 Yes 2.2 Yes

HPR 2.3 Yes 2.4 Yes

JNK 5.5 Yes 5.8 Yes

JKD 23.5 26.1

KAR 0.8 Yes 0.8 Yes

KER 1.4 Yes 1.4 Yes

MPR 1.1 Yes 1.2 Yes

MAH 1.2 Yes 1.3 Yes

MEG 12.1 12.9

MIZ 7 7.4

NAG 6.8 7.2

ORI 2 Yes 2.1 Yes

PUN 1.5 Yes 1.6 Yes

RAJ 1 Yes 1.1 Yes

SKM 22.2 24.6

TND 1.2 Yes 1.2 Yes

TRI 2.8 Yes 2.9 Yes

UPR 1.4 Yes 1.4 Yes

UTT 6.1 6.4

WBN 2.6 Yes 2.7 Yes

DEL 1.7 Yes 1.8 Yes

Decision = ‘Yes’ (for N, Nr ≤ 6 months): 6 month is assumed to be the managerial

decision.

A design of distribution network and development 125

Assuming that the demand data generated for the case being yearly, the breakeven period

is calculated and then converted in months. The decision to go for new proposed

warehouse locations was taken based on this period. For a state, if the opening of new

proposed warehouses is breaking even in less than or equal to six months, then we decide

to go for the opening warehouses in that state.

6 Conclusion

The problem addressed in this study is of considerable interest to operations managers

because of rapidly changing environment in which they are operating. Moreover, changes

in the tax policies by government affect the bottom-line costs of the companies. This

encourages operations managers to re-look at their distribution network and reconfigure

its design to cut their distribution costs to achieve competitive advantage. In the literature

review, we have not observed this type of reconfiguration of supply chain distribution

network with inclusion of CST.

The problem was taken as a two-stage distribution network design problem. First,

a mathematical model is developed to solve the facility location and production

distribution policy for a company by minimising the cost comprising production costs at

factory, fixed and labour cost of new warehouses and shipment cost from factories to

warehouses and warehouses to distributors. Second, a breakeven analysis procedure is

proposed for carrying out to compare the new proposed network with the existing

network based on the distribution cost. The following methods were suggested to find

breakeven period namely, (i) without considering the time value of money, (ii)

considering time value of money.

A pseudocase is developed based on the observation made in the large consumer

electronics company located in South India to demonstrate the workability of proposed

solution framework. The case study problem is solved in two stages as proposed in the

solution framework. We also developed a LINGO set code, which generate the required

ILP model as in Section 4 for any given data, and a Report Generator Programme using

C++, which converts the LINGO output (non-zero decision variables) into three easily

interpretable reports for warehouse selection, distribution policy for factories and

distribution policy for states.

ILP model proposed for stage 1 of the decision problem, The LINGO set code

developed and presented in the appendix for the proposed ILP model, the Breakeven

Analysis procedure proposed for the second stage of the decision problem, and the

Report Generator Programme developed are very simple to implement and to solve any

large-scale problems, similar to the pseudocase study presented here.

There are few limitations experienced by us during the study. One major limitation is,

there is no complete data available for the real case problem, so we developed a

pseudodata and termed our case study as pseudocase study. Although we tried to generate

data meaningfully and close to reality, it would have given more satisfaction if the real

data was available. We also did not consider the effect of inventory in developing

the model because the complexity would have increased drastically if inventory issues are

introduced in the model design. The increase in number of warehouses will increase

126 M. Mathirajan et al.

the total inventory for the company, which will affect the overall benefit gained. This can

also be taken as the future work to include inventory issues along with other issues.

Another extension of this study can be taken as incorporating the breakeven period

analysis in the mathematical model itself and convert the solution into single stage

solution. Lastly, the model proposed in this study does not involve routing decisions for

serving the warehouses from the plants and from the warehouses to distributors and this

issue can be addressed following TSP modelling process as third phase in this study.

Acknowledgements

The authors are most grateful to the referees for their valuable comments and suggestions

that helped to improve the presentation of the paper considerably.

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128 M. Mathirajan et al.

Appendix 1: A LINGO set code for FLPDP

SETS:

STATE: R_WH, P_WH, DBUTOR;

WAREHOUSE;

DISTRIBUTOR;

FACTORY: C_F, PC_F;

STATE_WH( STATE, WAREHOUSE): FC_SW, LC_SW, Y_SW;

STATE_DBUTOR( STATE, DISTRIBUTOR): N_SD;

FACTORY_WH(STATE_WH, FACTORY): X_SWF, TC_SWF;

WHOUS_DBUTOR(STATE, WAREHOUSE, DISTRIBUTOR): X_SWD,

TC_SWD;

ENDSETS

DATA:

!Data input through Excel Sheet;

STATE = @OLE('E:\PROJECT\DATA.XLS');

WAREHOUSE = @OLE('E:\PROJECT\DATA.XLS');

DISTRIBUTOR = @OLE('E:\PROJECT\DATA.XLS');

R_WH = @OLE('E:\PROJECT\DATA.XLS');

P_WH = @OLE('E:\PROJECT\DATA.XLS');

DBUTOR = @OLE('E:\PROJECT\DATA.XLS');

FACTORY = @OLE('E:\PROJECT\DATA.XLS');

N_SD = @OLE('E:\PROJECT\DATA.XLS');

FC_SW = @OLE('E:\PROJECT\DATA.XLS');

PC_F = @OLE('E:\PROJECT\DATA.XLS');

C_F = @OLE('E:\PROJECT\DATA.XLS');

TC_SWF = @OLE('E:\PROJECT\DATA.XLS');

TC_SWD = @OLE('E:\PROJECT\DATA.XLS');

LC_SW = @OLE('E:\PROJECT\DATA.XLS');

CAPACITY = 50000;

!Exporting Result to Excel Sheet;

@OLE('E:\PROJECT\RESULT.XLS') = Y_SW, X_SWF, X_SWD;

ENDDATA

A design of distribution network and development 129

!Defining Variable types;

@FOR(STATE_WH:@BIN(Y_SW));

@FOR(WHOUS_DBUTOR:@GIN(X_SWD));

@FOR(FACTORY_WH:@GIN(X_SWF));

!Objectve Function: Minimising Total cost;

MIN = @SUM(FACTORY_WH(j, k, i)| k #LE# P_WH(j): (PC_F(i) +

TC_SWF (j, k, i))* X_SWF (j, k, i)) + @SUM(STATE_WH(j, k) |

k #LE# P_WH(j): FC_SW(j, k) * Y_SW(j, k)) +

@SUM(WHOUS_DBUTOR(j, k, m) | m #LE# DBUTOR(j): (LC_SW(j, k)

+ TC_SWD (j, k, m)) * X_SWD(j, k, m));

!Constraint Set (2): Capacity constraints at Factory;

@FOR(FACTORY(i):

@SUM(FACTORY_WH(j, k, i)| k #LE# P_WH(j): X_SWF(j, k,

i)) <= C_F(i));

!Constraint Set (3): Relation between X and Y Decision

Variables;

@FOR(STATE_WH(j, k):

@SUM( WHOUS_DBUTOR(j, k, m) | m #LE# DBUTOR(j):

X_SWD(j, k, m)) <= CAPACITY * Y_SW(j, k));

!Constraint Set (4): Flow Balance at Warehouses;

@FOR(STATE_WH(j, k) | k #LE# P_WH(j):

@SUM( FACTORY_WH(j, k, i): X_SWF(j, k, i)) =

@SUM(WHOUS_DBUTOR(j, k, m) | m #LE# DBUTOR(j): X_SWD(j,

k, m)));

!Constraint Set (5): Demand Constraints at Distributors;

@FOR(STATE_DBUTOR(j, m)| m #LE# DBUTOR(j):

@SUM( WHOUS_DBUTOR (j, k, m) | k #LE# P_WH(j): X_SWD(j,

k, m)) = N_SD(j, m));

!Constraint Set (6): Required no of warehouses for each

state;

@FOR(STATE(j):

@SUM(STATE_WH(j, k)| k #LE# P_WH(j): Y_SW(j, k)) =

R_WH(j));

@FOR(STATE(j):

@SUM(STATE_WH(j, k)| k #GT# P_WH(j): Y_SW(j, k)) = 0);

!Non- negativity Constraints for Decision Variables;

@FOR(STATE_WH: Y_SW >= 0);

130 M. Mathirajan et al.

@FOR(WHOUS_DBUTOR: X_SWD >= 0);

@FOR(FACTORY_WH: X_SWF >= 0);

END

Appendix 2: Additional data for the case study

N_SD, Demand data for state distributors based on U(50, 1050)

State N_SD

APR 388 370 688 841 120 965 525 938 709 218

ARP 441 172 385 644 484 404 437 297 866 776

ASM 902 976 200 903 956 77 962 61 124 157

BIH 813 806 1003 534 593 600 229 77 837 101

CHT 1007 353 313 102 475 762 787 600 821 375

GOA 343 304 584 528 519 255 132 762 184 649

GUJ 550 337 311 144 60 884 492 255 566 247

HAR 464 426 918 616 472 1037 96 884 516 344

HPR 525 762 612 445 952 957 783 1037 752 719

JNK 766 273 101 95 900 744 81 957 504 924

JKD 108 140 105 239 57 840 711 744 549 564

KAR 255 62 283 750 800 616 197 840 981 687

KER 558 820 735 290 234 994 576 616 272 863

MPR 129 793 579 910 125 828 474 994 706 656

MAH 710 757 620 521 290 615 723 828 620 757

MEG 649 656 706 440 226 480 466 615 579 793

MIZ 210 863 272 810 173 868 389 480 735 820

NAG 357 687 981 875 246 942 327 868 283 62

ORI 207 564 549 798 617 419 934 942 105 140

PUN 847 924 504 653 381 894 889 419 101 273

RAJ 362 719 752 664 621 1005 95 894 612 762

SKM 92 344 516 198 457 453 565 1005 918 426

TND 790 247 566 496 428 451 88 453 311 337

TRI 488 649 184 1000 71 660 926 451 584 304

UPR 222 375 821 380 381 828 800 660 313 353

UTT 745 101 837 105 915 205 358 828 1003 806

WBN 679 164 124 900 960 520 915 205 200 976

DEL 510 453 866 404 484 644 385 520 101 337

A design of distribution network and development 131

Appendix 2: Additional data for the case study (continued)

FC_SW: Fixed opening cost of state warehouses based on U(30,000, 90,000);

LC_SW: Labour cost (operating cost) of state warehouses based on U(25, 75)

State FC_SW LC_SW

APR 79,987 86,170 58,057 56,551 41,664 33 52 42 52 28

ARP 67,968 72,860 69,290 76,224 37,997 56 54 70 39 50

ASM 61,101 64,768 84,534 83,408 39,616 29 52 36 57 53

BIH 62,309 79,653 52,332 52,123 73,693 44 32 45 60 43

CHT 47,650 77,668 32,522 63,223 39,870 51 64 58 60 34

GOA 35,724 55,681 37,545 75,207 60,726 27 57 47 42 73

GUJ 41,989 85,660 30,088 56,425 55,415 59 53 28 26 73

HAR 80,804 86,174 83,592 53,495 83,989 49 44 41 69 27

HPR 69,562 57,401 45,422 52,102 77,215 71 49 32 61 73

JNK 58,649 60,262 66,669 79,476 77,348 71 47 66 74 67

JKD 81,666 84,766 84,408 50,609 63,474 45 61 74 51 71

KAR 38,476 33,828 82,310 77,425 82,491 27 69 59 46 49

KER 79,422 43,236 68,782 64,278 70,316 34 31 25 39 74

MPR 78,662 65,247 52,905 33,409 40,850 53 65 56 68 63

MAH 62,240 32,136 70,738 44,678 72,369 47 61 44 56 73

MEG 67,582 70,604 53,662 55,513 45,199 63 47 48 26 64

MIZ 81,708 78,338 37,523 57,814 89,414 61 32 49 47 62

NAG 37,918 45,335 63,214 49,394 52,068 62 29 67 68 67

ORI 87,394 72,998 37,797 45,232 74,055 38 41 40 27 55

PUN 34,686 40,317 69,257 68,239 64,111 57 48 36 67 61

RAJ 36,384 30,431 69,855 62,512 43,020 25 28 70 70 45

SKM 64,969 58,488 42,717 73,930 82,660 59 42 34 60 53

TND 38,321 62,762 82,220 48,064 32,709 34 71 29 59 59

TRI 41,626 85,225 85,386 84,390 40,077 39 64 43 39 27

UPR 37,020 45,977 35,273 56,420 49,708 49 26 75 38 37

UTT 84,052 63,951 77,702 69,384 50,548 68 26 38 41 33

WBN 62,017 53,320 65,244 53,233 38,675 28 54 32 40 65

DEL 76,131 54,255 62,619 74,802 46,953 39 69 67 63 58

132 M. Mathirajan et al.

Appendix 2: Additional data for the case study (continued)

TC_SWF: Unit transportation cost of shipment from factories to state warehouses based

on inter-city distances

A design of distribution network and development 133

Appendix 2: Additional data for the case study (continued)

TC_SWF: Unit transportation cost of shipment from factories to state warehouses

based on inter-city distances (continued)

134 M. Mathirajan et al.

Appendix 2: Additional data for the case study (continued)

TC_SWD: Unit Transportation cost of shipment from state warehouse to distributors

based on intercity distances

A design of distribution network and development 135

Appendix 2: Additional data for the case study (continued)

TC_SWD: Unit Transportation cost of shipment from state warehouse to distributors

based on intercity distances (continued)

136 M. Mathirajan et al.

Appendix 2: Additional data for the case study (continued)

TC_SWD: Unit Transportation cost of shipment from state warehouse to distributors

based on intercity distances (continued)

A design of distribution network and development 137

Appendix 3: Existing cost of distribution for the case study data

S. No. State State

Total transportation cost

(from factory to distributor) CST incurred on trade

1 Andhra Pradesh APR 91011 1087875

2 Arunachal Pradesh ARP 1863 137925

3 Assam ASM 41213 467550

4 Bihar BIH 43740 1047375

5 Chattisgarh CHT 21419 376425

6 Goa GOA 13109 145575

7 Gujarat GUJ 52382 809775

8 Haryana HAR 9013 651600

9 Himachal Pradesh HPR 1412 427275

10 Jammu and Kashmir JNK 5559 233775

11 Jharkhand JKD 7663 133200

12 Karnataka KAR 114606 1230975

13 Kerala KER 73047 593325

14 Madhya Pradesh MPR 25816 756900

15 Maharashtra MAH 97908 1449225

16 Meghalaya MEG 33927 293625

17 Mizoram MIZ 2673 241425

18 Nagaland NAG 26216 234900

19 Orissa ORI 51058 709650

20 Punjab PUN 9657 744525

21 Rajasthan RAJ 43104 1150200

22 Sikkim SKM 11092 98100

23 Tamil Nadu TND 97480 861750

24 Tripura TRI 20728 255825

25 Uttar Pradesh UPR 20766 1154925

26 Uttaranchal UTT 1090 378675

27 West Bengal WBN 52759 958950

28 Delhi DEL 15178 1058400