ISSN 2454-7115

Working Paper 293

AN OPTIMISATION MODEL FOR A DAIRY CO-OPERATIVE

FOR PROMOTING SUSTAINABLE OPERATIONS

FOR MILK COLLECTION

Shivshanker Singh Patel, Rajeev Pandey and Harekrishna Misra

Working Paper 293

AN OPTIMISATION MODEL FOR A DAIRY CO-OPERATIVE FOR

PROMOTING SUSTAINABLE OPERATIONS FOR

MILK COLLECTION

Shivshanker Singh Patel, Rajeev Pandey and Harekrishna Misra

Institute of Rural Management Anand

Post Box No. 60, Anand, Gujarat (India)

Phones: (02692) 263260, 260246, 260391, 261502

Fax: 02692-260188 Email: corpas@irma.ac.in

Website: www.irma.ac.in

May 2019

The purpose of the Working Paper Series (WPS) is to provide an opportunity to IRMA

faculty, visiting fellows, and students to sound out their ideas and research work before

publication and to get feedback and comments from their peer group. Therefore, a working

paper is to be considered as a pre-publication document of the Institute. This is a pre-

publication draft for academic circulation and comments only. The author/s retain the

copyrights of the paper for publication.

This work was supported by the Verghese Kurien Centre of Excellence (VKCoE) under its

sponsored Project “ An Optimisation Model for a Dairy Co-Operative for Promoting

Sustainable Operations for Milk Collection ”

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An Optimisation Model for a Dairy Co-Operative for Promoting Sustainable

Operations for Milk Collection

Shivshanker Singh Patel1, Rajeev Pandey2and Harekrishna Misra3

Abstract

This paper presents a milk collection route optimisation problem. The model focusses on the

development of an optimal routing plan for a designated fleet of milk tankers used in the

collection and transportation of milk from farms to processors over a road network. A broad

outline of the complex milk assembly process involving the Kaira Milk Union of Gujarat

(INDIA) is explained. Further, a model is described that has been designed to cater robustly to

the specific characteristics uniquely occurring within the dairy industry. The well-known Vehicle

Routing Problem (VRP) across multiple environments has been implemented for the Kaira Milk

Union milk collection process. The application of a widely-used heuristic technique, known as

the large neighbourhood search (LNS) algorithm, has been conceived and tested allowing for the

formation of scheduled collection and delivery routes to efficiently resolve routing problems

distinctive to the dairy industry, principally those of the Kaira Union. Furthermore, the model

has also been designed with the intention of minimising GHG emissions from the milk supply

chain. Future research can use this base model as a benchmark for more in-depth research in

sustaining the evolving area of supply chain management.

Keywords: Milk transportation, milk collection, Vehicle Routing Problem, Simulation, Large

Neighborhood Search

1 Assistant Professor, Institute of Rural Management Anand. Email: shivshanker@irma.ac.in 2 Principle data scientist, IHS Markit 3 Professor, Institute of Rural Management Anand. Email: hkmishra@irma.ac.in

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1. INTRODUCTION

In this paper, the efficiencies of the bulk collection of freshly produced milk from farms to

processors have been investigated. This process is also known as milk assembly (O’Dwyer and

Keane, 1971). This paper especially focusses on the Kaira Milk Union Gujarat (INDIA).

Dairy co-operatives play an important role in nurturing and strengthening rural households.

Dairying has been a regular source of income for farmers. Dairy co-operatives provide several

crucial inputs in the form of dairying resources and technical information to farmers which have

proved significantly helpful.

The dairy industry suffers from problems including the fluctuation of milk procurement on a

seasonal basis even as the demand remains relatively stable. In order to understand this

variability Mahida et al. (2018) indicated that socio-economic factors including membership with

a co-operative dairy society, access to information, non-farm annual income, and herd size

significantly influence the technical efficiency of farmers along with seasonal variations.

Transportation plays a major role in the supply of milk from milk co-operatives to the plant for

milk production. The total transportation cost is based on available quantity of milk at the

village-level milk co-operative society and demanded milk at the plant along with the associated

constraints of distribution (type and number) of vehicles and their transportation cost parameters.

The main focus of this research paper is to present an efficient and dynamic routing solution that

may be used to produce a cost-efficient route for milk collection schedules given the variability

of milk availability. The milk collection process comprises input variables that are often unique

to the activity.

Changes on the farm supply side and factors including a trend to lower dairy farm numbers

combined with a parallel increase in dairy cow numbers have led to a dramatic increase in the

average population size of the typical dairy herd and overall dairy herd yields. All this has

enhanced the quality of the product while (Donnellan et al., 2015) creating long-range effects on

supply sustainability (Dillon et al., 2010; McElroy, 2015). The processing side has witnessed

major investments in the industry along with modernisation (Quinlan, 2013).

This paper makes the point that the solution must provide a highly flexible working model that

may be efficiently tested with the available Kaira Union data. The model should be capable of

supporting the milk collection route scheduling. Based on research in the area of logistical

optimisation, the model must also be able to provide practical routes to be used by schedulers to

service their load building needs. Initially, the model should be able to recommend realistic

routes for milk collection taking into account unique factors encountered by the Kaira Union. In

order to achieve this, a Vehicle Routing model has been adapted to the Kaira Union Milk

collection data. The scenarios were run several times separately to validate the accuracy of the

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model. In order to build a Vehicle Routing model, the next section discusses the milk collection

process and associated milk supply chain.

1.1 Milk Collection Process and Milk Supply Chain

This is a three-tier structure housing a primary village-level dairy co-operative society (DCS), a

district union, and the state federation. The milk collection process of AMUL starts from the

village and ends up at milk processing units; products are marketed by the state co-operative

federation. Earlier, the milk would be collected in cans from the village milk co-operative

societies and transported to the plant through trucks. Such practices, being time-consuming,

caused deterioration in milk quality. Over the course of time, milk was preserved at village-level

dairy co-operative societies with the help of a bulk milk cooler (BMC) system. The chilled milk

was transported to the plant with the help of insulated milk collection tankers causing reduced

milk wastage.

The milk is chilled below 4°C at the dairy co-operative society while milk collection tankers

hired by the union come with varying capacities depending on the day-to-day requirements of

milk collection. The Kaira Union has milk collection tankers consistent with their milk

forecasting, tanker capacity, and road connectivity relevant to distance from the plant. Chilled

milk gets transferred to the union’s milk collection tankers through pumps. Samples are drawn

from the bulk milk coolers for analysis at the milk processing plant. Tanker milk first undergoes

a quality test at the milk processing plant. After quality clearance, the milk is transferred from

milk tankers to raw milk silos at the raw milk reception dock. The collected milk is processed

into various products i.e. pasteurised milk, curd, yogurt, butter, buttermilk, ghee, dried milk, ice

cream, cheese, and so on. Figure 1.1 illustrates the complete milk procurement process of the

Kaira union.

Fig. 1.1 AMUL milk collection process and brief supply chain (Authors)

Milk Producer

Milk Pouring to Village level Dairy Co-operative Society

(Timings: Morning- 6 to 9 am and Evening 5.30 to 8 pm)

Bulk Milk Cooling (Below 4°C)

Chilled Milk Transfer to Milk Collection Tanker (with BMC Sampling)

Milk Collection Tanker Collect the Milk from Multiple DCS’s as per its Capacity

Milk Weight Measurement and Quality testing

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As discussed in Section 1, the uncertain environment surrounding milk availability is seen in Fig.

2. It depicts milk yield variability on a daily basis and also across seasons. Vehicle routing

conducted on an ad hoc daily basis leads to extra fuel costs and extra miles travelled along with

extra time for milk collection.

Fig. 1.2 Daily milk yield for year 2016-2017 (Kaira Union)

A sustainable milk supply chain strategy aims to reduce environmental impacts through a

combination of cleaner vehicles and fuels, fuel-efficient operation and driving, and by reducing

the quantum of road traffic it generates. In doing so, the fleet minimises fuel and vehicle costs

Quality Testing at Plant Level

Milk Processing and Product Manufacturing

Milk Marketing and Dispatch by State Cooperative Federation

Consumer

Milk Collection at District Milk Processing Plant from Tanker

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while improving the safety and welfare of employees and reducing its exposure to the problems

associated with congestion.

Fulfilling the central objective of this study involves discovering an optimal transportation route

based on the distance, cost, quantity, time, and number of vehicles. This paper proposes that an

optimisation model for the milk collection system will stimulate a reduction in the cost of

transportation, travelling path that implicitly addresses fuel consumption, traffic, and

environmental pollution.

This article is organised as follows: Section 2 provides a literature underpinning. Section 3

presents the optimisation model and analyses the results generated. Section 4 presents results and

discussion. Finally, the conclusions and the following work are presented in Section 5.

2. RELATED LITERATURE

Under the milk collection scenario farm locations are dispersed over a wide rural area. Hence,

milk collection schedulers face challenges while deciding on the allocation of routes for tankers

during milk collection. The problems facing the schedulers when designing routes could include

the inadequacies of rural road networks regarding transporting freshly produced milk to

processing depots, besides the need to re-route because of traffic or road works.

Milk collection and related problems have been widely studied in the past (Les Foulds et al.,

1996; Laporte, 2009; Lahrichi et al., 2012) depicting real world logistical challenges. Advanced

techniques of information technology and operations research have significantly improved the

data generated from dairy activities used for analysis and the presentation.

Besides, these advances have enabled the building of complex decision support systems (DSS)

aiding, thereby, collection schedulers in their daily route building processes (Keenan, 1998;

Butler et al., 2005). Butler et al considered benefits to a scheduler when a geographical

information system (GIS) was used in conjunction with a DSS, allowing them the opportunity to

take advantage of optimisation algorithms, such as optimising routing algorithms, to efficiently

plan milk collections, (Tlili et al., 2013). Timon et al. (2006) investigated the parameter settings

of a real-time vehicle-dispatching system for consolidating milk runs.

The Systematic Travelling Salesman Problem (STSP) (Freisleben and Merz, 1996) was a method

used to solve a problem consisting of 42 nodes (41 dairy farms and 1 depot) with different

collection periods and schedule. While several Integer Programming formulations were used the

authors identified heuristic methods to solve the problem including vehicle capacity constraints

to their model. The paper also deals with the problem of distances between the nodes in a

Euclidean fashion drawing straight lines between the various nodes. While this approach is

useful from a research point of view, lack of traversable route information limits the paper as

regards a practical solution of this real-world problem. These optimisation models have evolved

further in better and more complex ways. Meethet and Lohatepanont (2006) applied optimisation

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techniques for the vehicle routing problem in a milk-run system to find the overall material

handling the cost, minimising milk-run plans, and satisfying demands. Additionally, they

proposed a mathematical model with two different solution approaches. Jianhua and Guohua

(2013) suggested a mutation ACO to solve the milk-run vehicle routing problem with the fastest

completion time.

This study, firstly, introduces the milk-run vehicle routing problem with the fastest completion

time. The customer division method based on dynamic optimisation and split algorithm used to

arrive at the optimal customer order come next. Scaria and Joseph (2014) optimised the

transportation route for a public sector milk dairy in Kerala. Their study showcased a comparison

of the current transportation route with the optimised route while taking into consideration

distance, cost, quantity, time, and the number of vehicles. They optimised four routes and found

an annual savings of more than Rs. 20 lakh per year. Claassen and Hendriks (2007) revealed the

periodic goat’s milk collection problem for the Dutch dairy industry. This study visualised the

importance of probable measures for processing goat milk along with a restricted schedule for

cow milk. In this study, the decision support system provided a starting point in the formulation

of the Vehicle Routing Problem (VRP).

In the recent past, the milk collection process was studied in countries like Canada, Chile, and

Kenya where researchers used the Vehicle Routing Problem (VRP) (Lahrichi et al., 2012;

Paredes-Belmar et al., 2016; Murimi Ngigi and Wangai, 2015). Literature reveals, so far, that the

VRP is definitely the better method for formulating the milk run problem; it has not been used to

model the milk collection problem for Kaira Union and, to an extent, in the Indian context.

2.1. Vehicle Routing Problem (VRP)

The Vehicle Routing Problem (VRP) is a widely researched field of operation research and

combinatorial optimisation. Dantzig and Ramser, 1959 offered an explanation in their seminal

work while investigating the optimisation of routing of a fleet of gasoline delivery trucks

between a storage terminal and a number of service stations (seven in total). A linear

programming approach was used to find an optimal solution for the supply of gasoline to the

various service stations. An attractive aspect of research in this area is that solutions to VRPs can

find a direct application in real world systems that plan and schedule the distribution and

collection of a wide range of goods and the provision of services. A large number of problems,

which may be solved using the VRP with many variants, have emerged. An example being areas

like the optimum routing for industries including milk collection. These constraints could

involve vehicle capacity constraints, homogeneous and heterogeneous vehicle fleets, multiple

depots and plants, pickup and delivery route scheduling, multiple time windows, (Eksioglu et al.,

2009) and so on.

The concept of the Large Neighborhood Search (LNS) (Shaw, 1997) suggests continually

reworking a solution by focussing on transforming local neighbourhoods created in the original

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solution. Later solutions use the previous solution as a basis for future searches with the goal of

finding the optimal solution to the problem. The basic principle of the LNS was further

developed by Pisinger and Ropke (2010). In their paper, they describe the destroy and repair

function of the LNS and show a visual demonstration of how the algorithm is likely to work in

practice. Furthermore, additional constraints involve quantity demand or supply, depending on

the problem to be solved, and the vehicles with limited carrying capacity; the problem then

becomes a Capacitated Vehicle Routing Problem (CVRP).

On the basis of literature survey and devilment in the OR methods the VRP formulation and LNS

solution has been used to solve the milk collection problem of the Kaira union.

3. DATA DESCRIPTION AND STUDY AREA

The turnover of the Kaira Union for the financial year 2017-18 reached Rs. 6256 crore, which

was a 10% increment compared to the previous financial year, 2016-17. The Kaira Union paid an

average of Rs. 783 per kg fat during the same financial year, which was a 12% increase

compared to the previous year’s average of Rs. 698 per kg fat. Average daily milk collection of

the Kaira Union is about 29 lakh litres.

The Kaira Union has a total milk handling capacity of 50 lakh litres per day. The Kaira Union

has a 150 metric ton per day milk drying capacity and a 60 metric ton per day whey drying

capacity. It also has a 2500 metric ton per day cattle feed manufacturing facility besides1250

dairy co-operative societies in different villages of the Anand district. Usually, dairy co-operative

societies start milk collection in the morning at around 6 am and finish at around 9.30 am.

Similarly, in the evening, milk collection starts at 5.30 pm and ends by 8.30 pm.

The Kaira Union hires tankers through a tendering process, making payments on a per kilometre

basis. Rate revision for the tanker on per kilometre basis depends on the revision of the price of

the diesel (see Table 1). The Balasinor and Kapadvanj milk chilling centres (MCCs) and the

Khatraj plant manage their individual milk collection routes. Appropriate tankers have been

allotted to the Khatraj plant in line with the plants’ milk requirement along with two MCCs

concomitant with milk forecasting and milk collection history. The Kaira Union has 170 routes

and 220 milk collection tankers with various capacities i.e. 5, 7, and 10 to 26 KL. Previously, the

Kaira plant managed 83 routes for the morning milk collection and 19 routes for the evening

milk collection from dairy co-operative societies. During flush and lean seasons milk route

optimisation, depending on the forecast supply of milk for that period, was conducted. A master

data table of historically produced daily quantity was taken as estimated milk production for a

day. The preliminary process used to locate the individual DC was based on GPS locations

(longitude/latitude) of these DCS. The DCs’ distribution information is further enhanced by

using realistic road distance to populate the distance matrix.

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Table1. Cost structure of tankers (Kaira Union)

Ton Vehicle Type Cost Per KM

10 ~10T 35

5 ~5T 25

15 ~15T 40

20 ~20T 45

12 ~12T 37

25 ~25T 50

17 ~17T 43

22 ~22T 47

The tanker capacity information is based on number plates and tanker capacities used as different

types of tankers to select the fleet type. The cost structure vehicle type is given in table-1.

4. VRP FORMULATION

As depicted in Fig.3, a cluster represents the set of DCs- one cluster can have multiple routes and

one route can have multiple tankers. -Four different depots, namely Khatraj, Khappadvanj,

Balasinor, and Anand are currently deployed for planning, intermediate storage, and processing.

These depots serve different numbers of DCs.

Fig.3: Representative General VRP Model

We first provide the notation that we will use to state the formulation. Let us define the node set

𝑉𝐷 to contain the depot(s), 𝑉𝐶 to contain the DCs and = 𝑉𝐷 ∪ 𝑉𝐶. Furthermore, we define 𝑉𝑀 ∈

9

𝑉𝐶 as the set of DCs that is required to be visited. Let G = (V, A) be the complete directed

network on which we will solve the VRP. We define the time interval for the DCs as [𝑎𝑖, 𝑏𝑖].

Note that there is also a time interval for each depot vertex. Let us denote the set of vehicles as 𝐾

and define for each vehicle 𝑘 ∈ 𝐾 the origin depot of the vehicle as 𝑜𝑘 ∈ 𝑉𝐷, the work start time

of the vehicle as 𝑡𝑘, the fixed cost of using the vehicle as 𝑓𝑘, the capacity of the vehicle as 𝑄𝑘,

the distance limit as 𝐷𝑘, the driving time limit as 𝐷`𝑘, the working time limit as 𝑊𝑘, and the

return depot of the vehicle as 𝑟𝑘. Associated with each arc (𝑖, 𝑗) ∈ 𝐴, there is a distance 𝑑𝑖𝑗 and

driving duration 𝑑`. In addition, for each vehicle 𝑘 ∈ 𝐾, there is a travel cost 𝑐𝑘 on arc (𝑖, 𝑗).

Next, we present the parameters related to the operational constraints. Let us define 𝑛 to be equal

to 1, if the vehicles have to return to their specified return depots and 0 otherwise. Similarly, let

us define 𝛽 to be 1 if there is a backhaul constraint and 0 otherwise. In addition, we define 𝑒 to

be equal to 1 if the time windows can be violated at the cost of a penalty n per unit time and 0

otherwise. We are now ready to define the decision variables. Let 𝑥𝑘 be equal to 1 if vehicle 𝑘

traverses arc (𝑖, 𝑗) and 0 otherwise. Furthermore, let 𝑦𝑘 be equal to 1 if vehicle 𝑘 visits and

serves vertex 𝑖 and 0 otherwise. The amount of the pickup commodity carried by vehicle 𝑘 on

arc (𝑖, 𝑗) is defined as 𝑤𝑘. We also define 𝑡𝑘 as the time at which vehicle arrives for milk

collection,

Optimisation Model:

We use the following notations:

Ti arrival time at node i

wi wait time at node i

xijk ϵ {0,1}, 0 if there is no arc from node I to node j, and 1 otherwise,

i ≠ j ; i, j ϵ {0, 1, 2, … , N}, k ϵ {0, 1, 2 … , K} Parameters:

K total number of vehicles

N total number of DCs

cij cost incurred on arc from node i to j

tij travel time between node i and j

mi demand at node i

qk capacity of vehicle k

ei earliest arrival time at node i

li latest arrival time at node i

fi service time at node i

rk maximum route time allowed for vehicle k

Minimize

∑ ∑ ∑ 𝑐𝑖𝑗

𝐾

𝑗≠𝑖,𝑘=1

𝑁

𝑗=0

𝑁

𝑖=0

𝑥𝑖𝑗𝑘

Subject to:

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∑ ∑ 𝑥𝑖𝑗𝑘 ≤ 𝐾, 𝑓𝑜𝑟 𝑖 = 0

𝑁

𝑗=1

𝐾

𝑘=1

(1)

∑ 𝑥𝑖𝑗𝑘 = 1, 𝑓𝑜𝑟 𝑖 = 0 𝑎𝑛𝑑 𝑘 𝜖 {1, , 𝐾} (2)

𝑁

𝑗=1

∑ 𝑥𝑗𝑖𝑘 = 1, 𝑓𝑜𝑟 𝑖 = 0 𝑎𝑛𝑑 𝑘 𝜖 {1, , 𝐾} (3)

𝑁

𝑗=1

∑ ∑ 𝑥𝑖𝑗𝑘 = 1, 𝑓𝑜𝑟 𝑖 𝜖 {1, , 𝑁} (4)

𝑁

𝑗=0,𝑗≠𝑖

𝐾

𝑘=1

∑ ∑ 𝑥𝑖𝑗𝑘 = 1, 𝑓𝑜𝑟 𝑗 𝜖 {1, , 𝑁} (5)

𝑁

𝑖=0,𝑖≠𝑗

𝐾

𝑘=1

∑ 𝑚𝑖 ∑ 𝑥𝑖𝑗𝑘 ≤ 𝑞𝑘 ,

𝑁

𝑗=0,𝑗≠𝑖

𝑁

𝑖=1

𝑓𝑜𝑟 𝑘 𝜖 {1, , 𝐾} (6)

∑ ∑ 𝑥𝑖𝑗𝑘 (𝑡𝑖𝑗 + 𝑓𝑖 + 𝑤𝑖) ≤ 𝑟𝑘, 𝑓𝑜𝑟 𝑘 𝜖 {1, , 𝐾} (7)

𝑁

𝑗=0,𝑗≠𝑖

𝑁

𝑖=1

𝑇0 = 𝑤0 = 𝑓0 = 0 (8)

∑ ∑ 𝑥𝑖𝑗𝑘 (𝑇𝑖 + 𝑡𝑖𝑗 + 𝑓𝑖 + 𝑤𝑖) ≤ 𝑟𝑘, 𝑓𝑜𝑟 𝑗 𝜖 {1, , 𝑁} (9)

𝑁

𝑖=0,𝑖≠𝑗

𝐾

𝑘=1

𝑒𝑖 ≤ (𝑇𝑖 + 𝑤𝑖) ≤ 𝑙𝑖, 𝑓𝑜𝑟 𝑖 𝜖 {1, , 𝑁} (10)

The objective function minimises the total cost of travel of all the vehicles in completing their

tours. Constraint 1 guarantees that the number of tours is K by selecting the most K outgoing

arcs from the depot (I=0). The constraint set 2 ensures that for each vehicle, exactly one outgoing

arc from the depot is selected. Similarly, the constraint set 3 ensures that for each vehicle, there

is exactly one arc entering into the node with respect to the depot (i = 0). These two constraint

sets (constraint set 2 and constraint set 3) jointly ensure that a complete tour for each vehicle is

ensured. The constraint set 4 makes sure that from each node i only one arc for each vehicle

emanates from it. The constraint set 5 ensures that for each node j, only one arc for each vehicle

enters into it. These two constraints (constraint set 4 and constraint set 5) make sure that each

vehicle visits each node only once. The constraint set 6 sees that for each vehicle, the total

demand (load) allocated to it is less than or equal to its capacity. The constraint set 7 ensures that

the total time of travel of the route of each vehicle is less than or equal to the maximum route

time.

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The constraint set 8 sets the arrival time, waiting time, and service time of each vehicle at the

depot to zero. The constraint set 9 guarantees that the arrival time of the vehicle at the node j is

less compared to the specified arrival time at that node. The constraint set 10 guarantees that the

sum of the arrival time and the waiting time of each vehicle at each node i is more than equal to

the earliest arrival time at that node and less than or equal to the latest arrival time at that node i,

i = 1, 2, 3, ···, N. Constraint sets 8-10 define the time windows. These formulations completely

specify the feasible solutions for the VRPTW.

5. RESULTS AND DISCUSSIONS

A Microsoft Excel platform, public GIS, and metaheuristics have been designed to search for

efficient routing solutions by using the LNS algorithm (Erdoğan, 2017a). The spreadsheet-based

solver is driven by the VBA code to run an algorithm that is based on the implementation of a

modified version of the LNS algorithm. It assigns various DCs to vehicles in a time-sequenced

manner generating vehicle routes for each vehicle in the fleet returning to the depot at the end of

the trip. For each trip, the total distance is calculated based on the sum of the distances of all the

edges in a closed loop of the vehicle route. The cost for each vehicle route is calculated based on

the total distance and the rate/km for the vehicle. The total logistics’ cost for one cluster is

calculated by aggregating the distances for all the vehicle routes. For instance, the vehicle route

for the Balasinor cluster is presented in Fig.4

Fig. 4 Balasinor Route Plan

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This has only one vehicle in its fleet with a carrying capacity of 15500 Ltrs and an operational

cost of 40 Rs/Km. The total distance covered is 141.23 km with a total cost of Rs. 1572. Clusters

with a larger fleet have as many routes as the number of vehicles represented with the total

distance and cost in table 2; @ represents the optimal solution over different cases comparing the

existing/actual solution and # is representative of when an optimal solution is coinciding with the

existing/actual solution.

Table 2: Cost and time with different routes

S.No Depot Case

No.

Fleet (tonnage * numbers) Total Distance

(km)

Total

Cost(Rs)

1 Balasinor 1 10 * 2 190 6655.5@

2 Balasinor 2 5.5 *3 255 6367.6

3 Balasinor 3 15.5 * 1 141 5649.4

4 Balasinor 4 10.5*1, 5.5*1 189 5882.4

5 Kapadvanj 1 10.5*1 63 2200

6 Kapadvanj 2 5.5*2 78 1966@

7 Khatraj 1 15.5*20 1502 52596@

8 Khatraj 2 15.5*10, 20.5*8 1448 57013

9 Khatraj 3 20.5*6,15.5*5,12.5*12,10.5

*1

1569 61904

10 Khatraj 4 Actual 2173 86355

11 Anand 1 Actual 12150 509871

12 Anand CL1 1 20.5*3,15.5*6,10.5*1 624 25248@

13 Anand CL1 2 15.5*9 644 25756

14 Anand CL1 3 Actual 789 32217

15 Anand CL2 1 15.5*10 1162 46464

16 Anand CL2 2 20.5*4,15.5*6 1090 45333

17 Anand CL2 3 Actual 1078 45164@#

18 Anand CL3 1 15.5*9 1062 42480

19 Anand CL3 2 10.5*1,

12.5*2,15.5*5,20.5*2

1056 41766@

20 Anand CL3 3 Actual 1160 46055

21 Anand CL4 1 15.5*11 1152 46060

22 Anand CL4 2 10.5*1,

12.5*1,15.5*2,20.5*5,25*1

1000 43811@

23 Anand CL4 3 Actual 1112 46663

24 Anand CL5 1 15.5*10 918 36726

25 Anand CL5 2 5.5*1,10.5*1,12.5*1,15.5*3,

25*4

846 33774@

26 Anand CL5 3 Actual 996 40184

27 Anand CL6 1 15.5*11 1362 54488

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S.No Depot Case

No.

Fleet (tonnage * numbers) Total Distance

(km)

Total

Cost(Rs)

28 Anand CL6 2 12.5*1,15.5*1,20.5*4,25.5*

3

1166 52452@

29 Anand CL6 3 Actual 1251 56636

30 Anand CL7 1 15.5*9 782 31269

31 Anand CL7 2 5.5*1,10.5*1,15.5*4,20.5*4 757 31110@

32 Anand CL7 3 Actual 984 38696

33 Anand CL8 1 15.5*9 785 31397

34 Anand CL8 2 5.5*1,10.5*1,12.5*3,15.5*3,

25*2

751 29123@

35 Anand CL8 3 Actual 804 31772

36 Anand CL9 1 15.5*14 2452 98112

37 Anand CL9 2 10.5*1,12.5*2,15.5*4,20.5*

6,25*2

2038 92446

38 Anand CL9 3 Actual 2236 94981@

39 Anand CL10 1 15.5*10 2192 87668

40 Anand CL10 2 12.5*1,15.5*2,20.5*6,22*1 1803 77710

41 Anand CL10 3 Actual 1739 75993@

Fig. 5 Percentage benefit

The findings indicate that except for one cluster the new solution for the others gives

significantly better results in the context of the total kilometres travelled along with cost. The

percentage benefit for each cluster and other depots are shown in Fig.5. It is found that for the

depots Balasinor, Khatraj, and Kapadvanj the optimisation modelled gives significant cost

0

10

20

30

40

50

60

70

80

% benefit

14

savings in the range of 20-70%. However, for clusters that are placed in the Anand milk plant,

the savings are in the range of 2% to 20%. While emphasising on two clusters, CL2 and CL10,

the original allocation gives only the best solutions.

6. CONCLUSION

As far as conclusion and future research directions are concerned, a milk collection network

design problem has been considered for this paper. We propose an integrated location routing

formulation to fix the problem with regard to milk collection of the Kaira union. We have

studied some useful insights regarding the existing fleet operations of the Kaira Union. Next, we

have developed a better milk collection network vehicle fleet mix. We then compared the results

with existing manual operations and developed an algorithm to solve the problems of a practical

size. The algorithm performs well on solution cost and computation time.

Future research may consider, specifically, soft as well as hard time constraints that need to be

applied for VRP. One such time constraint occurs when there is a cut in electricity supply

leading to dysfunction of chilling centers at some of the DCs. In such cases, the vehicle needs to

arrive at these DCs before a stipulated time. Such a case may be analysed based on data

availability.

7. REFERENCES

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