working paper 293into various products i.e. pasteurised milk, curd, yogurt, butter, buttermilk,...
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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: [email protected]
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: [email protected] 2 Principle data scientist, IHS Markit 3 Professor, Institute of Rural Management Anand. Email: [email protected]
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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
4
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.
8
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:
10
∑ ∑ 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
13
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.
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