MORE s Logistics Distribution Department

MORE s Logistics Distribution Department - Transcript

Institute of management technology ghaziabad
pgdbm pT 2008 11
Operations Research
Under the supervision of
Dr Mrinalini Shah
Associate Professor
Submitted by
Group 9
Team Members
Aakash Saxena 08EM 001
Ankur Saxena 08EM 011
Manish Shukla 08EM 021
Satyendra Singh Rajawat 08EM 038
T Sudhakar 08EM 058
Sanjeev Kumar Singh 08EM 059
Operations research uses analyses and techniques from a variety of branches of Mathematics statistics and other scientific disciplines Certain analytical results arise repeatedly in applications of operations research to industrial and service operations
The objective of this assignment is to apply wide range of operations research models and tools in analyzing the different situations and optimizing the results in a concise format to take the critical decisions
Science of OR
Focuses on impact and implementation
Improves decision processes
Helps operations become stronger
Establishes a disciplined consultant s approach
Transfers technology to your department so you can take over the project
The following section explains about the various Operations Research techniques used in the business scenario using Transportation problems and Assignment problem
OR Analysis of following Aditya Birla Group companies
Aditya Birla Retail Limited
Birla Sun Life Distribution Company Limited BSDL
The Aditya Birla Retail Company Limited Determine the optimal distribution for this company to minimize total shipping cost Evaluate your output
The retail promise of the Aditya Birla Group is aptly called MORE brand of Aditya Birla Retail Ltd The product offerings include a wide range across fresh fruits vegetables groceries personal care home care general merchandise a basic range of apparels Currently there are over 600 MORE for you supermarkets across the country
The consumer products industry is cost driven and a lot of it is commodity type in nature so very efficient and effective supply chains are critical for success and the ultimate profitability of the company OR techniques when utilized effectively save costs reduce cash investments and inventory and can even improve top line growth
Source HYPERLINK http www morestore com www morestore com and from Aditya Birla Retail Company ltd where one of our friend is an employee
Transportation concerns the movement of products from a source such as a plant factory or work shop to a destination such as a warehouse customer or retail store The goal for any business owner is to minimize transportation costs while also meeting demand for products Transportation costs generally depend upon the distance between the source and the destination the means of transportation chosen and the size and quantity of the product to be shipped
A programming problem that is concerned with the optimal pattern of the distribution of goods from several points of origin to several different destinations with the specified requirements at each destination is called as a Transportation problem
In a transportation problem the initial feasible solution can be generated by a number of methods Three of the most commonly methods are
The North West Corner Rule NWC Rule
Least Cost Method LCM
Vogel s Approximation Method VAM
After developing the initial feasible solution by any one of the above three methods the solution thus obtained has to be tested for optimality Basically 2 methods are widely used
Stepping Stone Method
Modified Distribution MODI Method
Applications
The transportation problem was often discussed as an application that would benefit from computerization because this type of problem can be formulated quantitatively and because such problems are often complex enough to benefit from using a model Also the allocation of transportation resources among competing uses is of interest to business decision makers in a number of different industries In general real world transportation problems are often important
Using Model Driven DSS to solve transportation problems can improve profitability
Mathematical programming provides quantitative bases for management decisions bases with which management manipulates and controls various activities to achieve the optimal outcomes of business problems Management can make better and more effective judgment by use of mathematical programming However it is no substitute for the decision maker s ultimate judgment
Need for Transportation Model
Consider the Aditya Birla Retail Company Ltd Determine the optimal distribution for this company to minimize total shipping cost in NCR where more has 43 stores and 5 warehouses for the supply Need for efficient supply to the demand is the key to achieve objective with the help of Transportation Model
MORE s Logistics Distribution Department have divided NCR into 3 region
North East NE North East Delhi Ghaziabad Noida
South Central SC South Central Delhi Faridabad
West W West Delhi Gurgaon
Below is the first transportation table with the transportation cost data received by the Distribution department cost are in 100 and for a week period from different warehouses to the 3 regions
Supply Dummy column D with the demand 160 is being introduced
W2 14 8 18 160
W3 26 24 16 90
W4 22 16 15 70
W5 11 4 2 90
Demand 180 120 150
450 610


NE SC W D Supply Remarks
W1 16 20 12 0 200
W2 14 8 18 0 160
W3 26 24 16 0 90
W4 22 16 15 0 70
W5 11 4 2 0 90
Demand 180 120 150 160 610

Computation of Transportation Cost under North West Corner Rule
NE SC W D Supply
W1 16 20 12 0 200 20 0
W2 14 8 18 0 160 60 0
W3 26 24 16 0 90 0
W4 22 16 15 0 70 0
W5 11 4 2 0 90 0
Dem 180 120 150 160 610
0 100 90 90
0 0 0
Calculation of total price using NWCR
Warehouse Region Quantity Unit price Total price
W1 NE 180 16 2880
W1 SC 20 20 400
W2 SC 100 8 800
W2 W 60 18 1080
W3 W 90 16 1440
W3 D 0 0 0
W4 D 70 0 0
W5 D 90 0 0
Total 610 6600
Hence the Total cost by NWCR is Rs 6600
Calculation of Total Price using Least Common Method
NE SC W D Supply
W1 16 20 12 40 0 160 200 40 0
W2 14 40 8 18 0 160 40 0
W3 26 90 24 16 0 90 0
W4 22 50 16 15 20 0 70 50 0
W5 11 4 2 90 0 90 0
Demand 180
140
90
0 120
0 150
60
20
0 160
0 610

Calculation of Total Price of LCM
Warehouse Region Quantity Unit price Total price
W1 W 40 12 480
W1 D 160 0 0
W2 NE 40 14 560
W2 SC 120 8 960
W3 NE 90 26 2340
W4 NE 50 22 1100
W4 W 20 15 300
W5 W 90 2 180
Total 5920
Hence the Total cost by LCM is Rs 5920
Vogel s Approximation Method
NE SC W D Supply P1 P2 P3 P4 P5
W1 16 20 12 40 0 160 200 140 0 12 12 4 4 4
W2 14 40 8 18 0 160 40 0 8 8 6 6 4
W3 26 90 24 16 0 90 0 16


W4 22 50 16 15 20 0 70 50 0 15 15

W5 11 4 2 90 0 90 0 2 2 2

Demand 180 140 0
120 0 150 60 0 160 70 0 610


P1
P2
P3
P4
P5
P6 3
3
3
2
2
2 4
4
4
12 10
10
10
6
6
0
0





Here Pi is difference between the smallest and next to the smallest costs in each row and column

Calculation of Total Price of VAM
From To Amount Unit Cost Route Cost
W1 NE 140 16 2240
W3 NE 60 12 720
W1 SC 40 14 560
W2 SC 120 8 960
W5 W 90 2 180
TOTAL 4660
Conclusion Compared to NWCR Least cost method the VAM method is giving the low cost transportation hence we can recommend this path
Test for optimality by MODI Method U V Method
Assigning value of u v with respect to allocated cells cost and allocating delta to cell 1 4
REGION U i
WARE NE SC W DUMMY
W1 16 12 0 0
W2 14 8 2
W3 0 0
W4 0 0
W5 2 10
V j 16 10 12 0
Assigning cost to the empty cell based on the values of u v
REGION U i
WARE W1 W2 W3 DUMMY
W1 10 0
W2 10 2 2
W3 16 10 12 0
W4 16 10 12 0
W5 6 0 10 10
V j 16 10 12 0
Actual cost of empty cell
REGION
WARE W1 W2 W3 DUMMY
W1 20
W2 18 0
W3 26 24 16
W4 22 16 15
W5 11 4 0
Reduction of cost from actual to allocated cost for empty cells
REGION
WARE NE SC W DUMMY
W1 10
W2 8 2
W3 10 14 4
W4 6 6 3
W5 5 4 0
Since all the cost obtained are positive therefore the solution will be considered as a optimal solution
Result of Optimal solution
Warehouse Region Quantity Unit price Total price
W1 NE 140 16 2240
W1 W 60 12 720
W2 NE 40 14 560
W2 SC 120 8 960
W5 W 90 2 180
Total 450 4660
Hence we can say that VAM method can be applied for solving this transportation problem and the minimized cost of transportation is Rs 4660
Case 2 Birla Sun Life Distribution Company Limited BSDL
BSDL is a premier wealth management company and ranks among the top players in this business segment BSDL offers wealth management and financial planning solutions which are facilitated mainly through twin products mutual funds and insurance
Sources of data Birla Sun Life Distribution Company Limited BSDL Delhi

Assignment model is useful to assign organization s salesman to specific territories based on the least incurred cost In the given example there are 4 sales team where each team has 10 member covering 4 territories of Delhi North South East West Cost of operation is on per day basis and the figures are in 100
Territories
Sales Team T1 T2 T3 T4
S1 25 27 28 37
S2 28 34 29 40
S3 35 24 32 33
S4 24 32 25 28
Minimization of cost
Step 1 Row reduction Step 2 Column reduction
T1 T2 T3 T4 T1 T2 T3 T4
S1 0 2 3 12 S1 0 2 2 8
S2 0 6 1 12 S2 0 6 0 8
S3 11 0 8 9 S3 11 0 7 5
S4 0 8 1 4 S4 0 8 0 0
From To Minimized Cost Result
S1 T1 25 This implies the minimum cost


n





D
w
x

w
x
y



h
h
h
h
h

gd
gd
H incurred while assigning territories
S3 T2 24 using Assignment Model
S4 T4 28
TOTAL 106