This study discusses the current scenario of Operations Research in the field of Logistics. Five sectors are considered in the study to form a brief understanding of how they use Operations Research techniques and why these techniques are used.
© October 2019  IJIRT  Volume 6 Issue 5  ISSN: 23496002
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Operation research techniques in warehousing and logistics
Palak Satra
1
, Pezan Dolasha
2
, Raj Manek
3
, Rheaa Lodha
4
, Rishit Jain
5 1,2,3,4,5
Student NMIMS, Anil Surendra Modi School of Commerce, Mumbai Campus
Abstract

This study discusses the current scenario of Operations Research in the field of Logistics. Five sectors are considered in the study to form a brief understanding of how they use Operations Research techniques and why these techniques are used. Operation research technique help in reducing cost and improve decision making. Index terms
Warehousing, Logistics, Operation research technique, Simplex, Transportation problems
INTRODUCTION I
nvestment into India‟s supply chain sector is gaining
momentum. The introduction of the Goods and Services Tax (GST), changes in foreign direct investment rules, and increased government spending
has helped the growth of this sector. India‟s dreams
of becoming a global manufacturing powerhouse and
the government efforts on „Make in India‟ also
helped the nationwide supply chain reforms, several federal and statebased schemes and investment incentives have been provided. (India briefing 2019). A study by Copgemini consulting, 2016 state of Thirdparty Logistics Study show 63% of people feel cutting transportation cost is important and 18% of the people feel reducing labor cost. Management science is a study which helps at arriving solution to complex decision making problems and thus can be very vital for business to make decision making simple. Operation research techniques like transportation problems and simplex methods can help to reduce the transportation cost and labor cost. This research paper aims to study the different operation research techniques one can use to optimize warehousing and logistics and resolve the issues faced by the industry by these techniques. There is a large scope of this industry in India due to recent policy changes and expected growth in the coming years make this a very good opportunity thus we would like to study on this topic. OVERVIEW OF THE INDUSTRY A modernized and efficient warehousing and logistics improves the ease of doing business, scales down the costs of manufacturing, and accelerates rural and urban consumption growth due to better market access. India has a 100 percent FDI for the development and maintenance of warehousing and storage facilities. Under the free trade warehouse zone (FTWZ) Scheme, there are several zones in India reserved for warehouse development. Panvel near Mumbai, Khurja near New Delhi, and Siri City in Chennai, are some of the FTWZs. These zones have good connectivities with major railways, roads, airways, and ports. Several incentives like duty free import of building material and equipment are provided in these zones to attract investors. Late last year, the 100 acre FTWZ in Nanguneri in the southern state of Tamil Nadu began operations. According to Nilesh Karkhanis, Milestone Capital in his article institutional interest in logistics, warehousing to continue growing (Economic times, 2017) With one nation one tax, locations are being selected by end users on the basis of optimum logistics route and availability of quality warehouses in such locations. A $100 billion infrastructure push in roadways, railways, ports, air cargo terminals etc., has provided a boost to the demand for quality warehousing services. The Make in India initiative, though in an early stage currently, is another big driver for warehousing and logistics demand. The warehousing industry is slated to grow at 8% to 10% per annum for the next few years. RESEARCH OBJECTIVES
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The objective of this study is to get an understanding of the workings of the Logistics industry from the perspective of Operations Research and using this understanding to gain a better picture of the shortfalls and limitations of current OR techniques in the sectors of warehousing and logistics. RESEARCH METHODOLOGY Studying the past research papers and understanding the current industry position and its limitations also solving a few examples by the research techniques. LITERATURE REVIEW The transportation problem was first done by the French mathematician (Monge, 1781). The Soviet/Russian mathematician and economist Leonid Kantorovich made major advances in this field during the world war 2. Kantorovich (1942), published a paper on the problem and later with Gavurian, and studied of the capacitated transportation problem (Kantorovich and Gavurin, 1949). The srcin of transportation problems was presented by Hitchcock,
(1941), in his study entitled “The Distribution of a
Product from Several sources to numerous Localit
ies”. This presentation came to be the first
important contribution to the solution of transportation problems. Koopmans, (1947),
presented a study called “Optimum Utilization of the Transportation System.” This helped in the
development of transportation methods which involve of shipping sources and a number of destinations. The transportation problem, received this name because of the applications that involve knowing how to optimally transport goods. A.C. Caputo. et. al. presented a methodology for planning road transport activities through proper system of customer orders in separate fulltruckload or shipments in order to minimize total transportation costs. Roy and Gelders (1980) solved a real life problem of a liquid bottled product through a 3stage logistic system; the stages of the system are plantdepot, depotdistributor and distributordealer. Adlakha et al. proposed a method for solving Transportation problems with mixed constraints. In this algorithm for an MFL solution in Adlakha et al, Vogel Approximation Method (VAM) and MODI (Modified Distribution) method were used. Linear Programming was introduced first by Lenoid Kantorovich in 1939. He used it to reduce the costs of army and to improve the battlefield efficiency in the worldwar 2. This method was not known to others as it was a secret until 1947, when George B. Dantzig published the simplex method and the introduction of the theory of duality by John von Neuman. After the Second World War many industries began to adopt lpp because of its usefulness in optimization. Linear programming is method in mathematics which is used to find the best possible solution of a particular problem, subject to different constraints. One of the simple but probably the most important and widely used techniques in the field of operations research is linear programming. Its ability to the practical applications in the field of economic management is responsible for its development today. The objective is to optimize (maximize or minimize as the case may be) the function f(x) where f(x) = FX + k is a vector function. It is linear. F is a functional, k is a constant, and X ranges over a convex polyhedral set of points. The maximization or minimization of the objective function is subject to certain linear constraints. The objectives covered under LPP can be maximization of profits, minimization of various costs like production, transport, agricultural cost, minimization of time. LPP can be solved graphically, algebraically and by using simplex. The simplex method becomes useful when the LPP has more than two variables. The simplex method is used to solve linear programming problems with the use of surplus, slack and artificial variables in a tabular form, depending on the type of problem (maximization or minimization). The storage assignment downside involves deciding wherever and the way to store a collection of items so as to confirm best operation of the supplying system (de Kosteret al., 2007). Since order choosing is the most important and toilsome operation in the warehouse, it's common to optimize a live of order choosing performance, e.g. to reduce expected choosing (or travel) times, or order cycle times. The two main families of storage methods area unit are the dedicated and also the shared methods. Dedicated methods store continuously identical item within the same slot. For this type of strategy and singlecommand choosing, Heskett (1963) evidenced that the cubeperorder index (COI) policy minimizes the typical choosing (or travel) time. This policy types the things by increasing COI, i.e. the
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quantitative relation of the stock volume to the demand rate, so places them consecutive to the highest free slots to the entrance. The reciprocal of COI is termed the ratio. Shared storage methods, in distinction, don't reserve slots for specific things, which makes them a lot of convenient stock levels modification over time. The most important representatives of shared storage methods area unit classbased storage strategies (Hausman et al., 1976; Petersen and Aase, 2004). These type categories of items and partition the warehouse floor to zones, and at last assign every category of items to a selected zone. Storage inside a zone is random. within the case of singlecommand (singleitem) choosing, it's typical to use 2
–
6 zones, and outline categories based on the turnover rates of the things. so as to complete inventory level changes, some empty reserve slots area unit unbroken in every zone. The positioning of zones is addressed, e.g. in (LeDuc and Diamond State Koster, 2005). Findings We try to solve a few examples by the OR techniques. The techniques we are using are Simplex, Transportation problem and assignment problem. 1.
Using Transportation problems There are three methods:
Northwest corner method: The name Northwest corner is given to this method because the basic variables are selected from the extreme left corner.
Least cost method: Here, the allocation begins with the cell which has the minimum cost. The lower cost cells are chosen over the highercost cell with the objective to have the least cost of transportation.
Vogel‟s approximation method (or Penalty
method): Example: A company has 4 manufacturing plants and 5 warehouses each plant manufactures the same product which is sold at different prices at each warehouse area. The cost of manufacturing and the cost of raw materials are different in each plant, the capacities of each plant are also different. The data for various plants is given below. The company has 5 warehouses, the sale price and transportation cost and demand are given below. 1 2 3 4 SALE PRICE DEMAND A 4 7 4 3 30 80 B 8 9 7 8 32 120 C 2 7 6 10 28 150 D 10 7 5 8 34 70 E 2 5 8 9 30 90 Now we need to find the optimal allocation in order to maximise profits. Step 1: Check for Existence of Feasible Solution. It is a necessary and sufficient condition for the existence of a feasible solution to the general transportation problem is that Total supply = Total demand In the above situation, Total Demand= 80+120+150+70+90 = 510 Total Supply= 100+200+120+80= 500
As demand doesn‟t meet supply, we see that in order
to match the two we introduce a dummy column. The supply of this will 10 units (total demand
–
total supply). Being a dummy column all the values present in the column will be zero. Step 2: We need to proceed solving this by creating a profit matrix. In order to find profit, we need to subtract all the costs from the sale price. For example, to find A1 : Sale price
–
Manufacturing cost
–
Raw material cost Transportation cost i.e: 301284 =6 Therefore, the profit made by plant 1 in warehouse A is 6 units. Similarly, we compute the data for the others.
1 2 3 4 Dummy Demand A 6 6 11 15 0 80 B 4 6 10 12 0 120 C 6 4 7 6 0 150 D 4 10 14 14 0 70 E 8 8 7 9 0 90 Supply 100 200 120 80 10
Step 3: Since the question is now a maximization one, we first need to convert it into a minimization one. In order to do this, we subtract the highest number from all the others in the table. Here, the highest profit is 15.
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Now we form the regret matrix
1 2 3 4 Dummy Demand A 9 9 4 0 15 80 B 11 9 5 3 15 120 C 9 11 8 9 15 150 D 11 5 1 1 15 70 E 7 7 8 6 15 90 Supply 100 200 120 80 10 510
Step 4: Solve the problem by using Vogel‟s
Approximation Method. Firstly, determine a penalty cost for each row (column) by subtracting the lowest unit cell cost in the row (column) from the next lowest unit cell cost in the same row (column). Based on the penalties computed, we allocate the to the lowest cost cell but with the highest penalty. Since the highest penalty is 15 we allocate in the first row. Step 5: Identify the row or column with the greatest penalty cost. Break the ties arbitrarily (if there are any). Allocate as much as possible to the variable with the lowest unit cost in the selected row or column. Adjust the supply and demand and cross out the row or column that is already satisfied. If a row and column are satisfied simultaneously, only cross out one of the two and allocate a supply or demand of zero to the one that remains. Repeat this process till the total demand and supply gets allocated in the cells. Step 6: Check for degeneracy. Here the no. of allocations greater than or equal to the addition of rows and columns minus 1. N >= (m+n1) 8 >= (5+51) 8 >= 9
As the condition doesn‟t satisfy we need to equate the
same. T
his can be done by introducing „e‟ (epsilon).
which not only has the lowest cost but also looping is not possible there. Step 8: Now since N >= (m+n1), it means that the solution is not degenerate. Now, we check for optimality. 1.
U+V for allocated 2.
U+V for unallocated 3.
Net Evaluation Table Since the NET Table is negative that means the solution is not optimal. Hence it order to make the solution optimal, we loop at the negative value.
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Step 9: Looping the negative value and adding/subtracting units. Now we check for the no. of units to be added or subtracted.
So θ = min (
ve corner cells) =min (70, e) =e This value is added and subtracted to the cells based on the signs. Reallocation Now we check for optimality. 1.
U+V for allocated 2. U+V for unallocated 3. Net Evaluation Table
5 3 2 X 5 4 X X X 2 X X 1 X X 8 0 X 2 6 2 X 5 5 4
Now the solution is optimal. However, the presence of zeros indicates that there is an alternative solution present. Reasons for choosing the VAM Method over the other two is that the other two are not as accurate. An example of LPP (simplex) Logistics of Formula 1 The real race of formula1 occurs behind the scenes. The logistics of transporting the equipment of 10 teams to 20 races 5 continents in a time of nine months is a very difficult job. The teams use a combination of road, air and waterways. When in one continent, a preference for transportation is given to roadways. Cars and equipment are transported through Lorries to race locations. The teams have to set up temporary garage at race location. The teams currently use cargo planes for transport. In case of races in different continents, some equipment like tools, jacks, materials required for setting up a garage are transported through waterways months before they are actually needed in order to save costs. An example The gap between 2 races is 7 days and the transport is between Italy and Spain. Waterways is not possible because of lower time availability. The total weight of cars, personnel, tools etc. to be transported is 2000kg. The cost per kg transported by air is 5000 and by road is 3000. The tools required for setup of garage, cables, computer racks and the personnel required for the job are to be transported through air (weight 500 kg) so that the garage is ready before the arrival of cars. We need to minimize the cost of the transportation. Solution Let quantity transported air transport be x1 and road transport be x2 The total quantity to be transported is 2000 kg Thus x1+x2=2000 We can say that
X1+x2≤2000 and
X1+ x2≥2000
Since the minimum amount to be transported by airways is 500,
X1≥500
Objective function Minimize Z= 5000x1 + 3000 x2 Since simplex cannot have inequalities, we add surplus, slack and artificial variables to convert these into equations without having an effect on their meaning Minimize Z= 5000X1 + 3000X2 + 0S1 + 0S2 + 0S3 +MA1 +MA2 Subject to,