Network Design for Mid-day Meal Program

Transcription

1 Network Design for Mid-day Meal Program by Priyanka Singh MBA, Marketing, Acharya Institute of Management & Sciences, AIMA, 2013 and Afsaruzzaman Noor MBA, Finance, Institute of Business Administration, University of Dhaka, 2017 BSc. in Industrial & Production Engineering, Bangladesh University of Engineering and Technology, 2012 SUBMITTED TO THE PROGRAM IN SUPPLY CHAIN MANAGEMENT IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE IN SUPPLY CHAIN MANAGEMENT AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE Priyanka Singh and Afsaruzzaman Noor. Cambridge. All rights reserved. The authors hereby grant to MIT permission to reproduce and to distribute publicly paper and electronic copies of this capstone document in whole or in part in any medium now known or hereafter created. Signature of Author... Priyanka Singh Department of Supply Chain Management May 11, 2018 Signature of Author... Afsaruzzaman Noor Department of Supply Chain Management May 11, 2018 Certified by... Tim Russell Research Associate, Center for Transportation and Logistics Capstone Advisor Accepted by... Dr. Yossi Sheffi Director, Center for Transportation and Logistics Elisha Gray II Professor of Engineering Systems Professor, Civil and Environmental Engineering

2 Abstract The Mid-day Meal program is an initiative taken by the Government of India to improve the nutritional status of school-age children nationwide. It involves many agencies and NGOs. Akshaya Patra is the most popular and largest NGO among them which in India is currently serving meals to 1.6 million children every day. It uses centralized kitchens to prepare meals and then deliver them to schools within a four hours of delivery window. Currently, it is facing the challenge of fulfilling the growing demand of meals within short delivery windows while keeping the transportation costs and the fixed costs of the kitchens low. Keeping in mind that food is a highly perishable item and has a very short delivery window (four hours), we designed a kitchen network to solve Akshaya Patra s problem by using an optimization method called Mixed Integer Linear Programming (MILP). We also tested various scenarios such as network design considering kitchens capacity constraint, design with cross docking, and the use of insulated containers. Our model suggests a network design approach using cross docking and insulated containers. The proposed model has lowest cost and can be replicated in other states also.

3 Acknowledgements We sincerely would like to thank Tim Russell, our advisor, for his guidance, expertise, and dedicated support throughout this process. He has been very helpful throughout the semester. We should express our special thanks to Sergio Alex Caballero (Research Associate, Center for Transportation & Logistics, MIT and Course Lead, MITx MicroMasters Program) and Francisco J. Jauffred (Research Associate, MIT FreightLab) for their consistent support whenever we needed them. We re indebted to our friends Tasnim Ibn Faiz (Graduate Research Assistant, Department of MIE, Northeastern University) and Sufian Latif (Graduate Research Assistant, The Ohio State University) for their time in sharing valuable insights and suggestions in formulation and building the model. We would also thank our classmates German Tisera, Ka Hing Mak and Jorge Garcia Castillo for the time they gave us in troubleshooting with the model. Our special thanks to staffs of sponsor company Akshaya Patra for their support, oversight, and valuable contributions. Last but not the least, we would like to thank MIT SCM cohort, all our friends and families for their endless patience and tireless support throughout the time we have been working on the project.

4 Table of Contents 1. Introduction Literature Review Perishability challenge in food industry Supply chain networks for food Cross docking Direct delivery to customers Solving quantitative aspects of the problem using optimization Methodology Model design Current supply chain analysis Geographic scope Model input Daily demand Centralized kitchen data Setup cost data Transportation data Truck size Cross docking data Data cleaning Model formulation Objective Model parameters Decision variable Assumptions Mathematical formulation without cross docking Mathematical formulation with cross docking Optimization tools Cost components Results/Data Analysis Scenario 1: Network design without capacity constraint... 25

5 4.2 Scenario 2: Network design with capacity constraint Scenario 3: Network design with insulated containers Scenario 4: Network design considering currently opened kitchens Scenario 5: Network design with cross docking and capacity constraint Scenario 6: Network design with cross docking and insulated containers Discussion Costs comparison of scenarios Minimum and maximum number of kitchens Effect of capacity constraint on optimal cost Common kitchen locations opened Cost analysis when fixed cost is spread over first year and five years Limitations Future analysis and exploration Conclusion References Appendix A- Python code using Gurobi engine for Network design Appendix B- Python code using Gurobi engine for Network design with cross docking... 55

6 List of Figures Figure 1: Current supply chain process of Akshaya Patra... 8 Figure 2: Current kitchen locations of Akshaya Patra in UP state... 9 Figure 3: Growing demand of mid-day meals in UP. Source: Government agency; author analysis Figure 4: Roti making machine at Akshaya Patra. Source: Akshaya Patra website Figure 5: Gravity flow mechanism at Akshaya Patra. Source: Akshaya Patra website Figure 6: Centralized kitchen of Akshaya Patra. Source: Akshaya Patra website Figure 7: Honey comb pattern of delivery truck. Source: Akshaya Patra website Figure 8: Histogram of trucks required by block Figure 9: Map of kitchen locations opened in scenario Figure 10: Map of kitchen locations opened in scenario Figure 11: Map of kitchen locations opened in scenario Figure 12: Map of kitchen locations opened in scenario Figure 13: Supply chain process using cross docking sites Figure 14: Map of kitchen locations opened in scenario Figure 15: Map of kitchen locations opened in scenario Figure 16: Tradeoff between fixed cost and transportation cost Figure 17: Fixed cost and transportation costs analysis for five years... 43

7 List of Tables Table 1: Capacity of centralized kitchen Table 2: Kitchen locations of scenario Table 3: Kitchen locations of scenario Table 4: Kitchen locations of scenario Table 5: Kitchen locations of scenario Table 6: Kitchen locations of scenario Table 7: Total cost (in INR) of different scenarios Table 8: Total number of kitchens opened in different scenarios Table 9: Minimum number of kitchens opened due to capacity constraint Table 10: Common kitchen locations opened in all scenarios Table 11: First year cost analysis Table 12: Five years of cost analysis... 43

8 1. Introduction Akshaya Patra (AP) is a non-profit organization headquartered in Bangalore, India. In partnership with the Government of India and the state governments, it provides mid-day meals to government schools and government-aided schools. The motivation behind this cause is two-fold. First is to reduce the number of dropouts in the government schools. Children from poor financial backgrounds often choose to work and earn money to feed themselves and their families rather than going to school. Second is to fight against malnutrition, which affects children s mental and physical growth and causes poor academic performance. Akshaya Patra was started in 2000 with 1,500 children. Currently, it is serving meals to around 1.6 million children every day in 12 states with 26 centralized and two decentralized kitchens. A centralized kitchen has minimum cooking capacity of 100,000 meals whereas a decentralized kitchen can cook maximum 20,000 to 30,000 meals and especially located in rough terrain, which does not allow large scale operation. Akshaya Patra has the world s largest kitchen which can process 250,000 meals in five hours. Currently, Akshaya Patra serves around 200,000 meals per day in two cities of Uttar Pradesh (UP). In 2020, it aims to serve mid-day meals to five million children in India. This includes approximately 500,000 meals in UP. Akshaya Patra has two reasons to consider the design of its network. First, if the state government provides the opportunity to Akshaya Patra to serve all the government schools of UP state, then Akshaya Patra must create an optimal kitchen network (supply chain network) to serve the children. Second, as demand for meals increases in current serving locations, Akshaya Patra has to investigate various kitchen options to fulfill the growing 1

9 needs. A huge cost, minimum 10 million INR (Indian Rupee), is involved in construction of a centralized kitchen or increasing the efficiency of an existing kitchen. If the kitchen network design of Akshaya Patra is not optimal, then it will have high impact on transportation costs, cost of meal per plate, and the quality of food (fresh food should reach to schools within four hours of cooking otherwise food will get spoiled). Complaints about lower food quality or delay in meal delivery may lead Akshaya Patra to lose the contract with the state government. The objective of this project is to design a network of kitchens in UP to serve the maximum number of children with the lowest possible cost. 2. Literature Review This section reviews the literature from previous studies related to this project. This review includes: (1) perishability challenge in food industry, (2) supply chain network for food (cross docking, and direct delivery to customer), and (3) solving quantitative problems using optimization. The above mentioned studies are included in this literature review because they helped us to understand the challenges, constraints, production process, and supply chain network design in food industry. In addition, we also reviewed a case study by Harvard Business School on Akshaya Patra to understand the company s operation process and constant learning and improvement. 2.1 Perishability challenge in food industry Application of supply chain management principles for the delivery of a variety of standardized low-cost perishable food products for mass markets is a challenge. The supply chain of fresh and perishable foods is characterized by short product lives and fast transportation. 2

10 Many studies have been conducted on the perishability challenge faced by the food industry. Examples discussed are fruits, vegetables, grocery, yogurt, and meat. Perishability of raw materials or finished goods has huge impact on supply chain design and the ultimate success or failure of the company. Many times it determines a company s raw materials procurement process, inventory, production process, and supply chain network design. For instance, Akshaya Patra received complaints from schools that yogurt tasted sour. Aware that it had taken care to ensure that the time of transportation and vehicles would not allow the spoilage to occur, Akshaya Patra approached the curd supplier and determined that it was the quality of the curd that was leaving a bad taste. A new supplier remedied the problem (Upton, Ellis, Lucas, & Yamner, 2007). The challenge for companies in managing the supply chain of perishable foods is that the value of the product deteriorates significantly over time at rates that are highly dependent on the environment. Without proper maintenance and transportation, food may spoil quickly before use, making stakeholders responsible for avoidable cost (Amorim, & Zavanella, 2012). Temperature and humidity are key factors in this process (Blackburn & Scudder, 2009). The quality of perishable food products also decays rapidly during the delivery. Often, companies choose justin-time production and delivery strategies to fill orders to reduce loss caused by the deterioration of perishable goods (Govindan, Jafarian, Khodaverdi, & Kannan, 2014). It is important that perishable food must be delivered within allowable delivery time window. Despite all the strategic importance of perishability in the supply chain, its management is far from at a satisfactory level (Govindan et al., 2014). To avoid a large amount of waste due to perishability advance inventory systems, robust supply chain networks, and strong distribution systems are required. 3

11 2.2 Supply chain networks for food In recent years, cross docking attracted the attention of many supply chain professionals and academic researchers. Recently cross docking have been used in designing supply chain networks for the food industry and highly perishable products. Cross docking is increasingly used to reduce inventory holding and the time products spend in the supply chain. It is especially suitable for fresh produce distribution with a short shelf-life measured in days Cross docking A cross docking is where items are unloaded from inbound trucks and loaded into outbound trucks potentially with other items. The inbound vehicle arrives at the cross docking sites and is processed in the inbound area and unloaded. After unloading, the orders can be sent directly to the outbound area for loading or stored in the intermediate storage area while the orders wait to be consolidated and loaded. Based on departure time and consolidation decisions, the orders are loaded onto outbound vehicles for deliveries (Agustina, Lee, & Piplani, 2014). The advantage of cross docking is cost savings compared to traditional warehouses. Costs are saved on storage, inventory, transportation, and labor (Saddle Creek Corp., 2008). Although cross docking has been recognized as one of the most effective distribution methods and many studies has been conducted on this, there is a lack of research looking at distribution within time windows, product consolidation, inventory management, vehicle scheduling, and vehicle routing at the same time (Agustina et al., 2014). 4

12 2.2.2 Direct delivery to customers The traditional way of distribution is direct shipment and its use is dependent on the nature of the product. It is a method of delivering finished goods directly from a manufacturer to customers. In this process, information directly flows between manufacturer and customers. This option has both benefits and cost associated with it. Customer service and product quality are high. Nevertheless, manufacturers have to be much closer to customers and need to keep high level of inventories. Transportation and facility costs are high because of last mile delivery and large number of facilities. Many studies suggest various approaches to deal with perishability and delivery of perishable food products. However, we found no research focused on delivery of cooked food with a transportation time window of maximum four hours. 2.3 Solving quantitative aspects of the problem using optimization Because of the supply chain complexities and rich sets of quantitative data, mathematical optimization technology is the best way to sort through the various options, balance the trade-offs, determine the best locations for facilities, and support better decision making (Watson, Lewis, Cacioppi, & Jayaraman, 2012). Best locations for facilities decisions are often strategic in nature and involve large sums of capital. Also, the overall effectiveness of the facility location depends upon distance among facilities and customers demand sites as well as the efficiency of vehicle routes. For instance, schools that are close to each other allowed Akshaya Patra in more efficient delivery of meals and improved 5

13 transportation times by using centralized kitchen where as dispersed location of schools especially in rural area increased the time of delivery and transportation costs (Upton et al., 2007). Academic researchers and supply chain professionals showed interest in mixed integer linear programming (MILP) and suggested various solutions of network design problems using MILP. It is widely used to model and optimize a distribution network due to its ability to incorporate key elements of a supply chain problem including decision options, constraints, and objectives, and provide an optimal solution (Shapiro, 2001). In fact, a distribution center location problem is a classic application of MILP. Although the impact of perishability is high in food industry, MILP has been used often. For instance, MILP was used to schedule a yogurt production line (Doganis & Sarimveis, 2007). Similarly, MILP has been suggested for planning at an operational level in a meat packing plant (Albornoz, Gonzalez-Araya, Gripe, & Rodriguez, 2014). A network design problem involves making a trade-off among conflicting factors, the most typical pair being cost and service level. Problems in the real world often involve multiple trade-offs which can be both qualitative and quantitative (Pornnoparat, 2016). Further, it is impossible to predict the future conditions under which facilities will operate. However, it is important that developed model and solution algorithm should account for future uncertainty explicitly to identify the robust solution with respect to uncertainty (Current, Daskin, & Schilling, 2001). 3. Methodology In this section, we discussed the detailed design of the optimization model to determine the optimal network configuration of centralized kitchens of Akshaya Patra. This section includes model 6

14 design, current supply chain analysis, geographic scope of this project, model input, and model formulation. 3.1 Model design The goal of this project is to determine what would be the best possible network configuration such that total costs are minimized. The total cost includes setup costs of centralized kitchens and transportation costs incurred to the company. Given these objectives, including costs and constraints, MILP can be appropriately used to model our problems of interest. The model is intended to address the key question: what would be the optimal centralized kitchens network design of Akshaya Patra to serve all the government schools of UP? To approach the above mentioned problem, we designed a model and then tested various scenarios to get the optimal solution. Scenario 1: Network design without capacity constraint Scenario 2: Network design with capacity constraint Scenario 3: Network design with insulated containers (vessels that can keep the food hot and fresh for longer period of time) Scenario 4: Network design considering currently opened kitchens Scenario 5: Network design with Cross docking and capacity constraint Scenario 6: Network design with Cross docking and insulated containers 7

15 3.2 Current supply chain analysis Akshaya Patra s current supply chain consists of procurement of perishable raw materials like fruits, vegetables, etc. from local vendors one day before processing. The Government provides grains through the Food Corporation of India and the Food & Civil Supplies Corporation. The other raw materials are purchased from vendors. The raw materials are stored in a warehouse and used according to First In First Out method. The procurement system is an Enterprise Resource Planning system, which assists the inventory manager in maintaining a stock of raw materials. Quality of the food, its nutritional value, and taste are assessed in quality tasting. After quality tests, meals are packed in different size containers and loaded on trucks for delivery. Route optimization software is used to optimize the delivery capacity. Delivery is based on the limitation that cooked meals should be delivered within the four hours of cooking. Schools Schools Production Plant/Centralize Kitchen Schools Figure 1: Current supply chain process of Akshaya Patra 8

16 3.3 Geographic scope The defined geographic scope of this project is narrowed to the state of Uttar Pradesh (UP) in India. Two centralized kitchens, one in Lucknow and another one in Vrindavan, are fully functional and serve approximately 200,000 children in UP. The mathematical model used here to design the supply chain network can be replicated in other states by using regional data sets. Figure 2: Current kitchen locations of Akshaya Patra in UP state 3.4 Model input This section explains about the collected, cleaned and aggregated data incorporated into the model as cost, distance, and constraint parameters. 9

17 NUMBER OF CHILDREN (IN MILLIONS) Daily demand Daily demand of meals of Akshaya Patra in UP state is divided into districts and then cities and blocks (blocks are district subdivisions for rural areas consisting of a cluster of villages). Customer demand is fixed throughout the year unless UP state government requests Akshaya Patra to add new schools in the customer list during the year. At present, Akshaya Patra serves two districts (Mathura & Lucknow) in UP with two centralized kitchens: one in Vrindavan and another in Lucknow. The daily demand of Mathura and Lucknow districts are 120,000 and 91,000 respectively. The demand of Mathura is fulfilled from Vrindavan kitchen whereas Lucknow s demand is satisfied from Lucknow s kitchen. The expected demand for the mid-day meal program is growing rapidly. Therefore, if the UP state government offers Akshaya Patra to fulfill the demand of all government schools, then demand will increase tremendously for Akshaya Patra (Projected) YEARS Figure 3: Growing demand of mid-day meals in UP. Source: Government agency; author analysis 10

18 3.4.2 Centralized kitchen data Centralized kitchen capacity of Akshaya Patra depends mainly on size of the kitchens and the technologies used to speed up the cooking process. Advanced technology has played a vital role in food making process especially when millions of meals have to be prepared in span of few hours. For instance, a fully automated flat bread (roti) making machine (Figure 4) has the capacity to produce minimum 20,000 flat breads per hour. Another technology is gravity flow mechanism (Figure 5) used to transfer large quantities (20-25 tons) of grains and food from one floor to another in less than a minute. Both the technologies are used at Akshaya Patra s kitchens. Usually, Akshaya Patra s centralized kitchens have minimum cooking capacity of 100,000 meals within five hours. Figure 4: Roti making machine at Akshaya Patra. Source: Akshaya Patra website 11

19 Figure 5: Gravity flow mechanism at Akshaya Patra. Source: Akshaya Patra website Table 1: Capacity of centralized kitchen Centralized Kitchen Cooking Capacity (Number of meals) Minimum for centralized plant 100,000 Maximum for centralized plant 300, Setup cost data Setup costs are associated with the construction of a centralized kitchen and the purchase and installation of cooking equipment. It plays a crucial role in business and has an impact on strategic decisions such as whether to open kitchen or not. The setup cost of a centralized kitchen is a minimum of 10 million INR. 12

20 Figure 6: Centralized kitchen of Akshaya Patra. Source: Akshaya Patra website Decentralized kitchens are set up where terrain and infrastructure do not permit a centralized kitchen to operate. These are run by women Self-Help Groups under the training, guidance, and monitoring of Akshaya Patra. Set up cost of a decentralized kitchen is approximately 30,000 INR. In our model, we have spread the one time set up cost of 10 million INR in one year and five years (in some scenarios) to compare the network design configurations and their optimal costs Transportation data For Akshaya Patra, transportation costs are crucial and divided into two categories: inbound and outbound costs. Inbound transportation costs are incurred while moving raw materials from suppliers to the centralized kitchen. Akshaya Patra gets shipments of grains (wheat and rice) from the state government s warehouse on a monthly or quarterly basis. Perishable items like vegetables and other items are purchased every day from local market (within the radius of 5-7 kms of a kitchen) using one or two trucks. Because perishable items suppliers are closely located to Akshaya Patra, it incurs low inbound transportation costs and therefore not included in cost calculation. Outbound transportation costs are incurred due to moving finished goods or meals 13

21 from a centralized kitchen to schools or a centralized kitchen to a cross docking site and then to schools. Akshaya Patra incurs huge outbound transportation cost in UP (serving in other 11 states also). Average outbound transportation cost per kilometer is 13 INR for a mid-size truck and 15 INR for a large truck. Delivery time limitation is maximum 4 hours. Trucks for delivery are customized in honey-comb pattern to fit maximum number of containers. The customization cost is minimal, so we have not included it in our model. Containers delivered in morning are collected during return journey of delivery trucks. Figure 7: Honey comb pattern of delivery truck. Source: Akshaya Patra website Truck size Two truck sizes have been considered in this project. The first is a large truck which carries food from the kitchen to a cross docking site with a capacity of 9,000 kg (36,000 meals). The second is a mid-size truck with a carrying capacity of 900 kg (3,600 meals) which runs between cross docking sites to schools. We have checked the utilization of the mid-size delivery trucks. If a truck carries less than a full truck load, then it will have some slack capacity (underutilized truck). 14

22 Number of blocks Number of trucks Figure 8: Histogram of trucks required by block Figure 8 shows the number of trucks required by block. For instance, approximately 190 blocks require less than a full truckload for food delivery. Utilization of the trucks is almost normally distributed and median of number of trucks used by blocks is three. Further, we also analyzed that Akshaya Patra will need around 2927 mid-size trucks to make deliveries in UP state, if it doesn t share trucks between blocks. Out of the total number of required trucks, 63.4% (1902 trucks) are fully utilized and 36% trucks are underutilized. To mitigate the risk of underutilization of trucks routing optimization software can be used Cross docking data Cross docking is a practice of unloading materials from an incoming trucks and loading those materials directly into outbound trucks, trailers, or rail cars, with little or no storage in between. For Akshaya Patra, all major 66 cities in Uttar Pradesh are considered as cross docking sites. We 15

23 assumed that no fixed cost (land and labor) is involved in cross docking. Akshaya Patra can use empty government sites or playgrounds of public school as cross docking sites by taking permission from local authority. Furthermore, we assumed there is no storage of any kind of product or vehicle at cross docking sites at any point of time. It is just an empty site for loading and unloading of food containers Data cleaning Process of detecting, correcting or removing inaccurate records from record set. After data collection for our model, we found certain discrepancies in data especially mismatch between demand of blocks & districts and distance of blocks cities data set. We also found some errors in rural-urban division and typographical errors like name misprint etc. All the errors of data were removed and now cleaned data set of blocks and districts demands is consistent with distance of blocks-cities data set. 3.5 Model formulation In this section, we explained the formulation of the problem into mathematical model that takes the input data explained above and optimizes to achieve a network design aligned with our objectives. We have included following five elements of the model: objective, model parameters, decision variables, mathematical formulation, and optimization tool. 16

24 3.5.1 Objective The objective of this project is to design supply chain network of centralized kitchens for Akshaya Patra to minimize total cost. Thus, the objective function of the model is to minimize the transportation costs and the fixed cost of centralized kitchens Model parameters Following parameters have been created to include in model without cross docking based on the input described above. Blocks = {1, 2, 3, 4,, 10000}: for indexing the locations of blocks Cities = {1, 2, 3, 4,.., 66}: for indexing the locations for opening kitchens and cross docking sites a ik = Number of trucks (each of 3600 meals capacity) of meals going from kitchen at i to block at k i Cities, k Blocks u k = Number of meals demand that was unmet due to infeasibility at block k k Blocks s k = 300,000 meals: kitchen capacity per day s s = 3,600 meals: mid-size truck s carrying capacity t ik = Time (in minutes) needed to go from kitchen at i to block at k t max = Four hours is the maximum time (six hours when insulated containers are used) allowed for meals delivery to blocks after cooking Z = Total Cost of opening the kitchens and delivery cost (per day) FC K = Fixed cost of opening a kitchen 17

25 d ik = distance between kitchen at i to block at k j Cities, k Blocks c s = Cost per distance (km) per mid-size truck (3600 kg capacity) Penalty = INR 1,000,000, the cost of not serving one meal Parameters of a model with cross docking sites Blocks = {1, 2, 3, 4,, 10000}: for indexing the location of blocks Cities = {1, 2, 3, 4,..., 66}: for indexing the locations for opening kitchens and cross docking sites a ij = Number of trucks (each of 9000 kg capacity) of meals going from kitchen at i to cross docking sites at j i, j Cities b jk = Number of trucks (each of 900 kg capacity) of meals going from cross docking at j to block at k j Cities, k Blocks u k = Number of meals demand that was unmet due to infeasibility at block k k Blocks s k = 300,000 meals: kitchen capacity per day s b = 36,000 meals: large truck carrying capacity s s = 3,600 meals: mid-size truck carrying capacity d k = Demand for block at k t ij = Time (in minutes) needed to go from kitchen at i to cross docking sites at j t jk = Time (in minutes) needed to go from cross docking at j to block at k t CD = 30 minutes is the time needed to load and unload at cross docking sites 18

26 t max = Four hours is the maximum time (six hours when insulated containers are used) allowed for meals delivery at block Z = Total Cost of opening the kitchen & cross docking sites and delivery cost (per day) FC K = Fixed cost of opening a kitchen FC DC = Fixed cost of opening a cross dock site (in reality zero). Just to make sure the model does not open more than required, we have imposed a 66.5 INR cost as FC DC) d ij = Distance between kitchens i to cross docking at j i, j Cities d jk = Distance between cross docking at j to block at k j Cities, k Blocks c b = Cost per distance (km) per large truck (36,000 meals capacity) c s = Cost per distance (km) per mid-size truck (3,600 meals capacity) a ij = Number of trucks (each of 9000 kg capacity) of meals going from kitchen at i to cross docking at j i, j Cities b jk = Number of trucks (each of 900 kg capacity) of meals going from cross docking at j to block at k j Cities, k Blocks u k = Number of meals demand that was unmet due to infeasibility at block k k Blocks Decision variable It defines what we allow the optimization to choose from. In optimization of physical supply chain the main decisions include how much finished goods move from one location to another, how many plants are opened, and what product is made in which location. The decision variables are not separate from the constraints. Hence, based on our problem of interest, following decisions should be made by the model:- 19

27 Which locations are opened for the establishment of centralized kitchens? Which blocks and schools should be served from which centralized kitchens considering all the constraint? Assumptions Capacity of one centralized kitchen is 300,000 meals produced per day On average number of children per school is 50. Assumption made after analyzing data of number of children in 2008 in UP state No fixed cost involved in cross docking because empty government sites or playgrounds will be used Cost of large truck per kilometer is 15 INR Cost of mid-size truck per kilometer is 13 INR Transportation costs only depend on distance Inbound transportation cost is insignificant compare to outbound cost Delivery truck customization cost is negligible Large truck carrying capacity is assumed to be 9,000 kg (36,000 meals) and mid-size truck capacity is 900 kg (3,600 meals) per truck On average a child would consume 250 g of food Mathematical formulation without cross docking Objective function: Minimize Z = x i * FC K + i k a ik * d ik * c s * Penalty 20

28 Constraints: For making sure a flow is there only if the kitchen is opened w ik x i (1) Kitchen capacity constraint k a ik s k / s s (2) Kitchen flow binding constraint a ik M * w ik where M is a big number (3) Block demand constraint i a ik * s s d k k Blocks (4) Time constraint w ik * t ik t max i Cities, k Blocks (5) Variables: x i = {0, 1}: i Cities (1 if kitchen is opened in city i, 0 otherwise) w ik = {0, 1}: j Cities, k Blocks (1 if meal goes from kitchen at i to block at k) Mathematical formulation with cross docking Objective function: Minimize Z = x i * FC K + y j * FC DC + i j a ij * d ij * c b + j k b jk * d jk * c s + k u k * Penalty Constraints: For making sure a flow is there only if the kitchen is opened 21

29 w ij x i (1) For making sure a flow (inbound to cross docking sites) is there only if the cross docking site is opened w ij y j (2) For making sure a flow (outbound form cross docking sites) is there only if the cross docking site is opened z jk y j (3) Kitchen capacity constraint j a ij s k / s b (4) Kitchen flow binding constraint a ij M * w ij Where M is a big number (5) Cross docking flow (outbound) binding constraint b jk M * z jk Where M is a big number (6) Block demand constraint j b jk * s s d k k Blocks (7) Time constraint: If i j: w ij * t ij + z jk * t jk + t CD t max i, j Cities, k Blocks (8) else: z jk * t jk t max Cross docking flow conservation constraint: i a ij * s b = k b jk * s s (9) Kitchen and cross docking co-location constraint: 22

30 x i y j for i=j i, j Cities (10) Variables: x i = {0, 1} i Cities (1 if kitchen is opened in city i, 0 otherwise) y j = {0, 1} j Cities (1 if DC is opened in city at i, 0 otherwise) w ij = {0, 1} i, j Cities (1 if meal goes from kitchen at i to cross docking at j) z jk = {0, 1} j Cities, k Blocks (1 if meal goes from cross docking at j to block at k) Optimization tools Due to the large amount of data, the standard excel solver was not sufficient for modeling purposes. It is usually limited to 200 decision variable cell and would be very time consuming. Therefore, we have used Gurobi (mathematical programing solver) with Python for modeling a MILP to design kitchens network Cost components In the models, the total objective function is divided by the following cost components: Total cost of opening kitchens: 10 million INR upfront cost for opening one kitchen Total cost of opening cross docking sites (only applicable to models where cross docking is considered): 66.5 INR just to ensure the model does not open unnecessary cross dockings. Practically, the cross docking cost is assumed to be zero. Transport cost from kitchens to blocks: The daily cost of going from one kitchen to one block, multiplying the total number of trucks with distance and per small truck per distance cost. 23

31 Transport cost from kitchens to cross docking sites (only applicable to models where cross docking is considered): The daily cost of going from one kitchen to one DC, multiplying the total number of large trucks with distance and per large truck per distance cost. Transport cost from cross docking sites to blocks (only applicable to models where cross docking is considered): The daily cost of going from one cross docking to one block, multiplying the total number of small trucks with distance and per small truck per distance cost. Penalty cost: For not meeting demand in a block due to infeasibility. In the model, we considered a slack variable u[k] ( k refers to the block index number) to designate unmet demand for a block due to infeasibility. The objective function carries a substantially huge penalty: 66,500,000 INR which ensures the model minimizes the penalty and puts something as slack only if there is no other way left. This is an imaginary cost and we have subtracted the amount from the objective value to present the real cost to be incurred as per model generated result. 4. Results/Data Analysis In this section, we demonstrate our results based on the model formulated above. We describe optimization results for the network design of centralized kitchen under different scenarios. As mentioned already, we used Gurobi optimization engine through Python code (source is included in the appendix section) to get the result. 24

32 4.1 Scenario 1: Network design without capacity constraint In this scenario, the model considered a network where food is directly delivered from centralized kitchens to schools in mid-size trucks. However, we did not include the kitchens capacity constraint here. It may sound unusual, but we ran this optimization model to explore what happens when you have the option of Super Kitchens or Mega Kitchens with a very high cooking capacity. Under this scenario, our model recommends below listed 10 cities (Table 2) to open centralized kitchens to fulfill the total demand of UP state. Furthermore, it also shows the costs (fixed cost of kitchen plus transportation cost) required in this set up. It should be noted that we considered the usual fixed (opening) cost for centralized kitchen in this hypothetical scenario. In reality, for very high capacity kitchen, the fixed cost would be much higher due to the high level of automation. Table 2: Kitchen locations of scenario 1 Total Cost = 106,296,264 Fixed Cost = 100,000,000 Transportation Cost = 6,296,264 Kitchen Location Demand Fulfilled Kitchen Location Demand Fulfilled Barabanki 1,042,800 Jhansi 291,100 Basti 1,064,650 Mau 833,550 Etah 1,336,200 Meerut 965,900 Fatehpur 999,100 Shahjahanpur 987,200 Gorakhpur 16,700 Varanasi 888,750 25

33 Figure 9: Map of kitchen locations opened in scenario Scenario 2: Network design with capacity constraint In this scenario, we added a capacity constraint to the centralized kitchens. Adding constraints limits the model during optimization. This setting is more realistic and matches the current operational situation of Akshaya Patra. Maximum cooking capacity of kitchens used in this model is 300,000 meals (or eight full medium sized truck loads considering each truck can carry up to 3,600 meals) and delivery time window of four hours. Under this set up, our model selected 37 cities to fulfill the total demand of UP state. Table 3 shows the selected locations to open centralized kitchens and the number of meals to be served from those kitchens. We can notice that, adding the capacity constraints increased the total costs. 26

34 Table 3: Kitchen locations of scenario 2 Total Cost = 373,280,870 Fixed cost = 370,000,000 Transportation cost = 3,280,810 Kitchen Locations Demand Fulfilled Kitchen Locations Demand Fulfilled Kitchen Locations Demand Fulfilled Agra 214,500 Etawah 232,700 Mau 231,050 Allahabad 236,500 Faizabad 261,800 Meerut 219,450 Azamgarh 243,100 Farrukhabad 237,200 Moradabad 225,750 Bahraich 268,150 Fatehpur 239,650 Mughal Sarai 230,750 Ballia 226,900 Gonda 234,600 Orai 217,700 Banda 247,350 Gorakhpur 7,150 Raebareli 239,000 Barabanki 237,350 Hardoi 256,000 Shahjahanpur 240,450 Bareilly 271,250 Hathras 247,100 Shamli 193,100 Basti 249,350 Jaunpur 249,150 Sitapur 250,150 Bijnor 176,550 Jhansi 161,200 Sultanpur 237,750 Budaun 210,450 Kanpur 243,100 Tanda 245,750 Deoria 220,600 Khurja 229,750 Vindhyachal 239,850 Etah 253,750 27

35 Figure 10: Map of kitchen locations opened in scenario Scenario 3: Network design with insulated containers This scenario tested the impact of delivery time window on our network configuration while keeping the other variables constant. We included the insulated containers in our model in addition to the cooking capacity and delivery time window constraints. The purpose of using the insulated containers is two fold: first, it will allow for an increase in the delivery time window. Instead of four hours, Akshaya Patra can use a six hour delivery window which will help in reducing the number of centralized kitchens to be opened. Second, it will help in keeping the food fresh and 28

36 hot for longer period of time while maintaining its nutritional value. With this change, our model suggested opening 36 centralized kitchens to fulfill the total demand of UP state. Table 4: Kitchen locations of scenario 3 Total Cost = 364,590,560 Fixed cost = 360,000,000 Transportation cost = 4,590,560 Kitchen Locations Demand Fulfilled Kitchen Locations Demand Fulfilled Kitchen Locations Demand Fulfilled Agra 157,200 Faizabad 247,100 Mau 225,700 Akbarpur 228,600 Farrukhabad 227,800 Mughal Sarai 220,150 Allahabad 259,450 Fatehpur 244,300 Noida 185,300 Amroha 242,800 Firozabad 246,750 Orai 236,600 Bahraich 284,000 Ghazipur 242,500 Raebareli 252,700 Ballia 235,100 Hapur 224,050 Rampur 226,250 Banda 239,400 Hathras 245,300 Sahaswan 220,150 Barabanki 238,800 Jaunpur 248,300 Shahjahanpur 240,500 Basti 242,300 Jhansi 230,050 Sitapur 250,800 Bulandshahr 231,350 Kanpur 252,000 Sultanpur 227,250 Deoria 220,200 Kasganj 188,450 Ujhani 235,250 Lakhimpur Etah 251,050 Kheri 242,850 Vindhyachal 235,600 29

37 Figure 11: Map of kitchen locations opened in scenario Scenario 4: Network design considering currently opened kitchens In this scenario, we consider the centralized kitchens already opened in UP state. At present, Akshaya Patra has kitchens in Vrindavan and Lucknow. After running optimization for the above mentioned scenarios, we found that locations where kitchens are already present were not opened by the model. Meaning Vrindavan and Lucknow were not chosen by the model. Since it is unlikely that Akshaya Patra would close its currently opened kitchens, we forced our model to open the current kitchen locations: Mathura (the city where Vrindavan is located) and Lucknow. In this scenario, in addition to forcing the model to open the current kitchen locations, we included capacity constraint and delivery time window of four hours. With this change, our model suggested 30

38 opening 37 centralized kitchens to fulfill the total demand. Similar number of kitchens is opened in scenario 2 but transportation cost of scenario 4 (3,297,892 INR) is very high compare to scenario 2 (3,280,810 INR). Table 5: Kitchen locations of scenario 4 Total Cost = 373,297,892 Fixed cost = 370,000,000 Transportation cost = 3,297,892 Kitchen Locations Demand Fulfilled Kitchen Locations Demand Fulfilled Kitchen Locations Demand Fulfilled Allahabad 246,700 Gonda 251,200 Shahjahanpur 240,450 Azamgarh 244,500 Gorakhpur 11,150 Shamli 193,100 Bahraich 263,300 Hardoi 243,750 Sitapur 236,300 Ballia 226,900 Jaunpur 243,600 Sultanpur 237,250 Banda 247,350 Jhansi 150,800 Tanda 245,750 Bareilly 271,250 Kanpur 243,100 Vindhyachal 233,550 Basti 249,350 Khurja 238,500 Moradabad 225,750 Bijnor 183,050 Lucknow 252,950 Mughal Sarai 242,600 Budaun 188,650 Mathura 224,350 Orai 215,200 Deoria 219,650 Faizabad 254,750 Mau 230,600 Etah 246,150 Farrukhabad 235,500 Meerut 223,900 Etawah 246,950 Fatehpur 239,650 Raebareli 238,750 Firozabad 239,650 31

39 Figure 12: Map of kitchen locations opened in scenario Scenario 5: Network design with cross docking and capacity constraint In this scenario, we incorporated cross docking in our model. Cross docking helps to reduce both transportation costs and the fixed cost of kitchens However, it also reduces the delivery time window by half an hour (time needed to cross dock). Food comes from centralized kitchens to cross docking sites and then delivered from there to blocks (demand of schools are clubbed into blocks). At cross docking sites, containers are unloaded from large trucks and loaded in mid-size trucks for delivery. Due to this loading/unloading at cross docking sites, delivery time window decreases by half an hour. 32

40 Now in transportation, we have two different types of cost: one for long hauls and another for short hauls. Further, two different sizes of trucks are used: one with carrying capacity of 9000 kg (~ 36,000 meals) and another one with capacity of 900 kg (~3,600 meals). Block Block Centralized Kitchen Delivery in large truck with capacity 9000 kg Cross docking Point (loading/unloading zone) Figure 13: Supply chain process using cross docking sites Block Block Block Food delivery to blocks and then schools in mid-size truck with capacity 900 kg In the formulation, we forced a cross docking facility to be opened in a city whenever a kitchen is opened in that city. This is done to ensure that the nearby blocks be served from that kitchen directly. We assume both the distance and time to reach from the kitchen to a cross dock facility in the same city to be zero. In reality, the cross docking can be held in an open area without any costly facility. In this scenario, the model opens 38 kitchens and 65 cross docking sites (Table 6). 33

41 Table 6: Kitchen locations of scenario 5 Total Cost = 382,969,716 Fixed cost = 380,000,000 Transportation cost = 2,969,716 (Kitchens to Cross dock transportation cost = 137,302 + Cross dock to Blocks transportation cost = 2,832,414) Kitchen locations Demand fulfilled Kitchen locations Demand fulfilled Kitchen locations Demand fulfilled Allahabad 236,383 Fatehpur 243,560 Moradabad 212,117 Azamgarh 230,550 Firozabad 224,333 Mughal Sarai 219,150 Bahraich 246,910 Gonda 244,600 Raebareli 234,807 Ballia 224,883 Gorakhpur 7,150 Sambhal 179,533 Banda 234,025 Hardoi 231,903 Shahjahanpur 242,671 Bareilly 246,250 Jaunpur 236,050 Shamli 179,700 Basti 232,850 Jhansi 230,125 Sultanpur 238,883 Bijnor 170,800 Kanpur 225,206 Tanda 237,917 Deoria 220,150 Khurja 244,050 Ujhani 210,138 Etah 236,429 Lakhimpur Kheri 238,191 Unnao 244,505 Etawah 223,108 Mathura 217,417 Varanasi 224,133 Faizabad 238,558 Mau 226,683 Vindhyachal 236,417 Farrukhabad 231,014 Modinagar 216,000 It is important to note that the model does not serve one block in this setup due to the tighter time constraint. The block is 'Sonbhadra Nagawa' and the nearest city from this block is 'Mughal Sarai' (164 km or 3 hours and 47 minutes away). The demand of this block is 8,800 meals, which is not fulfilled. This indicates that to meet the demand of all blocks is not feasible under this setup. 34

42 Figure 14: Map of kitchen locations opened in scenario Scenario 6: Network design with cross docking and insulated containers This scenario is similar to scenario 5, but with insulated containers meaning a six hours of delivery window instead of four hours. Table 7 summarizes the result of this scenario where the model opens 37 kitchens and 64 cross docking facilities. Unlike scenario 5, which does not serve the demand of Sonbhadra Nagawa, scenario 6 fulfills all the demand due to increase in delivery time. 35

43 Table 7: Kitchen locations of scenario 6 Total Cost = 372,763,304 Fixed cost = 370,000,000 Transportation cost = 2,763,304 ( Kitchen to cross docking = 137,302 + cross docking to Blocks transportation cost = 2,605,356) Kitchen Locations Demand fulfilled Kitchen Locations Demand fulfilled Kitchen Locations Demand fulfilled Agra 217,200 Etawah 226,346 Orai 213,233 Aligarh 235,175 Faizabad 238,371 Raebareli 236,200 Allahabad 236,889 Farrukhabad 229,500 Shahjahanpur 238,703 Amroha 207,209 Fatehpur 240,733 Shamli 186,850 Azamgarh 231,956 Ghazipur 188,446 Shikohabad 243,467 Bahraich 246,750 Gonda 239,067 Sitapur 243,837 Ballia 226,797 Hapur 226,996 Sultanpur 239,300 Banda 234,267 Hardoi 231,110 Tanda 236,785 Barabanki 233,600 Jaunpur 233,760 Ujhani 216,250 Bareilly 243,450 Jhansi 187,854 Unnao 242,950 Basti 234,171 Mau 222,128 Vindhyachal 235,994 Bijnor 207,733 Mughal Sarai 226,660 Moradabad 228,487 Deoria 217,725 36

44 Figure 15: Map of kitchen locations opened in scenario 6 5. Discussion This section explores the patterns found in the result section. We discuss the costs comparison of above mentioned scenarios, minimum and maximum number of kitchens analysis, common locations opened in all scenarios, first year cost analysis, five years cost projection, limitations of this research, and suggest some potential future analysis and exploration. 5.1 Costs comparison of scenarios For the total cost calculation, we included the fixed cost of opening kitchen and the transportation costs. Operational or any other cost have not been included in total optimal cost. When comparing the costs of the scenarios, network design without constraint (scenario 1) has the highest cost. Due to the lack of capacity constraint, the model suggests ten kitchens to cook until 37

45 the demand of blocks, which are in four hours radius from a kitchen, is fulfilled. It makes this option of network design bit unrealistic. However, this network design helps in analyzing the option of Mega kitchens. With the advancement of technology and increase in operational efficiencies, Mega kitchens can be implemented in future. We further noted that insulated containers with cross docking (scenario 6) gives the lowest optimal cost while fulfilling all the constraints (capacity as well as delivery window). When we compared the one year cost of scenario 2, (current operation style of Akshaya Patra) with scenario 6, it saves 116 million INR over scenario 2. The costs of scenarios 2 and 4 are almost the same because 37 centralized kitchens are opened in both the scenarios. Hence, fixed cost is same and there is not much difference in transportation costs of these two scenarios. Difference between transportation cost of scenarios 2 and 4 is 0.38 million INR. Scenario 4 has slightly higher transportation cost. To calculate the transportation cost over a year, we multiplied the daily transportation cost by 225 as an average of the total number of school days in a year suggested by The national Curriculum Framework of India (Ullas, 2012). 38