2. Here, from the above network model the red nodes represents both factory and warehouse, blue nodes represents only warehouse.
3. Thus the following methods were used to forecast the minimum cost for the transportation.
4.
5. Vacuum cleaner (CASE-2).August Inventory forecasting for Water Purifiers Aquasure 3ltrsCityBilled for JulyInventory for AugustJuly InventoryTotal requiredBangalore28509981503698Hyderabad27639671693561Chennai2550892173425Mumbai24408542553039Delhi2750962323680Kolkata1650577752152August Inventory forecasting for Water Purifiers Aquasure 5ltrsCityBilled for JulyInventory for AugustJuly InventoryTotal requiredBangalore1650577132214Hyderabad14264991321793Chennai1520532232029Mumbai2050717212746Delhi17506121422220Kolkata900315121203August Inventory forecasting for Vacuum Cleaners Trendy SteelCityBilled for JulyInventory for AugustJuly InventoryTotal requiredBangalore1225428321621Hyderabad1060371451386Chennai1063372621373Mumbai1438503421899Delhi12454351341546Kolkata9233231341112August Inventory forecasting for Vacuum Cleaners Trendy XeonCityBilled for JulyInventory for AugustJuly InventoryTotal requiredBangalore1065372321405Hyderabad895313451163Chennai890311621139Mumbai1200420421578Delhi10003501341216Kolkata8763061341048<br />ExpectedWarehouse CapacityWPVCTotalActual CapacityBangalore59123026893810000Hyderabad5354254979039000Chennai5454251279669000Mumbai57853477926210000Delhi5900276286629000Kolkata3355216055157000<br />CASE-1:<br />In this case only BANGALORE, HYDERABAD and BHIMTAL are the only factories who are producing the WATER PURIFIERS and those units have to be transported from different factories to different warehouses in the country.<br />Thus the following is the transportation model:<br />HYDERABADBANGALOREBANGALOREBHIMTALMUMBAICHENNAIHYDERABADDELHIKOLKATAWATER PURIFIER TRANSPROTATION MODEL<br />Particulars(in Rs)WAREHOUSESBangaloreHyderabadChennaiMumbaiDelhiKolkataFACTORYBangalore04351011.6Hyderabad405599Bhimtal11.210121039<br />DECISION VARIABLE:<br />The decision variables are the units and the cost per unit which is going to give cost estimation, are as follows:<br />OBJECTIVE FUNCTION:<br />This function is going to give the minimized cost of the transportation:<br />0*X11 + 4*X12 + 3*X13 + 5*X14 + 10*X15 + 11.6*X16 + 4*X21 + 0*X22 + 5*X23 + 5*X24 + 9*X25 + 9*X26 + 11.2*X31 + 10*X32 + 12*X33 + 10*X34 + 3*X35 + 9*X36<br />CONSTARINTS:<br />SUPPLY CONSTRAINTS:<br />0*X11 + 4*X12 + 3*X13 + 5*X14 + 10*X15 + 11.6*X16 <= 11000.<br />4*X21 + 0*X22 + 5*X23 + 5*X24 + 9*X25 + 9*X26 <= 11000.<br />11.2*X31 + 10*X32 + 12*X33 + 10*X34 +3*X35 + 9*X36 <= 11000.<br />DEMAND CONSTRAINTS:<br />0*X11 + 4*X21 + 11.2*X31 = 5912.<br />4*X12 + 0*X22 + 10*X32 = 5354.<br />3*X13 + 5*X23 + 12*X33 = 5454.<br />5*X14 + 5*X24 + 10*X34 = 5785.<br />10*X15 + 9*X25 + 3*X35 = 5900.<br />11.6*X16 + 9*X26 + 9*X36 = 3355.<br />USING EXCEL THE ANSWER REPORT IS AS FOLLOWS:<br />Microsoft Excel 12.0 Answer ReportWorksheet: [Inventory2.xlsx]Sheet6Report Created: 12/7/2009 11:42:08 AMTarget Cell (Min)CellNameOriginal ValueFinal Value$B$22OBJECTIVE FUNCTION X113176031760Adjustable CellsCellNameOriginal ValueFinal Value$B$5X1100$C$5X12660$D$5X1300$E$5X14481157$F$5X15590522$G$5X162890$H$5X21066$I$5X2200$J$5X2310911091$K$5X2411090$L$5X25076$M$5X260373$N$5X31422403$O$5X32509535$P$5X3300$Q$5X3400$R$5X3500$S$5X3600ConstraintsCellNameCell ValueFormulaStatusSlack$B$10SUPPLY CONSTTRAINTS X1111000$B$10<=$D$10Binding0$B$11X119760$B$11<=$D$11Not Binding1240$B$12X1111000$B$12<=$D$12Binding0$B$14DEMAND CONTRAINTS X115912$B$14=$D$14Not Binding0$B$15X115354$B$15=$D$15Not Binding0$B$16X115454$B$16=$D$16Not Binding0$B$17X115785$B$17=$D$17Not Binding0$B$18X115900$B$18=$D$18Not Binding0$B$19X113355$B$19=$D$19Not Binding0Microsoft Excel 12.0 Sensitivity ReportWorksheet: [Inventory2.xlsx]Sheet6Report Created: 12/7/2009 11:42:08 AMAdjustable Cells FinalReducedObjectiveAllowableAllowableCellNameValueCostCoefficientIncreaseDecrease$B$5X110001E+300$C$5X120041E+300$D$5X130031E+300$E$5X14115704.99999999901E+30$F$5X1552201000$G$5X160011.61E+300$H$5X21660400$I$5X220001E+300$J$5X2310910501E+30$K$5X240051E+300$L$5X257608.99999999800$M$5X2637308.99999999801E+30$N$5X3140301400$O$5X3253501001E+30$P$5X3300121E+300$Q$5X34009.9999999981E+300$R$5X350031E+300$S$5X36008.9999999981E+300Constraints FinalShadowConstraintAllowableAllowableCellNameValuePriceR.H. SideIncreaseDecrease$B$10SUPPLY CONSTTRAINTS X1111000011000684.99999981240$B$11X1197600110001E+301240$B$12X11110000110002661240$B$14DEMAND CONTRAINTS X115912159121240266$B$15X115354153541240266$B$16X1154541545412405454$B$17X115785157851240684.9999998$B$18X115900159001240684.9999998$B$19X1133551335512403355<br />Microsoft Excel 12.0 Limits ReportWorksheet: [Inventory2.xlsx]Limits Report 1Report Created: 12/7/2009 11:42:09 AM Target CellNameValue$B$22OBJECTIVE FUNCTION X1131760 Adjustable LowerTargetUpperTargetCellNameValueLimitResultLimitResult$B$5X110#N/A#N/A#N/A#N/A$C$5X120#N/A#N/A#N/A#N/A$D$5X130#N/A#N/A#N/A#N/A$E$5X141157#N/A#N/A#N/A#N/A$F$5X15522#N/A#N/A#N/A#N/A$G$5X160#N/A#N/A#N/A#N/A$H$5X2166#N/A#N/A#N/A#N/A$I$5X220#N/A#N/A#N/A#N/A$J$5X231091#N/A#N/A#N/A#N/A$K$5X240#N/A#N/A#N/A#N/A$L$5X2576#N/A#N/A#N/A#N/A$M$5X26373#N/A#N/A#N/A#N/A$N$5X31403#N/A#N/A#N/A#N/A$O$5X32535#N/A#N/A#N/A#N/A$P$5X330#N/A#N/A#N/A#N/A$Q$5X340#N/A#N/A#N/A#N/A$R$5X350#N/A#N/A#N/A#N/A$S$5X360#N/A#N/A#N/A#N/A<br />Thus the above are the excel reports where the minimized cost is 16486.<br />CASE-2:<br />In this case only two factories BHIMTAL and CHENNAI produce the VACUUM CLEANERS.<br />Thus the transportation model is as follows:<br />BANGALORECHENNAIBHIMTALMUMBAICHENNAIHYDERABADDELHIKOLKATAVACUUM CLEANER TRANSPORTATION MODEL<br />Particulars(in Rs)WAREHOUSESBangaloreHyderabadChennaiMumbaiDelhiKolkataFACTORYBhimtal1412.51512.53.7511.25Chennai3.756.25010.516.2516.25<br />DECISION VARIABLES:<br />In this the decision variables are the units and also the cost incurred to transport those units.<br />OBJECTIVE FUNCTION:<br />The objective function gives the minimized cost.<br />14*X11 + 12.5*X12 + 15*X13 + 12.5*X14+ 3.75*X15 + 11.25*X16 + 3.75*X21 + 6.25*X22 + 0*X23 + 10.5*X24 + 16.25*X25 + 16.25*X26<br />CONSTRAINTS:<br />SUPPLY CONSTARINTS:<br />14*X11 + 12.5*X12 + 15*X13 + 12.5*X14+ 3.75*X15 + 11.25*X16 <= 10000.<br />3.75*X21 + 6.25*X22 + 0*X23 + 10.5*X24 + 16.25*X25 + 16.25*X26 <= 10000.<br />DEMAND CONSTRAINTS:<br />14*X11 + 3.75*X21 = 3026.<br />12.5*X12 +6.25*X22 = 2549.<br />15*X13 + 0*X23 = 2512.<br />12.5*X14 + 10.5*X24 = 3477.<br />3.75*X15 + 16.25*X25 = 2762.<br />11.25*X16 + 16.25*X26 = 2160.<br />USING THE EXCEL THE REPORTS:<br />Microsoft Excel 12.0 Answer ReportWorksheet: [Inventory1.xlsx]Sheet5Report Created: 12/7/2009 11:29:36 AMTarget Cell (Min)CellNameOriginal ValueFinal Value$B$22OBJECTIVE FUNCTION x111648616486Adjustable CellsCellNameOriginal ValueFinal Value$B$5x1100$C$5x1200$D$5x1300$E$5x1400$F$5x15169.97169.97$G$5x16132.92132.92$H$5x21216.14216.14$I$5x22203.92203.92$J$5x23167.47167.47$K$5x24278.16278.16$L$5x2500$M$5x2600ConstraintsCellNameCell ValueFormulaStatusSlack$B$11SUPPLY CONSTRAINTS x1153$B$11<=$D$11Not Binding9947$B$12x1169$B$12<=$D$12Not Binding9931$B$15DEMAND CONSTRAINTS x113026$B$15=$D$15Not Binding0$B$16x112549$B$16=$D$16Not Binding0$B$17x112512$B$17=$D$17Not Binding0$B$18x113477$B$18=$D$18Not Binding0$B$19x112762$B$19=$D$19Not Binding0$B$20x112160$B$20=$D$20Not Binding0<br />Microsoft Excel 12.0 Sensitivity ReportWorksheet: [Inventory1.xlsx]Sheet5Report Created: 12/7/2009 11:29:36 AMAdjustable Cells FinalReducedObjectiveAllowableAllowableCellNameValueCostCoefficientIncreaseDecrease$B$5x11003.751E+300$C$5x12006.2500000021E+300$D$5x130001E+300$E$5x140010.51E+300$F$5x15169.9692308016.2501E+30$G$5x16132.9230769016.2501E+30$H$5x21216.142857101401E+30$I$5x22203.92012.501E+30$J$5x23167.46666670151E+301E+30$K$5x24278.16012.501E+30$L$5x25003.751E+300$M$5x260011.251E+300Constraints FinalShadowConstraintAllowableAllowableCellNameValuePriceR.H. SideIncreaseDecrease$B$11SUPPLY CONSTRAINTS x11530100001E+309947$B$12x11690100001E+309931$B$15DEMAND CONSTRAINTS x113026130261E+303026$B$16x112549125491E+302549$B$17x112512125121E+302512$B$18x113477134771E+303477$B$19x112762127621E+302762$B$20x112160121601E+302160<br />Microsoft Excel 12.0 Limits ReportWorksheet: [Inventory1.xlsx]Limits Report 1Report Created: 12/7/2009 11:29:36 AM Target CellNameValue$B$22OBJECTIVE FUNCTION x1116486 Adjustable LowerTargetUpperTargetCellNameValueLimitResultLimitResult$B$5x110016486016486$C$5x120016486016486$D$5x130016486#N/A#N/A$E$5x140-4.33093E-1416486-4.33093E-1416486$F$5x15169.9692308169.969230816486169.969230816486$G$5x16132.9230769132.923076916486132.923076916486$H$5x21216.1428571216.142857116486216.142857116486$I$5x22203.92203.9216486203.9216486$J$5x23167.4666667167.466666716486167.466666716486$K$5x24278.16278.1616486278.1616486$L$5x250016486016486$M$5x260016486016486<br />CONCLUSION:<br />Thus from the above analysis this is to say that the cost occurred to transport the WATER PURIFIER and VACUUM CLEANERS are 31760 and 16486. <br />
![BUSINESS MODELAn end term project on operations Research Submitted to: Prof. Raju Gundala.Members of group –Fahim- 20, Vijay – 25, Ranjan-41, Rosh-44, Anoop-57PGBM-IB (2009-11), Section-c, Term - 2<br />ACKNOWLEDGEMENT<br />First we would like to extend our gratitude to our faculty Prof. Raju Gundala for supervising and guiding us throughout the various stages of our project.<br />We thank one and all who have helped in making key decisions and held discussions which helped us to complete this project successfully in time.<br />Last but not least we would like to thank our families for extending their support.<br />This project is not the Endeavour of any one individual, but is the result of valuable time, effort and co-operation of one and all of us. So, we would like to acknowledge each other for a great teamwork, Thank You. <br />Members of group – <br />Fahim- 20<br />Vijay – 25<br />Ranjan-41<br />Rosh-44<br />Anoop-57<br />Introduction<br />In this paper, we solve a transportation problem which is a real time problem at Eureka Forbes. In which n vehicles, (of given capacity) are routed in real time in a fast varying environment to deliver m Products. When both n and m are big from different locations to meet the demand according to supply. The aim is to minimize the cost. Therefore, the formulation has to take in to account the cumulative Cost incurred.<br />Due to the optimization being based on the product cost functions as opposed to being driven by cost window constrains as used in package delivery optimization, this problem is fundamentally done because at Eureka Forbes Ltd., the billing would be more at the Last date of the Month. For an example, if the monthly sales are around Rs 1 crore then almost Rs 65 lacks worth of billing is done on the last date of the month, which mean almost 65% of supply is billed on that day but not delivered, and the time available is approximately within 3 days to deliver the products to retailers from the date of Billing. As Eureka Forbes Ltd., uses SAP (ERP), so the time take to virtually transfer the Products from one warehouse to another warehouse would take less than 15min. The interesting fact is that the warehouses are located at all the major cities across India and one for every state. This Business model is focused mainly on such a procedure, since it represents the most difficult piece of the Cost minimization which in turn help the company to maximize the profits and improve the customer relation.<br />The speed required to attain a solution strongly depends on the specific type of problem. For instance, it is not necessary for a truck company (performing interstate services) to have a transportation model that attains the solution in 5 seconds to route their vehicles. This issue is particularly important, and it is clear that the computational speed needed to reach a solution of a given problem depends on the time scale and of course cost incurred.<br />The problem treated is stochastic in nature, both in terms of network conditions and in future occurrence of demand points. A possible way to tackle the entire problem would be to solve it in Network model. The importance of network models for many business problems lend themselves to a network formulation. Optimal solutions of network problems are guaranteed integer solutions, because of special mathematical structures. No special restrictions are needed to ensure integrality. Network problems can be efficiently solved by compact algorithms due to their special mathematical structure, even for large scale models. <br />can be efficiently solved by compact algorithms due to their special mathematical structure, even for large scale models. <br />Problem Definition<br />At Eureka Forbes Ltd., there are two manufacturing plants, one for Aquasure Water purifier which is manufactured by Aquamall water solutions ltd., a 100% fully owned subsidiary of Eureka Forbes ltd. Aquamall have three manufacturing houses which are located at Bangalore, Hyderabad, and Bhimtal (Uttaranchal), which have a capacity of 11 thousand units per month of water purifier from each manufacturing house. The manufactured water purifiers would then be transported to various regional warehouse and finally to the Retail outlets. On the other side Aquamall water solutions ltd’s have 100% fully own subsidy, Forbes Aquamall Ltd. (FAML) have 2 units set up at Bhimtal in Uttaranchal and at Chennai in Tamil Nadu for manufacturing Vacuum Cleaners, with a current capacity of manufacturing 10 thousand units of vacuum cleaners per month, which are then transported to various regional warehouses and finally to retail outlets.<br />Due to the economic condition and the competition from all the major consumer durable companies, Eureka Forbes ltd., want to minimize the transportation cost and the time taken to deliver so it can compete with the competitors, Below table gives the current inventory at different warehouses, and for the month of August 35% of the July billed inventory is forecasted.<br />Inventory as on 01-08-2009 at 00:00amWater purifiersVacuum CleanersCityAquasure 3ltrsAquasure 5ltrsTrendy SteelTrendy XeonBangalore150133222Hyderabad1691324524Chennai17236254Mumbai255214212Delhi32142134134Ahmadabad 63176223Kolkata 75121340Total761519451269<br />Below is the table for the Inventory billed on 31-07-2009<br />Inventory Billed on 31-07-2009 Water purifiersVacuum CleanersCityAquasure 3ltrsAquasure 5 ltrsTrendy SteelTrendy XeonBangalore2850164012251065Hyderabad276314261060895Chennai255015201063890Mumbai3440205014381200Delhi2750175012451000Kolkata 1650900923876Total16003928669545926<br />Below is the table which shows the transportation cost from different factories to different warehouses per truck:<br />Particulars(in Rs)FactoriesBangaloreHyderabadChennaiMumbaiDelhiKolkataWarehousesBangalore02000015000250005000058000Hyderabad20000025000250004500045000Bhimtal560005000060000500001500045000Chennai15000250000420006500065000<br />Each truck have a capacity of 5000units of water purifiers or 4000units of Vacuum cleaner or 2500 units of Water purifier &2000units of Vacuum cleaner.<br />PROBLEM OBJECTIVE:<br />Minimizing the total shipping cost of supplying the destinations with the required demand from the available supplies at the sources (warehouses).<br />centercenter<br />APPROACH:<br />,[object Object]](https://image.slidesharecdn.com/finalreportor-100823133234-phpapp02/85/Transportation-Model-1-320.jpg)
