UPS Virginia District Package Car Fleet Optimization

Transcription

1 UPS Viginia Distit Pakage Ca Fleet Otimization Tavis Manning, Divaka Mehta, Stehen Sheae, Malloy Soldne, and Bian Togesen Abstat United Pael Sevie (UPS) is onstantly haged with ealigning its akage a fleet to aommodate the vaying volume of akages duing diffeent times of the yea. Fatos involved in detemining fleet alignments inlude akage volume on a given oute, total distane of a oute, and if a akage a s engine tye is suoted at a atiula ente. The goal of this ojet was to otimally distibute the UPS fleet in the Viginia distit aoding to two diffeent iteia: minimizing fuel onsumtion and maximizing like vehiles at a given ente. Intege ogams wee fomulated fo eah of these altenatives based on the data ovided by UPS. The two intege ogams allow UPS to use histoial data fo a given season to ealign the fleet seasonally with the intent of eduing ost. I. PROBLEM STATEMENT The Viginia distit of UPS is omised of 23 entes with ove 1300 akage a outes to ovide ustomes with thei akages in a timely manne. These outes vay in thei distanes, volume of akages, and ente loations. Duing diffeent seasons of the yea, these outes flutuate in the volume of akages and the miles taveled due to ineasing and deeasing demand. Fo examle, thee is a muh highe volume of akages to be deliveed duing the holiday season in Deembe than in the evious months. In ode to aommodate all outes, UPS has to ealign its akage a fleet of aoximately 1100 vehiles aoss all 23 entes in the Viginia distit to ensue all demand an be met. Pakage as vay in thei make, model, aaity, and miles e gallon atings. Cetain entes in Viginia an only suot seifi makes and models of akage as due to the availability of ats fo maintenane and eai in thei loation. Fo examle, the Lynhbug ente an only suot akage as made by Intenational. Any othe make o model at the Lynhbug ente equies ats to be shied in with high shiing osts and long delays. Eah tuk has a ooate ating fo its miles e gallon atings and aaity. The oblem addessed in the equest fo oosal by UPS was oviding them with two diffeent akage a fleet alignments based otimizing two diffeent senaios. The fist senaio is minimizing fuel onsumtion. This senaio aims at eduing the ost of fuel fo the Viginia distit. The seond senaio is keeing like vehiles togethe by ente and division. This senaio is aimed at aligning the fleet in suh a manne that akage as ae assigned to entes that an suot thei make and model without high shiing osts and long delays on eais and maintenane. The equest fo oosal equies akage a fleet ealignments fo both senaios. The gou also deided to ovide UPS with standad oeating oedues fo eliating the esults. This would allow UPS to un both models on diffeent seasonal data to find otimal fleet alignments duing diffeent seasons of the yea. II. DATA COLLECTION & ANALYSIS All data fo akage as and entes was ovided by UPS. The data ovided an be lassified into two ategoies, vaiable and fixed data. Vaiable data was given fo the outes fo the miles e oute and the numbe of akages e oute. This data was given fo two months out of the yea. The fixed data efleted ooate standads fo the akage as, suh as miles e gallon atings, akage a aaities, and whih vehile makes and models wee suoted at whih entes. The vaiable data, whih is used to haateized outes, had to be teated befoe any modeling ould be omleted. The data fo the numbe of miles and numbe of akages deliveies and ikus on eah oute is eoded by the dives. Sine this data is eoded by dives on handhelds at the end of eah day the data is only as auate as the dive inuts it. This led to two diffeent tyes of oblemati enties. The fist ase had two seaate enties fo a oute with the same mileage, one enty with a numbe fo deliveies and zeo fo the ikus and anothe enty with zeo fo the deliveies and a numbe fo the ikus. The seond ase had miles that wee eithe negative, zeo, o extemely high. The fist ase was esolved by using a mao in Miosoft Exel that ombined onseutive enties with zeos fo eithe ikus o deliveies. The seond ase was esolved using a mao in Exel that deleted enties that wee outside of a given ange. The ange of aetable enties was geate than 0 and less than o equal to 240 miles. The ue limit of 240 miles was detemined based on a maximum oute distane of 120 miles fo any akage a in the Viginia distit. This numbe was doubled to allow akage as to delive to two outes on a given day, a ommon atie at UPS. Afte teating the data to emove all outlies and unealisti oints, it was aveaged ove the two month eiod to find 1324 outes and thei esetive aveage miles and numbe of akages. The fixed data fo the ojet ovided infomation about the akage as, akages, and entes. Miles e gallon atings and aaity atings wee ovided fo all akage as based on UPS ooate standads. In onveting the numbe of akages on a given oute into a volume to omae it with akage a aaity atings thee was the need fo selet an aveage akage size. Initially this was suosed to be obtained though ube audits. Cube audits

2 involved totaling the numbe of akages in a given akage a and detemining the eentage of aaity used by the vehiles fo those akages. Using the numbe of akages, the eentage of aaity and the volume size fo the tuk an estimate fo aveage akage size an be detemined afte eeated ube audits. Due to omliations ube audits wee neve omleted UPS ovided an aveage akage size of fou ubi feet. Afte omaing this value with the numbe of akage as it was detemined a lage numbe of outes would have volumes of akages too lage to be aommodated by any of the akage as in the UPS fleet. The value of fou ubi feet was eassessed and it was edued to two and a half ubi feet to onside akages that ouy atially no volume, suh as enveloes. Often akage as ae equied to ay hundeds of enveloes whih ouy minimal volume in thei akage a. Afte this aveage akage a volume was used to detemine oute aaities the volume of outes with volumes ove 1100 ubi feet wee edued by 20 eent to aount fo outes with a high numbe of enveloes. These modifiations eliminated all issues involving akage a aaity. The final sets of data gave infomation on the 23 entes in the Viginia distit. A table of all 23 entes and thei suoted vehile makes and models was ovided to allow fo like vehile analysis. The aoah to solving this oblem was data-diven. Due to the limited infomation ovided and available the oblem was aoahed deteministially athe than stohastially. This meant that statistial analysis, suh as maximum, minimum, and aveages, wee needed to be omleted along with eliminating outlies to teat all infomation about the outes. All vaiable data had to be tuned into deteministi, fixed data in ode to eate intege ogams fo the fuel minimization and like vehile solutions. III. MODEL FORMULATION Two binay intege ogams wee eated to align akage as fo UPS, one that minimized fuel onsumtion and one that maximized the ositioning of akage as at entes that suoted them. A binay deision vaiable was eated fo eah ente, akage a, and oute ossibility. Theefoe, the thee indexes in the model ae fo the entes, fo akage as, and fo outes. Eah ogam evaluates, though the use of, whethe akage a should be assigned to ente on oute. The goal of eah intege ogam was to make equal to one wheneve this assignment should ou. Both models had a simila stutue and shaed etain key onstaints. Howeve, eah ontained a diffeing objetive funtion and aametes elated to that objetive funtion. A. Fuel Minimization Model The fist intege ogam fomulated was fo the fuel minimization alignment. The fuel minimization solution aligns the UPS akage as to edue the amount of fuel used e day by assigning vehiles with highe miles e gallon (lowe gallons e mile) to longe outes wheneve ossible. The objetive funtion fo this model was to minimize the summation aoss all entes, akage as, and outes multilied by the miles e oute, R, and gallons e mile fo eah akage a, G. Objetive Funtion: min whee: 1, if akage a is assigned to oute at ente = 0, othewise R is the numbe of miles in oute at ente G is the gallons of fuel e mile fo evey akage a R G Fig. 1. The objetive funtion of the fuel minimization intege ogam. It should be noted that only a subset of the total outes is esent at eah ente. Theefoe, to indiate this fat to the model, R is set to 1,000,000 miles fo evey oute that does not exist at a ente. Sine the objet funtion minimizes times R, setting R to 1,000,000 fo oute and ente ombinations that do not exist in the eal wold foes the model to not onside these ossibility. By minimizing the gallons of fuel onsumed with this alignment, UPS an save money on fuel daily. B. Like Vehile Maximization Model The seond intege ogam fomulated was fo the like vehile maximization alignment. As eviously mention, eah of the 23 UPS Viginia entes only suots akage as with etain engines (Intenational, GM, Fod, Meedes-Benz, et). In this ase, suot efes to the ability of a ente to have ats in inventoy to quikly sevie and eai akage as, whih saves shiing osts and time delays on eais and maintenane. Sometimes a ente an only suot a single tye of engine, while othe times a ente an suot multile engine tyes. The objetive funtion fo this model was to maximize the summation aoss all entes, akage as, and outes multilied by a utility aamete, U, that ewaded aligning akage as at entes whee they ae suoted. Objetive Funtion: max whee: 1, if akage a is assigned to oute at ente = 0, othewise 1, if akage a is suoted at ente U = 0, othewise Fig. 2. The objetive funtion of the like vehile maximization intege ogam. By maximizing the alignment of akage as at entes that suot them, UPS an outinely save money on eais and maintenane beause moe entes will have ats ondemand to sevie thei akage as. U

3 C. Constaints While the two models have diffeing objetive funtions and aametes assoiated with these objetive funtions, they both shae the same set of onstaints. The fist onstaint is that all outes must have one, and only one, akage a assigned to them. This is aomlished by setting the summation of, the binay assignment deision vaiable, aoss entes and akage as fo eah oute and setting this equal to one. The summation an go aoss entes beause the oute only exists at a single ente. = 1, Fig. 3. This onstaint ensues that all outes have a akage a assigned to them. The seond onstaint is that fo a akage a to be assigned to a oute, it must be lage enough to hold that oute s volume of akages. Fo examle, this events a akage a with a 500 ubi feet aaity fom being assigned to a oute with 750 ubi feet of akage volume. This onstaint is aomlished when the summation of, the binay assignment deision vaiable, multilied by the aaity in ubi feet e akage a, C, aoss entes and akage as must be geate than o equal to the numbe of akages e oute, V, multilied by the aveage akage size in ubi feet, S, fo all outes. As in the fist onstaint, the summation an go aoss entes beause the oute only exists at a single ente. The summation an go aoss akage as beause the evious onstaint limits a single akage a to eah oute. C V S, whee C is the volume aaity (in ubi feet) fo eah akage a V is the numbe of akages fo eah oute S is the aveage akage size (in ubi feet) Fig. 4. This onstaint ensues that a akage a is only assigned to a oute if it is lage enough to hold that oute s volume. The fist two onstaints exist to make the outut of the model meaningful. Without the fist onstaint, the fuel minimization intege ogam would not assign any akage as to any outes at any ente. Similaly, the like vehile maximization intege ogam would assign evey akage a to evey oute at evey ente. Without the seond onstaint, the fuel minimization ogam would assign the smalle, moe fuel effiient akage as to the longest outes even if they wee not lage enough to ay the outes volumes. Similaly, the like vehile maximization ogam would send all of the akage as to entes that suot them, even if some of the akage as wee too small to handle thei oute assignments. Sine thee ae moe outes than akage as, some akage as have to be assigned to moe than one oute. To mimi how these multile oute assignments ou in eal life at UPS, the thid and fouth onstaints wee eated. In the uent UPS fleet alignment, akage as ae assigned to two outes at the most. So, the thid onstaint was eated to set a two oute limit e akage a. In the model, this was aomlished by setting the summation of, the binay assignment deision vaiable, aoss entes and outes less than o equal to two. 2, h i il li it Fig. 5. This onstaint ensues that a akage a is not assigned to moe than two outes. Additionally, in uent UPS atie, when a akage a is assigned to two outes, these outes ae geneally shote in length, so that the dive has enough time to tavel both outes. If the intege ogam assigns a akage a to moe than one oute, the fouth onstaint sets a mileage limit to event that akage a fom being assigned to moe miles than it an hysially handle. Beause some entes ae in moe ual aeas that equie longe outes than othes and some akage as hold moe akages that take longe to delive than smalle as taveling the same distane, the mileage limit an vay by ente and akage a. The mileage limit onstaint was aomlished by foing the summation of the miles e oute, R, multilied by, the binay assignment deision vaiable, to be less than o equal to the maximum total miles a akage a an tavel at a ente, M, fo all entes and akage as. g R M,, whee M is the maximum miles fo akage a at ente Fig. 6. This onstaint ensues that a akage a does not exeed mileage limit that vaies by ente and akage a. The fouth onstaint also has the side benefit of ensuing that a akage a is not assigned to a oute that does not exist in eality. Sine R is equal to 1,000,000 miles fo evey oute that does not exist at ente, in addition to onstaining double oute assignments, this onstaint will also be violated if, the binay assignment deision vaiable, is set to one fo any oute that does not exist. Finally, sine akage as an be assigned to moe than one oute, the situation needs to be evented whee a akage a is assigned to outes at two diffeent entes. A akage a annot be in two loations at one. The fifth and sixth onstaints wee eated to event this situation. A new binay deision vaiable, Y, was eated to be used

4 in these onstaints. In the fifth onstaint, Y is set to one fo evey ente that a akage a is assigned to by. This is aomlished by foing Y to be geate than o equal to, the binay assignment deision vaiable, fo evey ente, akage a, and oute. Y,,, 1, if akage a is assigned to ente whee Y is a binay deision vaiable = 0, othewise Fig. 7. This onstaint foes Y to equal one at evey ente that a akage a is assigned to. The sixth and final onstaint then uses Y, as set in the fifth onstaint, to event a akage a fom being assigned to outes at moe than one ente. This was aomlished by foing the summation of Y ove entes to be less than o equal to one. Y 1, Fig. 8. This onstaint does not allow a akage a to be assigned to moe than one ente. These six onstaints ombined with the objetive funtions fom the two binay intege ogams, the fuel minimization model and the like vehile maximization model. IV. RESULTS The team had initially lanned to un the data fo the entie state of Viginia as one single data file, howeve, afte finishing the fomulation, it was found that the esoues available to the team would not be suffiient fo unning an intege ogam of suh size. Given this oblem, the team had to analyze the situation and it was deided that the state of Viginia would be boken into fou diffeent egions. The egional alloations wee as e UPS standads and wee not iked by the gou. Uon ontat, UPS ovided the team with the diffeent egions and thei esetive alloations, whih wee then used to un the ogam. Eah of the intege ogams, one fo fuel minimization and one fo like vehiles, was un aoss fou diffeent sets of data. The fou diffeent sets of data eflet the fou diffeent egions in the Viginia distit: Rihmond, Southwest, Noth, and East. Eah egion is made u of aoximately six entes. This beakdown was used fo unning the model beause of infomation ovided by UPS fo moving akage as fom ente to ente. Cuently outside omanies ae used to move tuks fom ente to ente and that is done on a egional level only. Due to time onstaints fom testing and debugging, the fuel minimization and like vehile models ae uently being un on the fou sets of data and esults ae being analyzed. The fuel minimization model was un on the Noth egion and found an otimal solution afte aoximately fifteen minutes. The othe models ae uently being un and the esults analyzed fo ost savings. In ode to quantify esults fo intege ogams, uently only a smalle vesion of data has been un to foeast esults and benefits. The fuel minimization model was un on the Fedeiksbug ente in the Noth egion to find ost savings fo fuel. With akage a oute ealignment within the Fedeiksbug ente thee wee gallons of fuel saved e day based on the otimal alignment. The like vehile solution has yet to have its esults analyzed beause it ould not be un on a single ente. V. COST/BENEFIT ANALYSIS Eonomi evaluation was omleted on the fuel onsumtion model by foeasting the Fedeiksbug ente onsideing fuel saved the ost of eloating akage as, and othe budgeted osts. The model leads to gallons of fuel saved in a day aoss the Viginia distit. A B/C atio of was omuted fo the fuel minimization model based on foeasting the Fedeiksbug esults aoss all 23 entes and uent fuel ies. This altenative allows fo ealignments thoughout the yea based on hanging demand duing eak seasons. Based on the B/C analysis with the given assumtions, the beakeven oint fo this altenative would ou at about 190 days exluding Sundays and holidays. This is how long it would take the ealignment to ay fo itself based on uent fuel osts. As fuel ies inease the benefits of the fuel minimization model also inease. Eonomi analysis fo the like vehile solution is uently undeway. VI. PROJECT MANAGEMENT Though all of the membes of ou design team ae Industial Engineeing students, eah membe has an aea of stength with egads to ou ojet. We established a ojet stutue simila to that of a oss-funtional team in ode to utilize ou stengths to ovide the geatest benefit to the ojet. While ou ojet is quite omat and onise, we found that the soe of wok ould be divided into five main aeas, eah to be the esonsibility of a atiula team membe. The wok beakout stutue in Aendix I indiates this stutue and the oesonding aeas of stength fo eah team membe. Eah wok akage eesented one deliveable o set of deliveables to eithe UPS o to the senio design ouse oodinatos. While one team membe was ultimately esonsible fo eah wok akage, the wok efomed to omlete eah was delegated out amongst all membes of the team. This system woked well, allowing eah team membe to at as a ojet manage fo thei atiula otion of the ojet by seuing the atiiation neessay to omlete the wok. By natue, this ojet is one that equies omliated logial and mathematial solution methods. While deent estimates fo task time duations wee detemined at the

5 beginning of the ojet, the team was unable to aount fo unfoeseen delays in data aquisition and model debugging. In an attemt to deal with the unetainty, an effot was made to omlete as muh wok as soon as ossible, allowing suffiient time fo handling any diffiulties that may have aisen. Seveal oblems with the mathematial solution model wee enounteed towads the end of the ojet timefame, but suffiient time emained fo the oblems to be addessed and the soe of wok to be omleted on time. VII. CONCLUSION The UPS Viginia distit akage a fleet ealignment was a data-based otimization oblem. The modeling equied using statistial analysis to onvet vaiable data into fixed, deteministi data in ode to eate intege ogams. Fom the fuel minimization and like vehile models a hybid model will be fomulated to eflet a eal wold solution. This model will be un and omaed with the two othe models to find diffeenes in hoes it ovides UPS with the best ossible ealignment. The data teating and model unning will be semi-automated using Miosoft Exel and othe tools to allow the intege ogams to be un thoughout the yea to allow UPS to ealign its fleet to oesond with the uent seasonal demand. The goal is to ovide UPS with a esoue fo ealigning its fleet to meet the seasonal akage demand.

6 Wok beakout stutue (WBS) fo the ojet team APPENDI I