all right welcome everyone I think I did

the right thing it's about 12:10 so I

hope many of you at least have had a

chance to enjoy the rest of your lunch

I'm here to introduce al 130 alo and

it's a pleasure to do that for those of

you who don't know alejandro

yet a few things about him so he has

long history with Georgia Tech in the

sense that his undergraduate here but

also his he graduated tour he finished

his PhD in 2010 I believe then he

accepted an assistant professor position

at the University of a very reputable

institution we tried our best to

convince him after a few years to come

back and we succeeded which we were very

happy with so when she came back to

Georgia Tech in 2013 he is been promoted

to associate professor well-deserved and

he's one of a few people in our group

that is very interested in all problems

related to last mile or same-day

delivery

[Music]

about historic visions in work on that

particular topic and it should be

incredibly insightful and entertaining

we hope thank you so if you're counting

that's 14 years I've been to Georgia

Tech in one capacity or another so I'd

like to say that I'm like a bad cold

that they just can't get rid of me so so

thanks very much for being here I'm

happy to be here as well I'm excited to

talk to you all I'm gonna try to make

this as informal as possible so please

interrupt me whenever you feel like and

if we don't get to the end it doesn't

matter so just please feel free to

interact raise your hand interrupt me

anything you like I'll point out that

this is joint work with a couple people

so my colleague Alan Herrera who

hopefully many of you all know and a

couple of students one former student

Matias who is now professor at the

Catholic University in Chile and the

current student Alex who is in the

audience and who can correct me if I say

something wrong so what are we going to

talk about so I I like keeping this

slide up as an introduction because when

I started giving talks about same-day

delivery this really did seem like the

pie in the sky and I'm gonna keep this

slide in my in my introduction to these

talks until I have to remove the

question mark because this is at some

point going to be actually what what

happens for the time being it's still a

little bit more of the pie in the sky

but there's still even if you don't yet

believe in drone delivery there's many

many reasons why you you want to study

problems like the one we're going to

talk about today so there's at this

point already a very well established

you know several years worth of these

different service offerings from a

variety of different companies the

obvious highlight being Amazon but many

many others and so it's it seems like a

interesting very very exciting area to

study with in logistics there's lots of

stuff going on and so what I'm going to

talk about is basically what we've been

looking at over the past few years of

the problems to relate in this area and

so try to maybe set the table

little bit at the beginning and talk

about some context and then we're gonna

spend probably the bulk of our time

talking about operational issues which

is where we've we've done more research

up to this point and this is essentially

what I'm going to show you is what

became most of Matias collapse thesis

and then I'm gonna talk a little bit

more briefly at the end or towards the

end about tactical design issues which

is an ongoing research project that

we're doing right now with Alex which

we're very excited about and then we'll

wrap it up from there so just the set

set the stage why why do we care about

these problems so at this point I think

eerie tale or e-commerce is really

retail this is a growing and completely

established part of the economy and of

how consumers buy products so I put up

some some a few salient facts up there

for you all in case you hadn't seen them

before so we're already it's been for

the last five years ecommerce or retail

has been at least ten percent of total

retail spending and at this point it's

more and at this point we're projected

this year to reach $2,000 per online

buyer a spent per you know per year and

so at least thinking of myself I think

I'm probably above the average already

and it's it's it's amazing how quickly

and how quickly you transition into

being one of these buyers and how at

once you've once you go that way it's

hard to go back because it's so much so

much more convenient so much easier the

big player in the room is of course

Amazon so Amazon this this year is

essentially breaking the half the 50%

threshold they're going to be more than

50% of e-commerce in the US now I should

point out here that when this this

statistic includes the Amazon

Marketplace which is of course processed

by Amazon but not products that are sold

by Amazon but of course they take their

cut of that as well and this is a big

part of the

revenue stream and so of course if you

count all of that together that's Amazon

is more than 50% of all of the stuff

that's sold online in the US and there's

a bunch of downstream impacts of these

facts so worldwide Amazon is now the

second largest US retailer so just to be

precise there of all private US

companies if you count their global

employment force their global work force

Amazon is number two

Walmart is number one now of course you

can see this has a bunch of impacts in

terms of how the economy works and it

has a bunch of impacts and things that

that that are salient in the news

nowadays things like the the development

of automation and are people going to be

replaced by robots in this kind of thing

because you can see the difference in

the in the work force when you go from a

retail operation to something like

e-commerce operation even though these

are big companies there's a change of

magnitude order of magnitude in the

number of people that they employ and of

course there's big news related to this

for example the fact that Amazon has

just decided to establish a 15 a a $15

per hour I guess I wouldn't call it

minimum wage but the minimum salary that

they pay their employees so any any kind

of decision like this that Amazon makes

has a tremendous impact on the US

economy in the world economy and so of

course this all come this all means that

the kinds of problems that Amazon cares

about and the kinds of problems that are

important in e-commerce are just

important problems period in the economy

and so this is just a a chart of the

projections that I was talking about

before so as you can see here this is

this year and we're already almost at a

50% and will exceed 50% of Amazon's

share of e-commerce next year and the

really remarkable thing is just the rise

in the total number that we're talking

about here so if you think about what

this means in terms of total ecommerce

in the US this is this year it's about

it's about half a half a trillion and

it'll be you know it's going to go up by

another you know 150 billion next

so it's quite a that's the growth is

explosive and so as this sector grows

it's of course it becomes more and more

important to compete it becomes more and

more important to drive innovation in

the sector and so the ultimate Holy

Grail is to compete with

brick-and-mortar stores right to offer

the same level of service that our

customers specs in a brick-and-mortar

store right and same-day delivery is

this idea right the idea that I don't

have to wait anymore than I would have

to wait for a product if I want to get

it online versus getting it at the store

and in some sense it's even more

convenient because I don't even have to

leave my house right so so this is one

of the things that's one of the

innovations that's really driving the

sector right now however on the

operational side are on the on the side

of the the administrators this really

causes a lot of problems so the the last

mile of this distribution when you go

into something like same-day delivery is

extremely costly because the number of

orders you're delivering is much much

much lower right so you can't take

advantage of the economies of scale that

you would in a in a more typical

distribution system like even a next day

distribution system where you can sort

of pull everything together right there

I looked up there's a recent survey this

was done last year survey that McKinsey

did it shows that less than a quarter of

customers of e-commerce customers are

actually willing to pay for delivery

services the vast majority of the

customers essentially want you to do it

for free or they're they're willing to

take your your the fastest delivery

option that is available for free and

even the ones who are willing to pay are

not willing to pay more than a very

small amount say a couple of dollars for

this fast delivery okay

however this there's some III have some

question personally about what this

exactly means because if you think about

something like Amazon Prime what Amazon

is really doing there is is making you

amortize these costs of delivery and

it's a site it's a it's a question of

behavioral economics really you know if

if you pay a single flat fee once a year

right and then you get your deliveries

for free you feel like you're getting

them for free but that's that's a

psychology more than anything else right

but this this clearly has an effect and

amazon is amazon has taken advantage of

this so so in some sense this survey is

is asking people what they think but

then if you look at what they're really

doing you know they're they seem to be

willing to pay for the service it just

depends on how you how you charge for it

okay okay so then when you actually

think from a manager's perspective on

what's new about same day delivery

specifically from the the distribution

or transportation side of things what's

going on here so the the the typical

model the traditional delivery model

will have all of the order management

the picking the packing of the orders

everything happens before you do any

just any last mile distribution right so

if you think even of next day delivery

what what's going to happen is you you

were really going to rely on a very

agile very nimble backbone network think

of something like you know the the air

networks that the UPS and FedEx have to

get stuff from one side of the country

to the other overnight and this this

relies on a really sophisticated a big

investment of your backbone network but

when you're actually thinking of this

from the the last-mile perspective this

is essentially that the typical UPS

think of UPS the problem that the driver

faces in the morning right so you have a

local warehouse and a bunch of packages

have come in overnight and the the

problem is I have a bunch of packages I

know exactly where these packages need

to go I have to divide them into subsets

that go into each truck and then plan

the route for each truck and this is

your classical vehicle routing problem

that we have studied for at this point

several decades and this is this is a

problem that that from a research

perspective and I think from a

practitioners perspective is is sort of

very well understood in terms of last

mile distribution

so the the challenge for same-day

delivery is that you are now have to do

these two things simultaneously the

acceptance of orders the picking of

orders the packing of orders happens at

the same time that you're already

dispatching orders that were ready

before so everything is happening

concurrently throughout the day and so

for the purposes of this talk we're

gonna focus specifically on a common

deadline so think here of not I'm not

ordering a pizza I'm not ordering

GrubHub I'm I'm I'm at work and I

remember that I need to order something

like I don't know I need my my

toothpaste or I need my dog's food or

something like this and I'm happy to

just have it be waiting for me when I

get home tonight so I don't I don't I

this isn't I'm not ordering my lunch now

if you are curious about those kinds of

problems like GrubHub and uber eats and

amazon restaurants these kinds of things

I haven't personally worked done on this

lately but some of my colleagues have

including Martin and and Alan and they

have specifically worked with GrubHub so

if you have questions about those kinds

of problems then ask them so in that

sense that is that is obviously an even

more challenging problem in terms of

economies of scale and it's more

applicable for perishables for food for

flowers for for groceries these kinds of

things but we're gonna focus more on the

common deadline type problem okay any

questions okay terrific so I stole this

this a picture from one of Alan's talks

because I think it's very illustrative

this is essentially the the problem I

was illustrating I was describing before

in pictures so if I had all of my orders

ready at the beginning of the day then

maybe I could do something nice like

this but the color coding in this

picture tells you some of the orders or

early some of the orders come a little

bit later in the day and some come very

late in the day and because the orders

come in this in this way I I can't wait

until the end of the day to serve

everything and do this because then the

orders would be delivered too late so I

basically have to deliver while orders

come in and do something that's way less

efficient this is essentially

the problem with with what we're talking

about so with this kind of setup in mind

let's think of what let's think of a

basic operational model and let's see if

we can extract some some insights from

it and some thoughts about how a

dispatcher ought to manage a system like

this and so our basic operational model

is going to have a couple of components

so we're going to look at it at the

level of a single dispatching facility

so think here of a local warehouse a

local DC or perhaps even a retail store

if you're doing omni-channel fulfillment

and you've already decided at some

higher level what what store or DC is

fulfilling orders for a particular

address so you've already partitioned

your your urban area let's say into

service regions and identified the the

DC that's going to serve that region and

you have so you have your known service

area and to keep it simple we're gonna

assume that there's a single vehicle

that's making the deliveries here and so

you have some kind of a same-day

delivery horizon so this is the time of

day in which you're accepting orders and

the orders are going to come in but it's

it's random I don't know where they're

gonna pop in from I don't know at what

time of the day they're gonna pop in

from so I in some sense have have taken

my service region and I've split it up

into neighborhoods or city blocks or

something like this and there's some

some underlying random process that's

that's that's producing orders and this

is probably based on a probabilistic

forecast that I have that is that this

based on data that I already have and

I'm going to assume that all of the

orders that pop in over this horizon are

served either by my delivery vehicle or

at a higher cost by a third-party

operation at which I offload all of the

the orders that I could not serve at the

end of the day and if you don't like

that assumption then think of that as

the the lost sale cost for the orders

that I could not serve okay both of

those are equivalent for our purposes

and so when the vehicle is available the

dispatcher has to decide what to do with

the knowledge that the the current

dispatch is going to influence the total

cost of the operation but also how long

the vehicle is occupied and the next

time at which the vehicle

be available to make another dispatch so

of course my decision has a very it has

an impact on my cost but more

importantly for our purposes it has an

impact on when I can make my next

decision so that's really the key here

and so for the purposes of what our

discussion let's assume that we're

minimizing our total operating costs

which will be our routing costs but you

can equivalently also think of of

maximizing their order fill rate if you

prefer that in which case what I would

want to do is minimize the number of

orders that are served by the third

party so we can also think of that and

I'll come back to that at the end ok and

so to make things even simpler what

we're going to do first is focus on the

absolute simplest version of the problem

that I can imagine that still captures

the elements of it better that are new

and interesting to us and so what we're

going to do first is think of the most

restricted geometry that we can think of

which is a single line so this is the DC

these are the potential order locations

and they're all going to be on the same

line so why are we doing this so clearly

we're not at this point talking about a

practical problem anymore

but the single line geometry is the

situation in which you maximize

economies of scale because the time and

the cost of the dispatch is purely given

by the farthest order you choose to

serve in any dispatch so this is the

maximizing this maximizes economies of

scale so if the system is not economical

with this geometry then you're going to

have real problems in general so what

we're going to try to do is analyze this

system for a little bit and extract

insights from it that we can then apply

to a real road network that's the idea

here ok so this is a picture of a

schematic of what the process would look

like so in this in this schematic the

horizontal axis is time and the vertical

axis is how far away orders show up from

the Depot and the at any point in time I

have to decide how far away I'm going to

dispatch the vehicle in this case maybe

2 units away and when I dispatch the

vehicle 2 units away it come

back at some later point I've covered

all of these orders these orders I did

not cover so they remain open and some

new orders might appear randomly and

then the process repeats right and I

keep doing this until the end of the day

and so what we're gonna try to do first

is try to understand this very very

simple system and see if we can extract

some structural insights that help us

understand how the real system would

operate so here's a representation of an

even simpler problem in this problem I

have removed the uncertainty so now I

not only know I'll not only have a

simplified geometry I have a simplified

order system in which I know exactly

when the orders are available

I still can't serve them before they

become available so think of this as the

point in time at which this this is the

point in time at which this order which

has to go to this distance is has been

picked and is ready for me to dispatch

from the from the Depot from the

warehouse and this is a schematic of

what one possible day might look like if

I do this and this is also an example of

a bunch of dispatches that I might make

in order to serve these orders so if my

objective is to minimize the total time

that my vehicle is traveling is this can

anybody suggest some possible

improvements to this example or any

corrections to up to my dispatch plan

and what could I do that Marlin yes so

one simple observation is again because

this is simplified as simplified

geometry in which everything is on a

line this dispatch goes farther and

leaves later than this dispatch so of

course everything that I covered with

the first dispatch I could just as

easily cover with the second dispatch so

that tells me that I will never send an

early dispatch closer if a later

dispatch will go farther ok this is kind

of a nice thing to keep in mind so hold

that thought is there anything else

about this solution that I might make

better so remember what I want to do is

cover as many of the red dots with a

gray rectangle as possible as and I want

to keep the the heights of the

rectangles as short as possible

I see a bunch of students who have taken

classes with me in the past or are

taking classes with me now any

suggestions yes we will outsource that

done yes so for example suppose you can

see here that the vehicle departs comes

back at this time and then waits before

leaving the next time

what if I delay my departure so that the

timing is works out and the return of

the vehicle coincides with the next

departure and if I do that then this

order here which I am not covering right

now I can cover at no additional cost

because I'm going just as far okay is

that clear so if I make those kinds of

fixes I might get a solution like this

right in this solution I see a couple of

things I see

dispatch early dispatches go far later

dispatches stayed closer and the waiting

is banked at the beginning of the day

the waiting is up front once the vehicle

starts operating the vehicle is in

continuous operation until the end of

the day and so those are structural

insights from a very very simple example

that are going to prove particularly

useful yes how far I went

yes so so exactly right so if you were

to plot this as a if you were to plot

this in terms of where am i at any point

in time the triangle would actually be

an isosceles triangle but I can only

serve orders that were ready at the time

of my departure which is why it makes

more sense to plot a vertical line

because even so imagine essentially if

you look at this order right here so if

you think about it right I would get to

that distance at this point but I cannot

serve this order because it was not

picked by the time I left that make

sense it's a great question yes Majerle

well this figure suggests that your

resources both workforce and vehicle are

not used for same-day delivery at the

beginning of the day so they could be

used for something else

yes and we'll talk definitely talk more

about that okay and so the takeaways are

precisely the the two things that I

pointed out the dispatches decrease in

length so think of this qualitatively as

at the beginning of the day I'm more

willing to serve a larger number of

orders and to go farther away from the

depot

later in the day I'm going to restrict

myself to sticking closer to the depot

and kind of making shorter runs and the

waiting is all upfront once I start

serving orders I'm essentially going to

want to keep the vehicle in operation

and for this specific problem we can we

can use these structural insights to

then solve the problem quite efficiently

but I still haven't told you what this

means for the actual problem and even

here I'm not even talking about the

actual problem but the actual

one-dimensional problem which is in

which I don't actually know when the

orders are ready right so the real

problem looks a little bit more like

this so maybe I have a couple of orders

that came in overnight and are actually

next day delivery orders and then I have

some forecasts of when different

neighborhoods might place orders

throughout the day and I have to make a

plan now

even though I don't know what's going to

happen later so the the the insight

that's going to help us take what we did

before and translate it into this

context is to basically say well let's

take a forecast like this that tells us

when we might see orders and let's break

it up and let's turn those into copies

of a particular order and these copies

are going to be essentially weighted by

the probability that an order actually

shows up at this time and now I have a

version of the problem I had before

where I have these multiple copies of

orders showing up in different places

which sort of represent my forecast but

now I'm going to treat each copy like an

individual order and I'm gonna solve the

problem like I solved it before and so

what this dispatch right here means is

if this order shows up at this time or

earlier I cover it if it shows up later

it's too late and I I let it go either I

outsource it or it's a lost sale

depending on my context and so this this

gives me a dispatch plan that I can make

at the beginning of the day that

basically roughly tells me at this point

of the day I should expect the dispatch

and it should expect to go this far and

it'll come back and then there's a next

dispatch at this point in the day which

I expect to go this far that's roughly

the idea right now of course once you

make the plan

so this some folks might call this a

route based plan perhaps or a route

based policy and so of course once you

go back to what's really happening you

will then observe things the forecast is

not always going to be accurate things

will happen later or earlier than when

you expect them and then something like

this might happen and then you'll say

well there's no point in me going this

far when there's nothing there for me to

do so I'll just delay and go a little

shorter for example this is kind of the

idea now this is a this is a static

dispatch plan so not very dynamic not

very adaptive to what's happening in

reality so even with these these short

fixes you you get a you get a plan but

you don't get a very nimble plan you

don't get a very good plan what you

really actually are going to do and

practice is essentially do this every

time so every time the vehicle is ready

to go you will compute one of these

plans but only implement the first part

and then when you come back you update

with the new information you have the

things that are not known you keep in

the forecast mode and you make it the

next decision but only implement the

first dispatch again so you always make

a dispatch with as much information as

you have at the moment and if you do

this this actually works really well and

so this is what sometimes it's called

rolling out essentially at every point

in time that you have to make a decision

you incorporate everything you know

right now so the orders that have

already arrived plus the forecasts for

the orders that might arrive in the

future and you make that plan but you

only implement the first part of that

plan okay does that make sense and I'll

show you an example of what this means

in an actual problem in a second okay

questions up to this point yes yes

so think think of this as a yes because

as I was pointing it sort of if you

think even in this simplified context if

I expect a far away order to show up

early in the day I'm much more likely to

want to go to service it than a far away

order that shows up later in the day so

what I'm going to really have in

practice is I'm going to have think of

this as for every neighborhood or every

city block in my service area I'm going

to have some kind of a some kind of a

probabilistic forecast that says these

number these many orders per hour are

showing up or something like this on

average or the probability of certain

things showing up and that's what you do

other questions yes

it's both so we're assuming here that

they're proportional so so the time I've

scaled my time in my distance such that

the time it takes for me to make a

dispatch that goes this far returns me

at this time

so it's both yes so the one thing I'll

say here is this at this point I have

not I'm not incorporating service times

so you're you're right that if I have a

service time then I will have to take

that into account and that will that

will impact this plan slightly and you

might want to do that then yes other

questions okay so so enough with

simplified examples let's talk about

something that's a little more realistic

so now think of really a general network

topology so I have a road network and

I've identified nodes in this network to

be the neighbourhoods or the city blocks

or the addresses that are of interest to

me within my service region and now I'm

gonna I'm gonna have to sort of do the

same thing I just did but actually route

this vehicle through this network from

the Depot and back and so this is an

example of what one of these problems

might look like as well as a solution to

the problem so think here of the number

as being how many hours were left in the

in the service day in the vehicles

operating day when this order showed up

so six means this order showed up very

early in the day and a 1 means this

order showed a very late in the day and

so in this particular case the example

that I'm showing you is I have two

dispatches 1 leaves 3 hours before the

deadline and takes one hour to

these orders down here and then a second

dispatch leaves when there's two hours

left and essentially the vehicle is at

that point in operation until the end of

the Working Day so I will point out

right away that this solution breaks

that rule that I had said before of you

know the longer dispatches first and the

shorter dispatches second this is a case

where that that relationship is broken

because of course in practice you would

not expect that to always hold okay is

the example clear okay so then let's

think conceptually of what this means if

we if we follow a similar reasoning

process that we just did for the for the

simple one-dimensional case what does

that mean for the general network

topology so now the the think of the

y-axis not as a distance anymore but

simply this is like a Gantt chart right

this is a different point and the y-axis

for every potential customer location

for every neighborhood and in the

deterministic context so if I know

exactly when an order is ready to go I

might have something like this and then

I might have a solution that looks like

this

so this solution says I dispatch the

vehicle at this time to serve these two

orders visits this order first this

order second and then comes back and

then I make a second dispatch that

serves these two orders and visits this

order for first then order three and

then back so this is no longer going on

a line this is simply conceptually what

would be the order in which I would

visit these customers exactly okay great

so just like in the one-dimensional case

even though I can no longer guarantee

that the distances are going to be

decreasing I can certainly in a

deterministic context if I know exactly

when every order is going to be ready I

can once again push all the all the

waiting to the front and push all the

operations to the back so once again I

can't expect that I would have a time at

which I accumulate orders but then once

I decide to start my operation the

vehicle and the the workforce will be

constantly working for the rest of the

day so once again here I have this this

is a managerially this kind of makes

sense

right you were basically going to have

an off period in an on period you're

going to have a point in time at which

you just let enough orders accumulate

and at some point you start dedicating

the resource and at that point the the

the vehicle is essentially operating for

the rest for the rest of the the time

that it has to be so obviously there are

differences so what are the differences

here we we cannot rely on these very

simple geometry to do the analysis we

now have to throw it throw this model to

a much you know much more of a workhorse

in this case an integer programming

solver of some kind for those of you who

are familiar with integer programming

models and specifically for routing

models what we basically have to solve

here is something that's called the

price collecting traveling salesman

problem that has a bunch of interesting

side constraints in this case there's

order release times which means an order

cannot be served before its release

which in this case would be when it's

picked and ready to go and the pickups

occur at the depot so this means I'm not

trying I'm not designing a single

vehicle route I'm designing a multiple

of route a multiplicity of routes in

which each route serves orders that were

ready at the moment in time when the

vehicle left the Depot potato potato

it just depends on what you want to call

it so so what I say price collecting TSP

but some people call it some people call

it when it's profits they call that

orienteering it's the same thing yeah

other questions what nobody else wants

to talk about orienteering okay this

game okay so so for a deterministic

problem you would basically solve an

integer programming model of this kind

and so you I'm not gonna promise that

it's gonna solve in seconds but it's

gonna solve in minutes so with the

integer programming technology we have

nowadays you can solve a model of this

kind in minutes or even less okay and so

how does this work in the general case

the the analysis is essentially very

similar to what I was describing before

so I now replace my known order time

with an order forecast that says I'm

might get in order sometime in this span

of time I might get an order sometime

here in this span of time I might not

and I replace all of those I replaced

the forecast with a bunch of copies of

those borders and those copies are once

again sort of discounted by their

probabilities and now I have a problem

pretty much like what I had before and I

can come up with a route plan kind of

like what I did before except now it's

an actual route plan and it might look

something like this

and then just like just like in the

other version of the problem

this route plan tells me here's what I

will do if the orders show up by the

time that I plan to make the dispatch

and so of course this is kind of my

coverage region so to speak for each of

these orders if the order shows up in

the time that's identified by the gray

rectangles then I will cover it and if

it doesn't then I will and so if I have

a realization which occurs after the

coverage moment so for example this one

then I can make an update I can simply

say well that order didn't show up in

time so I'm not going to cover it in

this in this particular case some extent

and so this is the basic idea although

once again if you simply implement this

plan and make these simple updates

you've got a rig to a much too rigid

plan that's not really going to be good

in practice so what you're going to want

to do in this case is do the rolling out

that we talked about before every time

you need to make a dispatch you will you

know essentially incorporate all the

information you've got right now so that

includes the actual orders that have

arrived in our open plus the forecast

for the orders that might show up in the

future

you solve a model of this kind and you

implement the decision that tells you to

make right now and once the vehicle

returns and you have to make another

decision you update your information and

repeat okay and here's an example of

what this looks like if you try to test

it on an actual instance on an on

something more closely resembling like a

a road network and you know order

forecast that kind of look realistic

this kind of a thing so I'm basically

showing you what happens if you just

implement the plan that I show

before with no updates and no dynamic

changes and then a bunch of versions of

this of this updating or this rolling

out that I was describing and which you

can see is basically that as you would

expect the the the cost goes down and

also the interesting thing that the

thing that we're not expecting is also

the variance goes down so you you lower

the cost the expected cost and you are

more confident that that's what the cost

is going to be in addition so in this

version of the model we're assuming that

you outsource all unserved orders to a

third party at the end of the day and

you're essentially paying a cost that's

perfect that's equivalent to just a

direct delivery for each of those orders

and with this the fill rate here is

describing is how many of the orders did

we serve ourselves and you can see that

by being nimble and dynamic like this

you lower your cost but you don't hurt

your fill rate you actually improve your

fill rate which is kind of nice because

you are essentially saying you can serve

both objectives simultaneously so if

your adaptive if you're nimble if you

take advantage of the information as

it's revealed to you you can actually

improve your service as well

exactly okay so back to fill rate so I

said at the beginning that in some sense

you can you can choose whatever

objective you like so you can choose an

objective that talks a little bit more

about operating costs which would want

to minimize the routing costs as some

proxy for for maybe for the workforce

costs and the vehicle utilization cost

in these kinds of things but if if if

those costs in many situations those

costs are going to be secondary to the

the lost sale costs let's say if you

can't serve an order for some reason and

and in many of these in many of these

models people care much more about

actually serving the orders that's

really the only objective and so in that

case you would want to do something like

maximize the fill rate and so our

experiment here is basically showing you

a a thought experiment of what happens

when you do this so think here of alpha

as how much do I penalize myself for not

serving an order

and the relative weight that I give and

not serving in an order versus the

routing cost so when I say alpha equals

1 this is the setup I showed you before

where I can essentially outsource to a

third party and every order is just that

I don't cover myself I cover with a

direct delivery alpha equals 2 means

that direct delivery costs me twice what

it would cost to send my vehicle to do

it this would be if the third party

charges you a high premium and then 100

basically means I'm losing that order if

I don't serve it myself so I I must at

all costs serve orders if at all

possible and the the routing costs are

secondary and are only simply I just

include them as a tiebreaker basically

and this sort of shows you what happens

so the punchline here is to increase

your fill rate even a little bit you

have to increase your costs by a lot so

we we find this to be kind of an

interesting an interesting insight

because a lot of people are concerned

only with maximizing fill rate and don't

care about the operating costs and what

our experiments show is that that last

percentage point of fill rate that

you're getting is costing you a

significant amount if you care at all

about operating costs and let me show

you one specific example of this so this

is the example I showed you at the

beginning the same exact data is sort of

like what if we had this data but in one

case we were maximum we were optimizing

routing costs in any other case we were

optimizing fill rate and this is the

solution I showed you before which looks

reasonably economical looks reasonable

reasonably kind of like well organized

if you want to serve one more order you

have to do this thing over here so you

haven't set a to dispatch dispatches you

have five and the the routing part of

the solution goes up by about 50 percent

so the punch down here if you want to

take one thing away is simply that you

you will see very very high to create

you know decreasing economies if you

really are pushing fill rate to the

limit

and you might want to think about is it

really you know is there some is there

some middle ground at which you're

willing to live with okay questions

alright so in my remaining time I'm

gonna sort of take a step back and think

then about this is this everything we've

seen up to this point is what would a

dispatcher do so I have my my service

region defined for me I have my horizon

defined for me I know what the forecast

is and I'm simply just dealing with it

as it comes but so what if we're going

to take a step back and maybe think a

little bit more about designing the

system and about how many of you know

how big should our fleet be for same-day

delivery how many resources should we

dedicate to this service or how late in

the day should we offer this service so

this is the kind of questions we're

actually thinking about now I'm going to

give you just a simple example of the

kinds of results that we've come up with

so if you take a step back the question

then is like instead of worrying about

the nitty-gritty what if we just worried

about what's gonna happen on the average

in any given day so I still have the

same set up I have a single Depot or a

fulfillment center and this fulfillment

center has some established service

region in which it's going to serve

same-day delivery orders and I want to

sort of think of what is this what is

this dispatch you're gonna see on

average so instead of thinking of a

probabilistic forecast let's just take

orders as arriving at some constant rate

such that over the service horizon the

constant rate will give me the number of

orders that I expect on an average day

so if on an average day I expect you

know a hundred orders and I have ten

hours in my in my service Rison that

means ten orders an hour and they're

spread exactly evenly so there's no

unpredictability here I'm just seeing

kind of a constant arrival of orders and

when they show up I don't know where

they're going to show up they're gonna

show up randomly somewhere in my service

region okay and then to serve them oh

and all of them have to be served all of

the I'm going to essentially make it

really simple on myself and I'm gonna

say I have some point in time at which

the the

orders accumulate I stopped accepting

new orders at this point in time in my

vehicle or vehicles have to be back at

some later time so I'm making my problem

I'm trying to simplify a lot of the

bells and whistles that I had before and

simply looking at something very very

simple and I'm going to further simplify

the problem by not worrying about the

routing too much in detail so if I'm

operating the system I have to worry

about when is the vehicle leaving when

is it getting to this address when is it

getting to this address but taking a

step back if I say well on average these

many orders will show up and they'll be

I expect them to sort of be randomly

dispersed within my service region then

I can I can do an estimate of how long

it's going to take to serve those orders

and these these kinds of estimates are

used a lot in in logistics contexts and

you can think of this as if maybe I

would a sample I would simulate you know

a hundred different order locations and

then figure out what the routing cost is

for those orders of the routing time I

can fit a model of this kind using

regression and I get very very accurate

measurements but once I do this I don't

worry this is not going to tell me where

at what time am i visiting this address

it's not going to tell me anything like

this it's simply going to give me an

estimate for how long

the vehicle is going to be out okay so

we're gonna use this to simply look at

what does the dispatcher expect to see

over the course of the day and so I'm

showing one example down here of what

the dispatch what the operator

operations might look like right and

what I'm saying here is my this is my

horizon in which I accept orders and

let's just pretend maybe that I split my

horizon into three equal parts and so at

at every at every third I dispatched the

vehicle with whatever's accumulated so

far the vehicle comes back at some point

I wait till the second third I dispatch

the vehicle again and then one last time

at the end of the day this is one

example of what I might do on an average

day and I'm gonna use this kind of a

this this model to sort of play some

what-if do some what-if analysis and say

what if I did this what if I did that

what if I increase this what if I

decrease that this is the idea so so

first think of the case in which I don't

have a single vehicle I have

a bunch of vehicles available to me what

would I want to do so it turns out what

you want to do in this case is have the

first vehicle wait and accumulate as

many orders as possible until the point

in time at which that vehicle leaves and

has just enough time to come back by the

deadline and then rinse and repeat the

second vehicle starts accumulating the

orders that showed up after the first

vehicle left and at some point that

vehicle has just enough time to leave

and come back right before the deadline

and that would be in this case the pink

dispatch and then in this case there's a

third vehicle that accumulates the

remaining orders until the end of the

the service window and then leaves and

comes back but it might be depending on

where you set you're at the end of your

service window that you only need two

vehicles or you might need four it

depends okay

now I've made the I've made the

simplification here that the service

vehicle serves the entire service region

so I can I can't tell one vehicle to go

only to the west and the other vehicle

to go only to the east this is a

simplification in which I serve I take

all comers when they come ok and so if I

make those assumptions this is what the

the average dispatch plan would look

like and notice a couple things one I

wait I accumulate and once I start I'm

in operation continuously until the end

of the horizon and every dispatch I

expect on average to be decreasing in

length so the first dispatch is the

longest the second dispatch is the

second longest the third dispatches the

third longest or the shortest in this

case so the the average behavior of my

system reflects some of the structural

properties that I had that I was

identifying in my very simple models up

front so that's kind of a nice sanity

check so then this is the example of

many vehicles so let's let's now look at

the one vehicle case what is that going

to look like in a sense it's going to be

very very similar but a little more

complicated what's basically going to

happen is I'm going to wait until some

point in time and that from that

forward the vehicle is going to be in

continuous operation until the end of

the horizon so exactly as we had

described before I simply I have an off

period in which I accumulate orders and

then once I start operating the vehicle

is in constant operation until the end

of the business day and I have again

decreasing dispatch lengths because at

the beginning of the day I'm banking

many more orders but as I get closer and

closer I have much less of a wiggle room

of how far the vehicle can go what word

can do so it just has to it has to take

fewer orders and in both cases this is

this is going to basically predict this

is predicting what might happen on an

average operating day and I can tell you

we've already I did not include the the

slide here but we've done validation

experiments sort of saying okay this

this looks nice but does this actually

work and so if you for example were to

calibrate something like this so you say

okay what is my service region look like

and let me fit a routing approximation

that captures the the the traffic the

travel times in traffic and the topology

of this network and now based on this

approximation let me make predictions

about what would the actual operating

day look like if I simulate different

days in which I simulate orders showing

up in different places you know at

different times and the the predictions

are remarkably accurate so in our we had

one example in which we do a setup just

like this any one in which we predict

three dispatches and we predict roughly

speaking on average your first dispatch

will take these many orders the second

dispatch will take these many orders and

the third dispatch will take the

remainder and we observe something like

in 98% of the cases there's three

dispatches and the average that we take

the empirical average we observe is on

the nose to what we're predicting so

this is actually going to tell you how

the system is going to work it most of

the time okay and so then let me give

you an example of then how do you

actually make decisions with these kinds

of models so imagine that I tell you

that you have a distribution center that

services an eight

by 8 mile service region and we expect

we have over a 10 hour service window

for same-day delivery we expect about 75

orders to show up and we have a vehicle

we we were conservative and we're going

to assume that the vehicle travels at

about 25 miles an hour on average and

there's a one minute service time to

deliver the order so the the the time

that it takes for the driver to park

drop-off the ordering and start up again

and we're gonna assume Manhattan

distances here just means rectilinear

distances so sort of the more reflective

of an urban road network right where

you're mostly moving east-west or

north-south okay so under these

conditions what do we expect to happen

what if we want it whether the question

here the the the sort of load the

illustrative question here is what if we

wanted to use many vehicles or just one

vehicle what would be the difference and

so if you crunch the numbers based on

the the examples I just showed you if

you use many vehicles it turns out you

only need two and the first dispatch

will take about 64 orders on average and

the second one will take the last 11 but

if you only use one vehicle you have a

slightly more symmetric dispatch plan

the first dispatch takes about 55 orders

on average and the second one takes 20

but the remarkable thing is if you look

at the expected routing cost of both of

these solutions there's an increase of

only 4% so what you're basically saying

is you're dedicating an extra resource

to this operation and if you take that

resource away and you you cut my number

of vehicles in half my routing time or

routing cost only goes up by 4% so that

seems like a no-brainer right yes Martin

well it's proportional to 64 and 55

right so I'm not doing the math here but

let's see so 75 orders over 10 hours

would be so if you do if you divide 64

by 75 that's the time of the first

mismatch if you divide 55 by 75 you get

the time of the of the first dispatch

for each of the two solutions so it's

proportional so it's certainly going to

be the case that the vehicle is going to

be operating longer but the the dispatch

time increases by only 4% so that tells

you how long the how much longer the the

vehicle is the single vehicle is in

operation compared to the two vehicles

in the mini vehicle case now a different

possibility here something else a

manager might do instead is to say well

if suppose I've already dedicated two

vehicles to this operation and I don't

want to take one vehicle away I have no

other use for at them at the moment then

an alternate thing to do here is to say

well let's I might notice that the

second dispatch has a bunch of slack and

so instead of taking only 11 orders I

might say well I'm gonna increase the 75

to maybe I think I did the numbers and

it was 79 right so I'll take four more

orders and that still gives me enough

time to come back right at the deadline

so on average right so if on average I

can accept orders past the 10-hour

service window that I did I establish I

can in fact take orders from movie

another 30 minutes right so the conclude

the the maybe the way to say it is not

that I'm gonna take four more orders but

rather I'm going to keep the service

open for another 30 minutes and my my

research without changing my resources I

can still serve four percent less

oh no no this is this this is the

dispatch time increase so this is saying

how much the total routing time of the

two dispatches here is four percent

higher than the total routing time of

the dispatches here so what this is

saying is if you wanted to dedicate so

if you didn't want to have the fixed

cost of having two vehicles dedicated to

this service then the operating costs

would go up by only four percent so so

in some sense you're saying if you if

you have two resources then you you your

operating costs would be lower and if

you're willing to if you're okay with

the the dedication of the two resources

to this service then that's how much

lower the service they're how much lower

the operating costs would be but in that

case I would I would also then say you

can also at that point extend this

service window another 30 minutes on

average that that would be another

possibility here and so this is

essentially the kind the kind of

analysis that we're doing with these

models other questions terrific

okay so wrapping it up

I'm very excited by problems in E retail

by problems in the last mile I think

there's a lot of cool stuff happening in

this space specifically for same-day

delivery it makes everything really

challenging which is in a sense good for

us it keeps us in business the the the

let's say if you wanted to sort of think

of what are the fundamental trade-offs

when you're making the the dispatching

decisions and when you're operating the

system it's really this this these two

things right here right I have to decide

do I keep my vehicle at the Depot do I

wait and get more information but then

if I wait I am less flexible later or do

I dispatch the vehicle now

but then the vehicle is not available

when new things come in or and if I

decide to make the dispatch do I make a

short dispatch which brings the vehicle

back sooner and lets me update more and

be more nimble or do I take advantage of

economies of scale and dispatch dispatch

it for longer these are these are

interesting difficult questions right

this is basically what makes the problem

so interesting and

what I've basically hopefully argued

here for a little bit is on the

operational side you can start with a

very simplified problem and still derive

some useful structural properties that

will help your dispatching plans but if

you want any hope of actually having low

cost dispatching plans you do have to be

adaptive and nimble you have to

incorporate information as it comes in

and be dynamic and on the tactical side

the the average behavior is surprisingly

reflecting a lot of the properties that

we saw in the operational models and the

other interesting thing we notice is

that the economies of scale in these

tactical models tell you that there's

going to be let's say maximum asymmetry

so you will you will not use your

resources equally in fact what you want

to do if you're optimizing your your

routing costs is to use them as

unequally as possible

which is kind of a weird thing to think

about right if you're thinking of

fairness if you're thinking of how long

two different drivers are working if

you're thinking of the the depreciation

or the just the the the the what's gonna

happen to the two different vehicles if

you're not careful you you're gonna have

an unequal utilization of resources and

in in general this this this also leads

to lots of interesting questions so

thanks very much for your time yes this

is something else that a lot of us are

looking at so in some sense you can

think of one of the versions of our

problem the version where we say we

outsource whatever's left as the version

with drivers on-demand although of

course what's happening in a lot of

situations is that's becoming the bulk

of the operation and the the the I would

say there's many many interesting

questions that come up in that case one

of them being in some sense you now have

a marketplace right it depends on so it

depends on what kind of drivers on

demand you have but if you really are

talking some kind of an uber model then

it's it's a marketplace and now you have

to worry about pricing on both sides you

price the service to the customer and

you price the the delivery cost to the

driver so that

I'm telling ya I mean that's I'm very

excited by these kinds of problems

they're very interesting and I think

there's lots to do there too yeah other

questions

yes so this this research does it feed

into when you companies develop like

softly now software custom software

interesting problem because it kind of

speak to like yeah so so to both I think

our thought here our thought process was

on the operational questions this would

really be how would you design a

software dispatching algorithm that

would help in the actual day-to-day

decision support of the operation of a

warehouse and we have we have talked to

let's say companies that shall remain

nameless about kind of what they do and

they take our you know they took our but

they give us some feedback on these

different questions and then on the on

the tactical side the the question there

really is should I offer this service

where should I offer this service how

big sure might should my service area be

these kinds of questions and that's more

what we're hoping to answer with the

second set of results yes yes so this is

a problem I find very interesting and

we're thinking about it right now

yes so the the the some of the

structural results that I've showed you

so far sort of indicate that you might

even want to think of designing a

dynamic service area right earlier in

the day the service area goes farther

out later in the day the service area

comes farther in comes closer in this is

definitely an interesting question for

sure well thank you very much