Missing From the Model

Optrak

Missing From the Model

Tim PigdenOptrak Distribution Software Ltd

Apologies for Abscence

What is a Model?

Working definition: A mathematical or computer representation of a real-world problem.

What is Operations Research?

"a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control.“British Army Report, 1947

My Assertion

For Operations Research to be useful we have to solve problems in such a way that the answers we provide are meaningful to and usable by the people tasked with creating a workable solution to the underlying problem.

The Problem

• The standard CVRP or CVRPTW is a long way from reality.

• Most academic work is aimed at solving this or other similar simplistic formulations.

• Most academics start with an assumption these models are good and useful.

• Few spend any significant time studying real problems with real end-users.

“Rich” VRP

• A step in the right direction.• But most papers start with academic models

So what do we do?

Real-world models are not hard to find.• Where businesses and operations are automated,

even if not optimised, there is going to be a good working computer model.

• Find the software, get the manuals, understand their model.

• Do the same for all aspects of the problem.• Remember their model has to work or they go

bust!

Example: VRP

• Understanding the demand side – JD Edwards / SAP

• Understanding the travel side – look at TomTom Business Solutions

• Understanding real-time and drivers – look at Peoplenet (or similar)

3 Aspects of VRP

• When did you last describe your demand for goods to Amazon?

• Have you ever seen a driverless truck making deliveries?

• Have you ever tried to fill the boot of your car entirely with boxes?

Or ..

• People place orders.• Tractors, trailers and drivers must be treated

properly.• Linear capacity constraints are best suited to

liquids.

Orders vs. Demand

Toth and Vigo describe one of the characteristics of customers as the “amount of goods (demand), possibly of different types, which must be delivered or collected at the customer”.[

People Place Orders

In General

• There may be multiple orders going from a supplier to a customer (or vice versa)

• The orders are split into order lines corresponding to quantities of different products.

• Different delivery constraints or service levels may apply to different orders.

• Different delivery constraints or service levels may apply within an order to different order lines.

Where to find out more about commercial models?

• JD Edwards (Oracle) manuals are on line http://docs.oracle.com/cd/E16582_01/doc.91/e15146.pdf

• Many books about SAP

Orders (and lines) for the same customer with different constraints

• Orders may be available at the dispatch depot at different times.

• Orders can be delivered separately or together.

• Orders may have different vehicle / order compatibilities.

• Orders may be placed at different times or have different service levels.

With “Classic” VRP model

Two strategies• Aggregate the orders so we have a single

“demand” per product per customer.• Treat each order as if it were being delivered

to a separate customer.

Aggregate the orders

Works if • The customer wants goods delivered together • All orders fit on the same vehicle• Co-delivery is almost always the best solution

Treat each order as if to separate customer

Works if there is no synergistic advantage in delivering the orders together.But almost always the best model for time at customer is fixed time plus variable amount per unit delivered.Treating them as 2 separate co-located customers will double count the fixed time.

Example: Weekend Newspaper Delivery

• Newspaper orders arrive at depot at 4am• Magazines and supplements arrive hours earlier• Pre-running magazines and supplements is

possible• Optimisation to decide whether to pre-run or

combine with main orders• Very time-critical• Fixed + Variable delivery time applies

Example: Bulk and Packed Lubricants

• Bulk tankers• Packed product on flat-bed trucks• Combi trucks that can hold both but cost more

to run.• Packed product can also be sent by 3rd party

carrier• Many customers with both packed and bulk

orders.

Other examples

• Multi-temperature food delivery – a mixture of refrigerated, non-refrigerated and multi-temperature fleets.

• Waste recycling– Collect on compartmented vehicles, keeping

streams separate– Collect on single compartment vehicles with

separate collections– Mix it all together then separate it again

Different Service Levels

Either• Different order dates and thus different due dates• Different guaranteed order lead timesDo we deliver together or separately?• We may be short of delivery resources on first

day.Again – fixed / variable time an important part of the model for time at customer.

Packing Issues

• Orders are often shrink-wrapped or consolidated into pallets and roll-cages at the customer level to facilitate delivery.

• If treated as separate sites they would require additional packaging and space.

Drivers, Tractors and Trailers

• Drivers have complex constraints around shift times and around when to take breaks. This is particularly important when considering– Tight time-windows– Different speeds at different times of day

• Drivers may change vehicle• Tractor units may change trailers• Trips may benefit from a co-driver• Deliveries may require 1 or even 2 extra crew members.

Example: Mates

• Common in a number of industries including beverages.• Company W delivers beer.• Some vehicles regularly have 2 crew members and

some 1.• Others have 1 normally but a floating mate.• A mate is required at some customer sites (trapdoors

and crime).• A mate speeds delivery at all customer sites.• Extra crew increases cost!

Example: Drivers allocated to area, heterogeneous fleet

Drivers are allocated to work in a given area:– Familiar with area (parking, navigation)– Familiar with customers– Customers familiar with driver

Demand is not consistent so sometimes a big truck needs to go to an area, sometimes a small one.

Complex Example

Company R: 3pl delivering petrol and diesel on behalf of several clients.Each client operates its own terminals and has its own customers.R uses vehicles taken from the clients, most still have livery (logos etc) plus its own, unliveried vehicles.

Constraints for R

• Driver training– Terminal – Product– Customer

• Liveries– Cannot mix liveries– But R branded tractors and trailers can mix– Many sites must have appropriately liveried trailer

Compatibility constraints for R

• Product / Trailer• Tractor / Trailer (pumping equipment)• Tractor / Trailer / Product • Tractor / Trailer / Customer – pumping

irrelevant for some customers because gravity off-load

The good news. Single Resource often works:

• Fixed allocation of driver to vehicle and tractor to trailer.

• Free allocation of driver to vehicle but drivers have identical constraints.

• No effective limit on drivers or vehicles.

Non-Linear Loading

• Standard CVRP uses a single measure of capacity and demand.

• Can be trivially extended to 2 dimensions (weight and volume)

• Or more

Company B: Roll-cages and Pallets

Packed Lubricants – Mobile Pump

• One tote takes a pallet space• The pump requires a pallet space• = 2 spaces• Two totes take 2 pallet spaces• The pump requires a pallet space• = 3 spaces

Pipes

Models

A workable solution requires either• An accurate model or• A conservative modelAcademic models are not accurate so their adoption forces conservative modelling.An optimal solution to a conservative model is unlikely to be better than a “quick and dirty” solution to an accurate model.What we need are better solutions to more accurate models.

Any Questions?