Inventory and Models in Project 3 Load Driven Systems John H. Vande Vate Spring, 2001

Outline What are the inventory implications How to build a model

Inventory Laurel, Montana Orilla, Washington

At the Plants Half a rail car load on average for each ramp Conclusion: Inventory at the origins depends on the capacity of the transportation units and the number of destinations served.

At the Mixing Center Models we have: –In Bound Only (if Out Bound is one-by-one) –In Bound and Out Bound (eg. Case #1) Simplicity of mixing center allows detailed model Model depends on operating policy

Two Operating Policies Minimum Inventory Policy –Whenever there’s a full load to a destination, bring in an empty rail car (if necessary) and haul it away –Requires an inventory of empty railcars Equipment Balance Strategy –Never bring in an empty rail car –Strive to have rail cars arrive full and depart full. –Sometimes, they may depart empty

Minimum Inventory Just like the plant! Expect half a rail car in each load lane Inventory depends on the capacity of the transportation units and the number of destination the mixing center serves Why no dependence on the number of plants the mixing center serves? Why no in-bound inventory?

Building the Lot How many vehicles can there be on the lot? How large must we make it?

Equipment Balance The inventory will slowly rise to a point where we achieve equipment balance and then remain there. A Fiction: –We serve r destination ramps so there are r load lanes –Each rail car holds c vehicles –Suppose each load lane had c-1 vehicles and one load lane, #1, was empty –What happens when the next railcar arrives?

The Fiction If all c vehicles go to load lane #1, we have a full load … If any vehicle goes to another load lane, we have a full load… Can’t haul away more than c vehicles … why not?

Why is this a fiction? Under the equipment balance policy we can have more than c vehicles in a load lane. How? Question: How many vehicles can there be at the mixing center?

An Answer No more than (r-1)(c-1) That’s as though we had one empty load lane and the rest just short of full. Argument: If we have (r-1)(c-1) and c vehicles arrive, then we have r(c-1) + 1. Some load lane must have at least c vehicles.

In Either Case Inventory at the mixing center depends on the capacity of the transportation units c and the number of destinations it serves r.

At the Ramps Inventory at the rail ramp? What does it depend on?

A Basic Model Cont. Variable: path from plant to ramp Examples: –Direct: plant to ramp without visiting mixing center –Mixing center: plant to mc to ramp Binary Variable: on each leg to count dest. –Plant to ramp –Plant to mc –mc to ramp...

Constraints Meet Demand –sum over all the paths out of the plant to a ramp = –demand at the ramp for the plants production. Count the destinations the plant serves – for each path that uses the leg from-to flow on the path  Demand at the destination ramp from the origin plant*binary variable on leg from-to

Complications What should the costs be? Long paths through several mixing centers How do different modes influence the question? –Do unit trains have different inventory influences at the plants and mixing centers than individual rail cars? –What’s the influence of speed? How to model different modes?