Inventory and Models in Project 3

Load Driven SystemsJohn 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?