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Modeling Service

When Transport is restricted to Load-Driven

Pool Points in Retail Distribution

John Vande Vate

Spring 2007

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Retail Inventory

• Single “Product”, many SKUs• Style

• Color

• Size

• Broad Offering attracts customers

• Depth in SKU avoids missed sales

• Stock enough in each SKU to cover replenishment time (OTD)

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Service Requirement

• Keep OTD short

• Reduce depth without losing sales

• Increase breadth to attract more customers and expand market

• OTD requirements differ by store– Manhattan, NY– Manhattan, KS

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What’s in OTD

• POS system records sale

• Transmitted to DC

• Orders batched for efficient picking

• Order picked

• Trailer filled (Load driven)

• Line Haul to Pool Point

• Delivery

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Pool Points

Asian Port

US Port

Pool

Store

Asian Factory

US DC

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Pools Influence

• Trailer Fill– The greater the volume to the pool the faster the

trailer fills

• Line Haul– Is determined by the distance from the DC to the

Pool

• Delivery– Messier

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The Trade-offs

• Too Few Pools– High Delivery Costs– More moving inventory– Less waiting inventory

• Too Many Pools– Low Delivery Costs– Less moving inventory– More waiting inventory

OTD Dissected

• POS system records sale

• Transmitted to DC

• Orders batched for efficient picking

• Order picked

• Trailer filled (Load driven)

• Line Haul

• Delivery

Constantcost & time

Cost & Time depend on Pool Assignment

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Line Haul

• Time & Cost Depend on – The Pool Assignment– Which DC’s serve the Pool

• NY DC to Chicago Pool

• LA DC to Chicago Pool

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Trailer Fill

• Time Depends on– The Pool Assignments

• Which pool this store is assigned to

• What other stores are assigned to this pool

• Rate at which the Pool draws goods

– How the Pool is served• The Rate at which the Pool draws goods from

each DC

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Drilling Down on Service

• Simple Model– Cube only (trailers never reach weight limit)– One DC only (don’t split volumes to Pool)

• Many DC’s– Cube only

• Weight & Cube and Many DC’s• Soft Constraints:

– Infeasible is not an acceptable answer

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Toward a Simple Model

Trailer Fill Time (for pool) * Rate Trailer Fills = Cubic Capacity of the Trailer

• Rate Trailer Fills– Translate annual demand at stores assigned to

the pool into cubic feet per day– Rate to pool is:

sum{prd in PRODUCTS, s in STORES}

CubicFt[prd]*(Demand[prd,s]/DaysPerYear)*Assign[s, pool]

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Make It Linear

Trailer Fill Time * sum{prd in PRODUCTS, s in STORES}

CubicFt[prd]*(Demand[prd,s]/DaysPerYear)*Assign[s, pool] = Cubic Capacity of the Trailer

• Trailer Fill Time * Assign

• What to do?

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Can’t Know Trailer Fill Time

Trailer Fill Time * Rate Trailer Fills = Cubic Capacity of the Trailer

Max Time to Fill Trailer * Rate Trailer Fills ? Cubic Capacity of the Trailer

Why Cubic Capacity of the Trailer?

What does this accomplish?

What’s Wrong?

Max Time to Fill Trailer * Rate Trailer Fills Cubic Capacity of the Trailer

Max Time to Fill Trailer*(sum{prd in PRODUCTS, s in STORES}

CubicFt[prd]*(Demand[prd,s]/DaysPerYear)*Assign[s, pool]) Cubic Capacity of the Trailer

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Our Simple Model

var Assign{STORES, POOLS} binary;

Service Constraint for each pool:

Max Time to Fill Trailer * sum{prd in PRODUCTS, s in STORES}

CubicFt[prd]*(Demand[prd,s]/DaysPerYear)*Assign[s, pool] >= Cubic Capacity of the Trailer

Max Time to Fill Trailer depends on the Pool:

Service Requirement, e.g., 3 days

Constant Order time, e.g., order processing, picking, etc.

Line haul time from DC to Pool – varies by Pool

Delivery time from Pool to Store

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Which Pools?

• If the Pool is open…– Ensure we get there in reasonable time

• If the Pool is NOT open…– No Time constraint, but – You can’t assign stores to it

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A Simple Modelvar Assign{STORES, POOLS} binary;

Service Constraint for each pool:Max Time to Fill Trailer * sum{prd in PRODUCTS, s in STORES}

CubicFt[prd]*(Demand[prd,s]/DayPerYear)*Assign[s, pool] >= Cubic Capacity of the Trailer*Open[pool]

Assignment Constraint for each store: sum {pool in POOLS} Assign[store, pool] = 1

Logical Constraint for each pool and store: Assign[store, pool] <= Open[pool]

var Open{POOLS} binary;

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Realities

• Silly to include every store-pool pair. Some pools are just too far away.

• Modeling the impacts on delivery costs is more complicated

• Operating fewer, larger pools offers economies of scale, e.g., automation