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ISyE 6203Modeling

Multi-DC version of Pooling

John H. Vande Vate

Spring 2012

Challenge 8• Challenge 8. With the consolidation point fixed in Indianapolis, use the simple

version of the ALT heuristic in which each store is assigned to the closest pool point, to determine how delivery cost changes with changing numbers of pool points. So, for each different number of pool points, determine the best locations and assignments to minimize delivery distance, plot the locations on a map and graph the curve of delivery cost as a function of the number of pools.

Select a single number n of pool points to base your further analysis on. For the configuration with n pools, estimate the total annual transportation costs,

including:– line haul from the plants to the consolidation point in Indianapolis (using the EPQ) – line haul from the consolidation point to the pools (using truck load rates and weekly

shipments) – delivery to the stores using $1.75 per mile times the distance between the pool point

and the store as the cost of a delivery – and complete a financial statement (i.e., estimate the inventories inherent in this

system)– Note that our analysis of where to locate pools and how to assign the stores to them did

not consider the line haul costs and so we are likely to see glaring problems with the configuration we chose. Highlight these. The point is that our more complex model would address the line haul costs and so would avoid such glaring problems.

Est. Delivery Cost

$-

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

0 2 4 6 8 10 12

1 Pool – Winona, Mo

Breeding, KY & Ridgecrest, CA

3 - Pools

• Artie, WV

• California Hot Springs, CA

• Achille, OK

4 Pools

• Alberta, VA• California Hot Springs, CA• Badgersville, IN• Waxahachie, TX

5 - Pools

• Philadelphi, PA• California Hot Springs, CA• Winamac, IN• Red Oak, TX• Davidsboro, GA

6 Pools

7 Pools

8 Pools

9 Pools

10 Pools

Financials

• I’ll do this for 10 pools• Transport

– Delivery: • Weekly delivery is $26,727• Annual delivery is $1.39 million

– Line Haul to Pools• Ideally, we would like about 10 stores per pool as that would mean

27,500 lbs per week• But our answer (which didn’t consider this aspect) has from 3 to 18

stores assigned to a pool• Compute weekly weight, translate into weekly trucks, compute distance

and annual line haul cost• $674K

– Line Haul to Indianapolis• Use EPQ• We did this $247K from Denver, $68K from Green Bay

– Total Transport $2.38 million

Inventories

• At Green Bay – from EPQ $186K

• At Denver – from EPQ $50

• At each store– Half of a week of sales– $30K

• At the Indianapolis Consolidation Point– Receiving: $236K (Green Bay + Denver)– Shipping:?

Indianapolis Shipping• Demand weighted average shipment size• We can use # of stores for the demand weighting (since

all stores are the same)• For those Pools receiving more than one truck, assume we

split the load (half the stores on each truck)• Weighted Average Shipment Size

– 20941 lbs

• Value density of freight– $1200/55 = $21.82/lb

• Value of Average Shipment– $457K

• Cycle Inventory at Indianapolis Shipping– $228K

Pipeline• Consider rate $ flow on each leg and time they spend in transit• Example: Indianapolis to Pool 1

– 10 stores translates to annual sales of $30 million (at component costs)– That’s $82K per day– The line haul is 640 miles or 1.28 days of travel– So there’s 1.28 days * $82K/day in the pipe – $105K in pipeline inventory on this leg

• Total over the legs– $1.35 million

• Average delivery distance is 200 miles or .4 days– $332K in pipeline inventory in delivery

• From Green Bay– $75 million in annual value and 0.68 days in transit– $140K in pipeline Inv

• From Denver– $25 million in annual value and 1.98 days in transit– $135K in pipeline inv.

Financial Performance• Transport

– Delivery $1.39 million– Line Haul to Pools $0.67 million– Line Haul to Ind. $0.36 million– Total $2.38 million

• Inventory– Stores $3 million– Indianapolis

• Receiving $0.236 million• Shipping $0.228 million• Total $0.464 million

– Plants $0.236 million– Pipeline $1.96 million– Total $5.661 million

Summary • Direct Full Truckloads

– $158 million in inventory– $435 thousand in transportation

• Single EOQ to All Stores– $15.8 million in inventory– $2.48 million in transportation

• Different EOQ shipments– $15.2 million in inventory– $2.47 million in transportation

• Simple TL Consolidation – $36.9 million in inventory– $654 thousand in transportation

• Pools and Consolidation

– $5.661 million in inventory– $2.38 million in transportation

Summary • Direct Full Truckloads

– Gross Margin %: 32.9%– ROIC 22.9%– SPEED 1.08– Days in Inventory: 191

• Single EOQ to All Stores– Gross Margin %: 32.5%– ROIC 33.5%– SPEED 1.65– Days in Inventory: 19

• Different EOQ shipments– Gross Margin %: 32.5%– ROIC 33.6%– SPEED 1.65– Days in Inventory: 18

• Simple TL Consolidation – Gross Margin %: 32.9%– ROIC: 31.7%– SPEED: 1.53– Days in Inventory: 45

• Pools & Consolidation– Gross Margin %: 32.5%– ROIC: 34.8%– Speed: 1.71– Days in Inventory: 7

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Context

• Two cross docks– Indianapolis– Denver

• Distribute to our 100 stores from these via Pool points

Assumptions• Demand(prod, store) instead of all stores being the same• Can handle TVs and Computers differently

– TVs assembled in Denver– Computers in Indianapolis– So a pool might get computers from Indianapolis and TVs from

Denver• Single Sourcing

– At the Stores – everything from one Pool– At the Pool

• All of a product from one cross dock• Simple approximation for delivery

– Delivery cost/mile and distance from pool to store• Truck load rates from cross docks to Pools• Prescribed frequency of deliveries • Full truckload shipments from plants to cross docks

What’s different?• Assign a store to a pool

– Assign(store, pool) = 1 if store is assigned to pool• Assign a pool to a cross dock for a product

– Source(prod, cd, pool) = 1 if pool gets prod from cd

• Have to figure out how much of each component we need at each cross dock

• Depends on which pools are assigned to it for which products and which stores are assigned to those pools

• How to model this?

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Variables

• Assign(store, pool) = 1 if we assign the store to the pool

• Source(prod, cd, pool) = 1 if the pool sources the sku from the cd

• Open(pool) = 1 if we open the pool

Path Variables

• To help us determine the requirements at each cross dock,

• Path(prod, cd, pool, store) = 1 if store gets prod from cd via pool

• Path strings together Assign and Source

Demand at the Cross Dock

• Data:– Recipe(prod, comp) = how many units of

comp are needed to make one prod

• How much prod do we ship out of cd?

• This only works because only one pool serves each store

),(*),,,( storeprodDemandstorepoolcdprodPathstorespools

Demand at the Cross Dock

• How much comp do we need at cd?• Amount of prod we ship out

• Translates into comp required

),(*),,,( storeprodDemandstorepoolcdprodPathstorespools

prod storespools

storeprodDemandstorepoolcdprodPathcompprodcipe ),(*),,,(*),(Re

Single Sourcing

• At stores: For each store

• At Pools: For each pool and prod

pools

poolstoreAssign 1),(

crossdocks

poolOpenpoolcdprodSource )(),,(

What else?

• Trucks from plants to cross docks (this can be fractional)

• Trucks from cross docks to pools as before (should be integral)

• Delivery Costs and Line haul costs

• Inventory costs

Is that it?• No!• Implied logical relationship among the variables

Assign, Source and Path, Open,• We have to enforce that relationship otherwise, • Open(pool) = 0 for each pool• Path(prod, cd, pool, store) = 0 for each prod, cd, pool,

store so there’s no demand for components at the cross docks and no transportation from the plants

• Assign each store to the closest pool• For each pool, source each prod from the closest cross

dock

What are the logical relationships

• Store can’t get prod from any dc via pool if store is not assigned to pool

• That only works because we single source at the store and at the pool

),(),,,( poolstoreAssignstorepoolcdprodPathcrossdocks

What are the logical relationships• Store can’t get prod from cd via pool if the pool

doesn’t get prod from the cd

• Is there more we can say?• Yes!• Path(prod, cd, pool, store) = 1 if and only if

Assign(store,pool) = 1 ANDSource(prod, cd, pool) = 1

• We’ve enforced “only if”

),,(),,,( poolcdprodSourcestorepoolcdprodPath

AND

• General Form– X binary

– Yi binary i = 1, 2, …n

• X = AND(Yi, i = 1, 2, …n)

• X ≤ Yi for each i = 1, 2, …n (only if)

• n-1 Y1 + Y2 + Y3 … + Yn - X (if)

“If”

• If store is assigned to pool AND pool gets prod from cd THENstore gets prod from cd via pool

• Assign(store, pool) + Source(prod, cd, pool) - Path(prod, cd, pool, store) ≤ 1

“Review/Clarifications”

• Cross Dock/Consolidation Point

• “Cross Dock” typically means no permanent inventory, just WIP

• So we should use “Consolidation Point” for our operations at Indianapolis and “Cross Dock” for our pool points

In-Bound Consolidation• I used the example of the “Parks & Resorts” company

to against LTL consolidation of in-bound flows• There certainly is consolidation of in-bound flows

– Consolidation of internationally sourced components or supplies, i.e.,

• BMW consolidates in Wackersdorf• PSA in Normandy or central France• Retailers consolidate in Asia

– Consolidation of returns/recycling• Newgistics• Genco

– These all involve secure infrastructure for accumulating inventory

Thursday

• I plan to review some old exam questions

• Bring questions of your own

• Last chance before mid-term