Use More Soap Building Supply Chain Models Fixed Costs Aggregation Transportation Costs Inventory Costs Basic Model Building

Fixed Costs Capital costs Operating costs Investments in depreciable assets buildings equipment patents Operating costs Recurring expenses labor rent fuel

Different Animals $4,000,000 to expand a plant Annual operating expenses Handling costs Transportation costs Ordering costs Do not mix

Cost of Capital Use Cost of Capital Careful about “fixed” costs Opportunity Cost Financing Cost, etc. Careful about “fixed” costs

Aggregation Aggregating Products Families or baskets Products with similar characteristics

Aggregating Customers By segment Commercial Consumer etc. Geographically Census Tract ZIP Code 3-digit ZIP State Territory

Calculating Transport Costs Regression against past costs Depend on Distance Location Order size!

Calculating Transport Costs Regression against past costs Depend on Distance Location Order size!

A Classic Trap Aggregating Large and Small Customers Total Cost Average Shipment Large Shipment Small Shipment Shipment Size

A Classic Trap Aggregating Large and Small Customers Cost of Average Shipment Total Cost Average Cost of Shipment Average Shipment Large Shipment Small Shipment Shipment Size

Aggregate Transport Costs Average of shipment costs Not cost of average shipment

What Problems? Changing Channels Must re-cost many shipments and average Easier to Cost a single average shipment

Inventory Typical Model Pull Model Inventory grows as sqrt of Throughput Pull Model Inventory depends on Shipment sizes Number of channels

Modeling Traditional Inventory Throughput

Approximating the curve Requires integer variables to force solver to take all the expensive Rapid Increase before any of the inexpensive Slow Increase Inventory Rapid Increase Slow Increase Break Throughput Max

How that works Throughput = CWT of throughput Rapid = CWT of throughput incurring high inventory cost (up to Break) Slow = CWT of throughput beyond Break incurring low inventory cost IsRapidFull = Binary variable indicating which region we are in IsRapidFull = 0 means Throughput is less than Break IsRapidFull = 1 means Throughput is more

Constraints Throughput = Slow + Rapid Rapid <= Break Rapid >= Break*IsRapidFull Slow <= (Max-Break)*IsRapidFull Cost = High Cost * Rapid + Low Cost * Slow

Modeling Pull Inventory Count the number of Channels Need Integer Variable for each channel IsChannelUsed = 1 if used, 0 otherwise Volume on Channel <= IsChannelUsed*Bound The smaller the bound, the better this works (typically).

Reality Probably some combination “Safety Stock” increases with additional distribution centers More smaller centers = more safety stock Quadratic relationship Pull inventory depends on channels and modes