Logistics Systems Analysis Mid-Term Review John H. Vande Vate Spring, 2001 1

Subjects Covered Supply Chain Costs EOQ Holding Moving Waiting Rent Moving Handling Transport EOQ Trade off Holding and Moving Costs cQ + d/Q minimized with Q = d/c 2

Subjects Covered Project Inventory Analysis Modeling At the Plant Shipments of size Q to DC Inventory at plant per shipment: (Q/2)*(Q/P) Shipments per year: D/Q Total Inventory: (Q/2)*(D/P) + Q/2 EOQ: minimize fD/Q + h(Q/2)*(1+D/P) Q* = (2fD/h)P/(P+D) 3

Project Inventory Analysis Plant to Warehouse Inventory at plant per shipment: (Q/2)(Q/P) Shipments per year: unknown Shipments generated by DC served through warehouse: D/Q Total Plant inventory per DC served through warehouse: (Q/2)(D/P) EOQ to warehouse: Q* = (2fDw/h)P/(P+Dw) but what’s Dw? 4

Warehouse Inventory Inbound Outbound Q/2 from each plant that serves it Outbound “Option” or mix of items shipped together Total Demand at warehouse for Assembly: DO “Production Rate” of Option at Warehouse: DO Inventory per shipment to DC: (Q/2)(Q/DO) Shipments per year: D/Q EOQ: min fD/Q + h(Q/2)(1 + D/DO) Q* = (2fD/h)DO/(DO +D) but what’s DO? 5

Outbound Inventory to DC Inventory per shipment to DC: (Q/2)(Q/DO) Shipments per year: D/Q Inventory per year: (Q/2)(D/DO) if served with this option DO= Sum of Demands at DC’s served with this option If Shipment size Q for this option is relatively constant across the DC’s Total Outbound Inventory Cost for the Option is (average Q/2)*[Do we serve any DC with this option?] 6

Modeling “Rules” Use meaningful (helpful) names Comment extensively Keep data and model separate Keep model general where possible 7

“Finance” Capital Utilization influences financial performance Total Capital influences Capital Utilization Inventory Levels contribute to Capital Cash-to-Cash Cycle influences Capital Value of Inventory Savings 8

H(t) = (2Fixed/cD’(t)) 1-1 Distribution Extension of EOQ to variable demand Simple formula for headways: H(t) = (2Fixed/cD’(t)) Estimate of Total Cost Reconstructing implementable headways 9

Models for Variable Demand Correct Models Relate decision whether or not to ship with volume shipped Q[t]  Ship[t]*Remaining Demand Better Models Do not aggregate constraints Q[s, t]  Ship[s]*Demand in Period t 10

Location Different Objectives Two varieties of models Item-miles miles max distance … Two varieties of models Do we locate here or not? What is the position of the facility? 11

Location Measures of Distance Rectilinear Euclidean Iterative scheme for locating a single facility using Euclidean Distances Extension to locating several facilities Locate Allocate 12