This lecture extends the production-consumption inventory model to allow for backordering, where demand can be unfulfilled temporarily. The model incorporates three cost components: setup costs for initiating production, inventory holding costs for items stored, and backorder costs for unmet demand. A key theoretical result derives the optimal production quantity and backorder level that minimize total system cost by balancing the tradeoff between holding excess inventory and incurring shortage penalties. Table of Contents: • Production-consumption model foundation: production rate P vs. demand rate D • Backordering mechanism: permitting unfulfilled demand with associated costs • Cost structure: setup cost C₀, holding cost Cc, and backorder cost Cs • Inventory dynamics during production, consumption, and stockout phases • Mathematical formulation: cost minimization over production quantity Q and backorder level s • Optimization solution: partial differentiation yielding optimal Q and s formulas • Key formula: Q = √(2DC₀(Cc+Cs)/(Cc·Cs(1-D/P))) • Numerical analysis showing cost reduction when backordering is allowed versus prohibited • Practical constraint: accuracy of backorder cost estimation critical for model applicability • Relationship between inventory buildup rate (P-D) and consumption rate during depletion
This lecture extends the production-consumption inventory model to allow for backordering, where demand can be unfulfilled temporarily. The model incorporates three cost components: setup costs for i…