Supply Chain and Logistics
This domain concerns the flow of material, information, and money across firms, and the inventory math that supports it.
Inventory
EOQ balances ordering and holding costs and assumes constant demand, known lead time, and no shortages: total cost = (D/Q)S + (Q/2)H. Reorder point = demand during lead time + safety stock. Safety stock = zσ; when both demand and lead time vary, combine variances as σ_dLT = √(L·σ_d² + d²·σ_L²). Common service-level z values: 90% = 1.28, 95% = 1.645, 99% = 2.33. ABC analysis puts tight control on the few high-value A items. For a single-season item, the newsvendor critical ratio is Cu/(Cu + Co), and the order quantity is the one where P(demand ≤ Q) equals that ratio.
Networks and logistics
Bullwhip amplification comes from forecast updating, order batching, price promotion, and rationing; it is damped by sharing point-of-sale data, shorter lead times, and vendor-managed inventory. Transportation modes: rail for bulk at low cost, truck for flexible door-to-door service, air for speed at high cost, water for the slowest and cheapest bulk movement, pipeline for liquids and gases. Total landed cost includes freight, duties, carrying cost, and risk - not just unit price. Cross-docking and postponement cut both inventory and lead time. Incoterms allocate cost and risk between buyer and seller (FOB, CIF, DDP).
Traps
Using average demand instead of demand during lead time in a reorder point; ignoring lead-time variability; applying EOQ without checking price breaks; confusing pipeline inventory with cycle stock.
Worked example
Daily demand 200, lead time 5 days, σ_d = 20, 95% service level: ROP = 200(5) + 1.645(20)√5 ≈ 1,000 + 73.6 ≈ 1,074 units.