lect9 - Inventory Management Time Varying Demand Fixed...

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Inventory Management Time Varying Demand Fixed Planning Horizon Chris Caplice ESD.260/15.770/1.260 Logistics Systems Oct 2006
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© Chris Caplice, MIT 2 MIT Center for Transportation & Logistics – ESD.260 Demand ± Constant vs Variable ± Known vs Random ± Continuous vs Discrete Lead time ± Instantaneous ± Constant or Variable (deterministic/stochastic) Dependence of items ± Independent ± Correlated ± Indentured Review Time ± Continuous ± Periodic Number of Echelons ± One ± Multi (>1) Capacity / Resources ± Unlimited ± Limited / Constrained Discounts ± None ± All Units or Incremental Excess Demand ± None ± All orders are backordered ± Lost orders ± Substitution Perishability ± None ± Uniform with time Planning Horizon ± Single Period ± Finite Period ± Infinite Number of Items ± One ± Many Form of Product ± Single Stage ± Multi-Stage Assumptions: Basic FPH Model
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© Chris Caplice, MIT 3 MIT Center for Transportation & Logistics – ESD.260 Example 0 50 100 150 200 250 300 Demand 123456789 1 0 1 1 1 2 Month When should I order and for how much? More Assumptions Demand is required and consumed on first day of the period • Holding costs are not charged on items used in that period • Holding costs are charged for inventory ordered in advance of need Costs D = 2000 items per year A = $500.00 per order v = $50.00 per item r = 24% per item per year C hm = rv/N = 1 $/month/item N = number of periods per year
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© Chris Caplice, MIT 4 MIT Center for Transportation & Logistics – ESD.260 Methods Used Different Approaches 1. Simple Heuristics ± The One-Time Buy ± Lot For Lot ± Fixed Order Quantity (FOQ) ± Periodic Order Quantity (POQ) 2. Optimal Procedures ± Wagner-Whitin (Dynamic Programming) ± Mixed Integer Programming 3. Specialty Heuristics ± The Silver Meal Algorithm ± Least Unit Cost (LUC) ± Part-Period Balancing (PPB)
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© Chris Caplice, MIT 5 MIT Center for Transportation & Logistics – ESD.260 Simple Heuristics One Time Buy Lot for Lot Fixed Economic Order Quantity Periodic Order Quantity
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© Chris Caplice, MIT 6 MIT Center for Transportation & Logistics – ESD.260 Approach: One-Time Buy 0 200 400 600 800 1000 1200 1400 1600 1800 2000 On Hand Inventory 123456789 1 0 1 1 1 2 Month 2000 Policy Buy D at time 0 0 50 100 150 200 250 300 Demand 1234567891 01 11 2 Month
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© Chris Caplice, MIT 7 MIT Center for Transportation & Logistics – ESD.260 Month Demand Order Quantity Holding Cost Ordering Cost Period Costs 1 200 2000 $1800 $500 $2300 2 150 0 $1650 $0 $1650 3 100 0 $1550 $0 $1550 4 50 0 $1500 $0 $1500 5 50 0 $1450 $0 $1450 6 100 0 $1300 $0 $1300 7 150 0 $1200 $0 $1200 8 200 0 $1000 $0 $1000 9 200 0 $800 $0 $800 10 250 0 $550 $0 $550 11 300 0 $250 $0 $250 12 250 0 $0 $0 $0 Totals: 2000 2000 $13100 $500 $13600 Approach: One-Time Buy
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© Chris Caplice, MIT 8 MIT Center for Transportation & Logistics – ESD.260 0 200 400 600 800 1000 1200 1400 1600 1800 2000 On Hand Inventory 123456789 1 0 1 1 1 2 Month Approach: Lot for Lot 300 250 200 250 150 200 50 100 100 50 200 150 Policy Buy D(t) at time t 0 50 100 150 200 250 300 Demand 1234567891 01 11 2 Month
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© Chris Caplice, MIT 9 MIT Center for Transportation & Logistics – ESD.260 Month Demand Order Quantity Holding Cost Ordering Cost Period Costs 1 200 200 $0 $500 $500 2 150 150 $0 $500 $500 3 100 100 $0 $500 $500 4 50 50 $0 $500 $500 5 50 50 $0 $500 $500 6 100 100 $0 $500 $500 7 150 150 $0 $500 $500 8 200 200 $0 $500 $500 9 200 200 $0 $500 $500 10 250 250 $0 $500 $500 11 300 300 $0 $500 $500 12 250 250 $0 $500 $500 Totals: 2000 2000 $0 $6000 $6000 Approach: Lot for Lot
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lect9 - Inventory Management Time Varying Demand Fixed...

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