Inventory Control
Lecture Topics • Week 1 Introduction to Production Planning and Inventory Control • Week 2 Inventory Control – Deterministic Demand • Week 3 Inventory Control – Stochastic Demand • Week 4 Inventory Control – Stochastic Demand • Week 5 Inventory Control – Stochastic Demand • Week 6 Inventory Control – Time Varying Demand • Week 7 Inventory Control – Multiple Echelons
Lecture Topics (Continued…) • Week 8 Production Planning and Scheduling • Week 9 Production Planning and Scheduling • Week 12 Managing Manufacturing Operations • Week 13 Managing Manufacturing Operations • Week 14 Managing Manufacturing Operations • Week 10 Demand Forecasting • Week 11 Demand Forecasting • Week 15 Project Presentations
Inventory in the US Economy $98.60 billion $122.10 Farm billion (7.9%) Other (9.8% $424.60 billion Manufacturing (33.9%) $290.40 billion Wholesale (23.2%) $316.00 billion Retail (25.2%)
Inventory Types
Inventory Types • Raw Materials • Work-in-process (WIP) • Finished goods inventory (FGI)
Inventory Location
Inventory Location • Manufacturing Facility • In-Transit • Warehouse • Retailer • Customer
Benefits of Inventory
Benefits of Inventory • Reduces ordering, setup & transportation costs (economies of scale) • Buffer against demand fluctuations • Buffer against supply fluctuations • Supply shortages • Variability in supply lead times
Benefits of Inventory (continued…) • Buffer against price fluctuations • Benefits from quantity discounts • Protects production capacity • Allows production smoothing • Reduces managerial complexity (eliminates the need for coordination) • Can increase demand
The Cost of Inventory
The Cost of Inventory • Tied up capital • Warehousing cost • Deterioration • Obsolescence • Demand shortfall • Quality defects • Changes in raw material prices • Changes in product design specifications
What if demand uncertainty and variability are eliminated?
What if demand uncertainty and variability are eliminated? • What if replenishment lead times are made insignificant?
What if demand uncertainty and variability are eliminated? • What if replenishment lead times are made insignificant? • What if ordering & setup costs are made negligible?
What if demand uncertainty and variability are eliminated? • What if replenishment lead times are made insignificant? • What if ordering & setup costs are made negligible? • What if production capacity is never a constraint?
Characteristics of Inventory Systems • Demand • Constant • Time varying • Stochastic • Supply lead time • Deterministic • Stochastic • Load-dependent • Review • Continuous review • Periodic review
Characteristics of Inventory Systems (continued…) • Excess Demand • Backordering • Lost sales • Impatient customers • Item substitution • Capacity • Unlimited • Limited • Deterministic • Stochastic
Characteristics of Inventory Systems (continued…) • Number of items & customer classes • Single item • Multiple items • Single customer class • Multiple customer classes • Inventory quality • Perishability • Obsolescence • Imperfect yield
Cost Measures • Holding cost (h) • Capital cost • Taxes and insurance • Deterioration, spoilage, obsolescence • Ordering (setup) cost (A) • Purchasing (production) costs (c) • Shortage cost (p) • backordering cost • lost sale cost
Example • h = ic (cost per unit per time period) • 28% = cost of capital • 2% = taxes and insurance • 6% = storage cost • 1% = breakage cost • 37% = total interest charge (i) per year • If c = $100, then h = ic = $37
The Economic Order Quantity (EOQ) Model
Assumptions of the Basic Model • Demand occurs continuously over time with a constant rate • Inventory can be replenished instantaneously • There are no capacity limits or limits on the size of replenishment orders • A replenishment order incurs a fixed ordering (or setup) cost • Multiple products can be analyzed independently of each other • No backorders are allowed
Notation • D: demand rate (units per unit time) • c: unit purchase/production cost (dollars per unit) • A: fixed cost to place an order (dollars) • h: holding cost (dollars per unit per unit time); if the holding cost consists entirely of interest on money tied up in inventory, then h=ic where i is an interest rate. • Q: the size of the order (a decision variable)
Inventory versus Time Q Inventory Time
Inventory versus Time Q Inventory Q/D 2Q/D 3Q/D 4Q/D Time
Costs • Holding cost:
Costs • Holding cost: • Ordering/setup cost:
Costs • Holding cost: • Ordering/setup cost: • Production cost: c per unit
Total Cost • Total cost per unit time:
Total Cost • Total cost per unit time: • Total cost per unit:
Economic Order Quantity hQ/2 Y(Q) AD/Q Q
The Economic Order Quantity
The Economic Order Quantity
Optimal Cost • Optimal average cost per unit: • Optimal average cost per unit time (e.g., per year):
Sensitivity to Order Quantity • Ordering and holding cost from using Q’: • Ratio
Sensitivity to Order Quantity • Ordering and holding cost from using Q’: • Ratio • Example • Q' = 2Q*, then the ratio of the actual to optimal cost is (1/2)[2 + (1/2)] = 1.25
Sensitivity to Order Quantity Large deviations from the optimal order quantity lead to relatively small deviations from the optimal cost.
Order Quantity versus Order Interval • Order Interval: Let T represent time between orders, then • Total cost: • Optimal Order Interval:
Some Limitations of the EOQ Model • Demand is deterministic and constant • Instantaneous replenishments • Ordering costs are constant and independent of order size • No accounting for interactions among multiple items • No backordering
Extensions • Non-zero order replenishment lead times • Non-zero safety stocks • Finite supply capacity • Backordering
Non-Zero Replenishment Lead Times
Non-Zero Replenishment Lead Times • If L is the lead time and r is the reorder point, then r = DL • A non-zero lead time has no effect on Q* or Y(Q)
Non-Zero Safety Stocks • If ss is the safety stock, then • A non-zero safety stock affects Y(Q) but has no effect on Q*
