Reasons for holding inventories

1. Economies of scale

   • Production in large batches of items is cheaper

   • Fixed setup costs are amortized over a large number of items

2. Uncertainties

   • Provides a buffer against uncertain demand, lead time, and supply

3. Speculation

   • Anticipation of a rise in their value or cost

4. Transportation

   • Pipeline inventories (transit invenrtories) from one location to another

5. Smoothing

   • Smoothing out an irregular demand pattern

6. Logistics

   • necessary because of the system constraints

7. Control Costs

   • Lower costs for monitoring a system

8. Protection against process errors

   • Coverage of processing irregularities or incidental manufacturing errors

Characteristics of inventory systems

1. Demand

   • Constant vs. variable demand

   • Known vs. random demand

2. Lead Time

   • If items are ordered from outside -> amount of time from order placement until its arrival

   • If items are produced internally -> amount of time required to produce a batch of items

3. Review Time

   • Continuous vs. periodic review

   • Continuous -> inventory level is known at all times

   • Periodic -> inventory level is only known at discrete points in time

4. Excess Demand

   • Demand that can not be filled immediately from stock

   • Backordering of demand vs. lost demand

Relevant costs

Inventory models are mainly use cost minimization as optimization criterion

1. Holding cost (carrying cost, inventory cost)

   • costs proportional to the amount of inventory physically on hand

   • capital cost, storage cost, taxes, insurance, breakage cost, spoilage cost

   • Holding cost (h) per item & time unit

2. Order cost (production cost)

   • costs that depend on the amount of inventory ordered / produced

   • Fixed (setup) cost A + unit-variable cost c

3. Penalty cost (shortage cost, stock-out cost)

   • costs incurred by not having sufficient stock on hand to satisfy a demand when it occurs

   • Loss-of-goodwill cost: Measure of customer satisfaction

     • Backorders: + bookkeeping + delay costs

     • Lost sales: + lost profit

   • Penalty cost (p) per item & time unit

Inventory Management

Two trade offs between cost types

• Setup costs vs. holding costs

• Holding costs vs. penalty costs

• In classical inventory models

  • demand = external

  • e.g., inventory is being acquired & produced to meet the needs of a customer

• Manufacturing environment (multiple level assemblies)

  • demand for certain parts = the result of production schedules for higher-level assemblies

    (in house demand)

  • Production lot-sizing decisions at one level result in demand patterns at other levels

• Terms inventory models (e.g., order size) and lot sizing (e.g., production quantitiy) are used interchangeably

The EOQ Model

(EOQ: Economic order quantity)

• most simple and fundamental inventory model

• trade-off between setup costs and holding costs

Assumptions

• demand rate is known and a constant D units per unit time

• Shortages are not permitted

• No order lead time

• entire order quantity is delivered at the same time

• Q: order quantity

• T: cycle length (the time between two consecutive orders)

• Replenishment takes place when inventory level I(t)= 0 (zero inventory ordering)

• DT: total demand required during T time units

• Q= DT (replenishment takes place when inventory level I(t) = 0 -> demand required during T unit times is ordered)

Decisions

• Order quantity (which amount Q should be ordered?)

• Cycle length (What time T should an order be placed?)

? 100% deviation from optimal order quantity Q* -> only 25% cost increase! -> K(Q) (total costs per unit time) is relatively insensitive to deviations from EOQ for Q