Deriving EOQ Total cost at every cycle T:hTQC=K+2 Average inventory level in a cycle: Q/2· Cycle time T=Q/D Average total cost per unit time:KDhQhTQC/T=(K2292KDQh6
Deriving EOQ • Total cost at every cycle T: • Average inventory level in a cycle: Q/2 • Cycle time T =Q/D • Average total cost per unit time: 2 hTQ C K h KD Q * 2 6 T hTQ C T K )/ 2 / (
EOQ: Costs$160$140$120Total cost$100HoldingcostSO$80$60Ordercost$40$20$o05001,0001,500Q*Orderquantity(numberofunits)FlG 2-4:Economic lot size model:total cost per unit time7
EOQ: Costs FIG 2-4: Economic lot size model: total cost per unit time 7 Q*
SensitivityAnalysisTotal inventory cost is relatively insensitivetoorderquantitiesActual order quantity: QQ is a multiple b of the optimal order quantity Q*For a given b, the quantity ordered is Q = bQ*b2.91.5.81.11.21.5025250.5.48.92.51.6Increaseincost(%)The total cost is minimal when order quantity is Q*Actually the cost increases a little when order quantitychanges
Sensitivity Analysis b .5 .8 .9 1 1.1 1.2 1.5 2 Increase in cost(%) 25 2.5 0.5 0 .4 1.6 8.9 25 Total inventory cost is relatively insensitive to order quantities Actual order quantity: Q Q is a multiple b of the optimal order quantity Q*. For a given b, the quantity ordered is Q = bQ* The total cost is minimal when order quantity is Q*. Actually the cost increases a little when order quantity changes
2.2.2. the Effect of DemandUncertainty on inventory3 rules:.Theforecastis always.It'shard tomatch supplywrongand demand;The longer thePredict demand for a longforecast horizon, theperiod of time?worse theforecastGeographicalaggregation,Aggregateforecastsproductaggregationare more accurate>centralized strategy9
2.2.2. the Effect of Demand Uncertainty on inventory 3 rules: • The forecast is always wrong • The longer the forecast horizon, the worse the forecast • Aggregate forecasts are more accurate. 9 • It’s hard to match supply and demand; • Predict demand for a long period of time? • Geographical aggregation, product aggregation centralized strategy