Forecasting, Ordering and Stock- Holding for Erratic Demand

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1 ISF rd o 26 h June 2002 Forecasing, Ordering and Sock- Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied

2 Inroducion Erraic and slow-moving demand Demand classificaion Spare pars invenory example Forecasing erraic demand Croson s mehod Modified mehods Means of comparison Forecas performance Implied sock-holdings Conclusions and quesions 2

3 Erraic and Slow-Moving Demand Erraic, or inermien, demand has infrequen ransacions wih variable demand sizes; ofen caused by: Many small cusomers and a few large Variaions magnified by muli-echelon sysem Correlaion beween cusomer requess Sympaheic replacemen of pars Aggregaion, or buckeing, of demand Slow-moving demand has infrequen ransacions wih low demand sizes. Common mehods for forecasing and sock-holding less effecive if demand no smooh and coninuous. 3

4 Demand Classificaion Lead-Time Demand Componen Transacion Variabiliy Demand Size Variabiliy Lead-Time Variabiliy Demand Paern Low Low Smooh Low Irregular Low Slow-moving Low Mildly Erraic ly Erraic Uilises an analyical mehod for classifying demand. Wha consiues Low and values are peculiar o he individual invenory. 4

5 Spare Pars Invenory Example Royal Air Force (RAF) invenory 684,000 consumable pars (or SKUs) 145 million unis of sock Toal value of 2.1 billion sock-holdings In case of war and disrupion o supply chain Long and variable replenishmen lead-imes procuremen cos afer iniial provisioning Low relaive cos of holding sock Demand over six years Demand Transacions 0 1 o 9 10 o Percenage of Line Iems 40.5% 37.3% 18.6% 3.5% Average Demand Size

6 Forecasing Erraic Demand Exponenial smoohing (ES) ofen used in realiy, bu Forecas highes afer a demand As order level broken by a demand occurrence here is a endency for unnecessarily high socks. Croson s mehod provides an alernaive Separaely applies ES o inerval beween demand and size of demands Only updaes if demand occurs y = demand for an iem a ime p = mean inerval beween ransacions z = mean demand size ŷ = mean demand per period (he forecas) q = ime inerval since las demand α = smoohing consan 6

7 Croson s Mehod If y = 0 hen p = p -1 z = z -1 q= q + 1 Else p = p -1 + α(q - p -1 ) z = z -1 + α(y -z -1 ) q = 1 Size and inerval combine as ŷ = z / p Croson s mehod reduces bias of ES bu does no eliminae i compleely. 7

8 Modified Mehods Syneos and Boylan (2001) seek o remove hisorical bias from he forecas. Revised Croson s mehod: yˆ = z p 1 c p 1 where c is an arbirarily large consan. Bias Reducion Mehod yˆ z α z 2 α ( p 1) p = 2 p Approximaion Mehod yˆ α = 1 2 z p 8

9 Means of Comparison Choice of radiional measures of forecas performance such as MAD, MSE, MAPE and MdAPE Choice of comparison beween acual value and forecas value One-period ahead demand Lead-ime demand in all periods Lead-ime demand in periods of demand only In a real seing i is demand over a leadime ha mus be caered for, herefore sensible o measure performance over his period. Replenishmen order is only placed afer a demand occurrence, herefore accurae forecas required a his ime. 9

10 Forecas Performance Using 18,750 line iems wih equal demand paern represenaion, resuls vary and no single mehod emerges as bes: Croson s mehod performs well for one-period ahead demand, paricularly wih weekly daa. ES compleely dominaes for lead-ime demand in all periods. Croson s mehod good for lead-ime demand in periods of demand only wih quarerly daa; simple previous year average mehod bes for monhly and weekly daa. Approximaion mehod consisenly beer han Croson s mehod bu no as good as ES for lead-ime demand in all periods. Differen conclusions arise depending on which measure is uilised an alernaive measure is required! 10

11 Implied Sock-Holdings Compare he average implied sockholdings from each forecasing mehod using common service level of 100 percen. Use back-simulaion o calculae exac safey margin ha gives a sock-ou quaniy of zero. More accurae forecasing require less sock. Able o aribue moneary coss o differences in accuracy Key invenory performance measure. Easily undersandable resuls. Approximaion mehod allows lowes sock-holdings across all demand paerns, wih greaes improvemens occurring wih erraic and slow-moving demand. 11

12 Conclusions Erraic and slow-moving demand common in spare pars invenories. ES ofen used for forecasing alhough Croson s mehod receiving increasing aenion. Recen modificaions o Croson s mehod provide viable alernaives. Opimal smoohing consan(s) can be obained from a hold-ou sample. Approximaion mehod provides bes resuls when assessed using implied sock-holdings - a key performance measure in he real world. 12

13 Furher Informaion Any quesions - now or laer? Andrew Eaves, Andalus Soluions Ld, 38 Salram Road, Farnborough, Hampshire GU14 7DX, England Telephone +44 (0) , [email protected] or visi hp:// I hope you enjoy he res of ISF