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{"sheet":"EXAMPLE","index":0,"n_rows":36,"n_cols":17,"rows_kept":36,"merged":[[0,0,0,16],[2,0,2,16]]}
["PERIODIC REVIEW STOCHASTIC INVENTORY MODEL  -  POISSON DEMAND"]
[]
["Bob Agnew, raagnew1@gmail.com, www.raagnew.com"]
[]
["Reference"]
["R. A. Agnew, Inequalities with Application in Retail Inventory Analysis, Journal of Applied Probability, Vol 12, pp 852-858, 1975."]
["Available for download at website above."]
[]
["Inputs & Outputs"]
["Time Units per Year",{"$nulls":3},52,"(assumed weeks)"]
["Inventory Carrying Cost Rate",{"$nulls":3},{"v":0.3,"d":"30%"},"(allows for annual cost of capital, spoilage, and obsolescence)"]
[]
[]
[null,"Mean","Delivery",null,"Expected","$ Unit",null,null,"Marginal",null,null,"Average","Marginal","Average","Average",null,"Average"]
[null,"Demand","Lead","Review","Order","Selling","$ Unit","Markup","Turnover","Optimal","Service","Unit","Turnover","Annual $","Annual $","Average $","Turnover"]
["Item","Rate","Time","Period","Quantity","Price","Cost","Rate","Minimum","OUTL","Level","Inventory","Rate","Sales","Throughput","Inventory","Rate"]
[1,50,3,0.5,{"$f":"B17*D17","v":25},{"v":1,"d":"$1.00"},{"v":0.85,"d":"$0.85"},{"$f":"F17/G17-1","v":{"v":0.17647058823529416,"d":"17.65%"}},{"$f":"$E$11/H17","v":{"v":1.6999999999999995,"d":"1.70"}},{"$f":"POISSON_OUTL($E$10,B17,C17,D17,I17)","v":204},{"$f":"POISSON_SVL(J17,B17,C17,D17)","v":{"v":0.9968272127807587,"d":"99.68%"}},{"$f":"POISSON_AVI(J17,B17,C17,D17)","v":{"v":41.51310330319847,"d":"41.51"}},{"$f":"$E$10*B17*(K17-POISSON_SVL(J17-1,B17,C17,D17))/K17","v":{"v":1.8083972936538077,"d":"1.81"}},{"$f":"F17*$E$10*$B17*$K17","v":{"v":2591.750753229973,"d":"$2,591.75"}},{"v":2202.9881402454766,"d":"$2,202.99"},{"$f":"G17*L17","v":{"v":35.286137807718696,"d":"$35.29"}},{"$f":"O17/P17","v":{"v":62.432112923494344,"d":"62.43"}}]
[2,15,3,0.5,{"$f":"B18*D18","v":7.5},{"v":3,"d":"$3.00"},{"v":2.5,"d":"$2.50"},{"$f":"F18/G18-1","v":{"v":0.19999999999999996,"d":"20.00%"}},{"$f":"$E$11/H18","v":{"v":1.5000000000000002,"d":"1.50"}},69,{"$f":"POISSON_SVL(J18,B18,C18,D18)","v":{"v":0.9947932946281962,"d":"99.48%"}},{"$f":"POISSON_AVI(J18,B18,C18,D18)","v":{"v":20.26128419849352,"d":"20.26"}},{"$f":"$E$10*B18*(K18-POISSON_SVL(J18-1,B18,C18,D18))/K18","v":{"v":1.677178649894849,"d":"1.68"}},{"v":2327.8163094299794,"d":"$2,327.82"},{"v":1939.8469245249826,"d":"$1,939.85"},{"$f":"G18*L18","v":{"v":50.6532104962338,"d":"$50.65"}},{"v":38.29662336347299,"d":"38.30"}]
[3,5,6,1,{"$f":"B19*D19","v":5},{"v":15,"d":"$15.00"},{"v":12,"d":"$12.00"},{"$f":"F19/G19-1","v":{"v":0.25,"d":"25.00%"}},{"$f":"$E$11/H19","v":{"v":1.2,"d":"1.20"}},47,{"$f":"POISSON_SVL(J19,B19,C19,D19)","v":{"v":0.9880097405770426,"d":"98.80%"}},{"$f":"POISSON_AVI(J19,B19,C19,D19)","v":{"v":14.522479369690746,"d":"14.52"}},{"$f":"$E$10*B19*(K19-POISSON_SVL(J19-1,B19,C19,D19))/K19","v":{"v":1.464808488924111,"d":"1.46"}},{"v":3853.237988250466,"d":"$3,853.24"},{"v":3082.5903906003728,"d":"$3,082.59"},{"$f":"G19*L19","v":{"v":174.26975243628897,"d":"$174.27"}},{"v":17.688614045213225,"d":"17.69"}]
[4,1,6,1,{"$f":"B20*D20","v":1},{"v":50,"d":"$50.00"},{"v":30,"d":"$30.00"},{"$f":"F20/G20-1","v":{"v":0.6666666666666667,"d":"66.67%"}},{"$f":"$E$11/H20","v":{"v":0.44999999999999996,"d":"0.45"}},14,{"$f":"POISSON_SVL(J20,B20,C20,D20)","v":{"v":0.9925270880362725,"d":"99.25%"}},{"$f":"POISSON_AVI(J20,B20,C20,D20)","v":{"v":7.505145750123527,"d":"7.51"}},{"$f":"$E$10*B20*(K20-POISSON_SVL(J20-1,B20,C20,D20))/K20","v":{"v":0.4811060666455253,"d":"0.48"}},{"v":2580.5704288943084,"d":"$2,580.57"},{"v":1548.3422573365851,"d":"$1,548.34"},{"$f":"G20*L20","v":{"v":225.1543725037058,"d":"$225.15"}},{"v":6.8768029690878025,"d":"6.88"}]
[5,0.1,8,2,{"$f":"B21*D21","v":0.2},{"v":250,"d":"$250.00"},{"v":125,"d":"$125.00"},{"$f":"F21/G21-1","v":{"v":1,"d":"100.00%"}},{"$f":"$E$11/H21","v":{"v":0.3,"d":"0.30"}},3,{"$f":"POISSON_SVL(J21,B21,C21,D21)","v":{"v":0.9368078850689865,"d":"93.68%"}},{"$f":"POISSON_AVI(J21,B21,C21,D21)","v":{"v":2.1164693798673495,"d":"2.12"}},{"$f":"$E$10*B21*(K21-POISSON_SVL(J21-1,B21,C21,D21))/K21","v":{"v":0.9125124154292862,"d":"0.91"}},{"v":1217.8502505896824,"d":"$1,217.85"},{"v":608.9251252948412,"d":"$608.93"},{"$f":"G21*L21","v":{"v":264.55867248341866,"d":"$264.56"}},{"v":2.301663822164083,"d":"2.30"}]
["Total",{"$nulls":12},{"$f":"SUM(N17:N21)","v":{"v":12571.22573039441,"d":"$12,571.23"}},{"$f":"SUM(O17:O21)","v":{"v":9382.692838002258,"d":"$9,382.69"}},{"$f":"SUM(P17:P21)","v":{"v":749.9221457273659,"d":"$749.92"}},{"v":12.51155588811393,"d":"12.51"}]
[]
[null,"Inputs"]
[null,"Outputs"]
[]
[]
["OUTL  =  Order-Up-To-Level"]
["Policy at a review is to order the positive difference between OUTL and Inventory Position (On Hand + On Order), else zero"]
["Demand is assumed to follow a Poisson Process (one-at-a time random, independent demands)"]
["Simple macro functions are POISSON_OUTL, POISSON_SVL, and POISSON_AVI (Click Alt-F11 to view Visual Basic codes)"]
["Review periods can be adjusted to allow for order quantity minimums (by item or across items)"]
["Can encompass a large number of items within Excel"]
["Can be utilized as an assortment planning tool for staple (limited seasonality) items, everything from shock absorbers to underwear in retail or service parts in wholesale"]
["Can be productionalized for inventory management with simple SKU-level demand rate forecasting/smoothing tools"]
["Calculations can be easily reproduced in an open-source analytical language like Python or R"]