Comparison Of Wagner-Whitin with other lot sizing techniques

lot sizingLot SizingReduce Costs (Inventory, Setup).

Adequate level of raw material available in the inventory.

Helps in plan the manufacturing and purchasing activities.

Meeting the demand timely.

Managing Capacity.

LOT SIZING TECHNIQUESLot for LotBulkEOQPOQPart Period Balancing (PPB)Least Unit CostSilver Meal (Minimum Cost per Period)Wagner-Whitin algorithmLeast Total CostMcLaren Order Moment (MOM)Groffs algorithmFreeland & Colley method

Lot for LotPeriod12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand3535000000000Net Requirement03040010403003055Planned Order Receipt 30401040303055Planned Order Release30401040303055Total Cost = Setups + holdingSetups = 7 costing $700Holding = 0Holding Cost = $1 per week/unitSetup cost = $100 per setupLead Time =1 weekBulkTotal Cost = Setups + holdingSetups = 1 costing $100Holding = 1030 x $1 = $1030TOTAL= $1130Period12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand35350205165165155115858555Net Requirement03000000000Planned Order Receipt 235Planned Order Release235Holding Cost = $1 per week/unitSetup cost = $100 per setupLead Time =1 weekEOQ Economic Order QuantityPeriod12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand3535043336626696939Net Requirement030007040016Planned Order Receipt 73737373Planned Order Release73737373Total Cost = Setups + holdingSetups = 4 costing $400Holding = 318 x $1 = $318TOTAL= $718POQ Periodic Order QuantityPeriod12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand353504000703008555Net Requirement030001000000Planned Order Receipt 708085Planned Order Release708085Total Cost = Setups + holdingSetups = 3 costing $300Holding = 280 x $1 = $280TOTAL= $580POQ = EOQ dWhere d = D average demand or demand rate 52From previous example POQ = 73 = 2.7 3 27 PPB Part Period BalancingEconomic Part Period = Setup = 100 Holding CostWhere Setup = cost of 1 setup Holding Cost = Cost per unit per weekPeriods CombinedTotal Lot SizePart Periods ($)Costs ($)SetupHoldingTotal230010001002,37040x1100401402,3,47040x1 + 0x2100401402,3,4,58040x1 + 0x2 + 10x3100701702,3,4,5,612040x1 + 0x2 +10x3 + 40x4100230330Select 2-5. Part period of $70, for periods 2-5 is as close to EPP as we can get640010001006,77030x1100301306,7,87030x1 + 0x2100301306,7,8,910030x1 + 0x2 + 30x3100120220Select 6-9. Part period of $120, for periods 6-9 is as close to EPP as we can get105501000100Select part periods that are closest to the EPP valuePeriod12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand3535050101006030300Net Requirement0300004000055Planned Order Receipt 8010055Planned Order Release8010055Total Cost = Setups + holdingSetups = 3 costing $300Holding = $190TOTAL= $ 490PPB Part Period BalancingLeast Unit CostTotal Cost Per unit =

Periods CombinedTotal Lot SizePart Periods ($)Costs ($)Cost per unit = Total/lot sizeSetupHoldingTotal230010001003.332,37040x11004014022,3,47040x1 + 0x21004014022,3,4,58040x1 + 0x2 + 10x3100701702.125Select 2-4. Cost per unit is least for periods 2-451001000100105,65040x1100401402.85,6,78040x1 + 30x21001002002.55,6,7,88040x1 + 30x2 + 0x31001002002.55,6,7,8,911040x1 + 30x2 + 0x3 + 30x41002203202.9Select 5-8. Cost per unit is least for periods 5-8930010001003.339,108555x1100551551.82Select that cost where per unit cost is lowestPeriod12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand35350400070300055Net Requirement0300010000300Planned Order Receipt 708085Planned Order Release708085Total Cost = Setups + holdingSetups = 3 costing $300Holding = 195 x $1 = $195TOTAL= $495Least Unit CostSilver Meal Algorithm (Minimum Cost per Period)Cost Per Period =Periods Combined# of periodTotal Lot SizePart Periods ($)Costs ($)Cost per period = Total cost / periodsSetupHoldingTotal2130010001001002,327040x110040140702,3,437040x1 + 0x21004014046.662,3,4,548040x1 + 0x2 + 10x31007017042.52,3,4,5,6512040x1 + 0x2 + 10x3 + 40x410023033066Select 2-5. Cost per period is least for periods 2-56140010001001006,727030x110030130656,7,837030x1 + 0x21003013043.336,7,8,9410030x1 + 0x2 + 30x310012022055Select 6-8. Cost per period is least for periods 6-89130010001001009,1028555x11005515577.5Select that cost where per unit cost is lowestPeriod12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand353505010100300055Net Requirement0300004000300Planned Order Receipt 807085Planned Order Release807085Total Cost = Setups + holdingSetups = 3 costing $300Holding = 155 x $1 = $155TOTAL= $455Silver Meal AlgorithmWagner-Whitin AlgorithmStep 1Total Variable Cost table (Zce)ce = 12345678910110014014017033048048069011302100100120240360360540925310011019028028043076041001402002003205955100130130220440610010016032571001302408100155910010Step 2Step 2Period12345678910Gross requirement353040010403003055Scheduled ReceiptOn hand353505010100300055Net Requirement0300004000300Planned Order Receipt 807085Planned Order Release807085Total Cost = Setups + holdingSetups = 3 costing $300Holding = 155 x $1 = $155TOTAL= $455Wagner-Whitin AlgorithmAssignmentLeast Total CostMcLaren Order Moment (MOM)Groffs algorithmFreeland & Colley method

Cost Comparison

Part Period BalancingSimplicity in calculations.

Focus = Short run planning.

Least Unit CostSimple Computation.Least Unit Cost.Info about future demand must be known.Minimized cost of lots only.Costs differ from period to period.

Economic Order Quantity (EOQ)Minimizes both ordering and holding cost at optimal quantity Q*Match customer demand.Exact estimation of costs are difficult.Does not allow combining several different products in the same order.Assumes Constant demand and disruptions in demand change the results.

Silver MealConsider variable demand.Easier to use than complex programming application models.More computations.Ineffective if demand drops in future periods.Decision depends upon future periods and demands.

ConclusionThank YouI hear and I forget, I see and I remember. I do and I understand. - Chinese ProverbSheet1Table.1Cost ($)Wagner-Whitin455Part Period Balancing490Silver Meal455Least Unit Cost490EOQ718

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Sheet1Cost ($)Wagner-Whitin258Part Period Balancing286Silver Meal258Least Unit Cost328EOQ418

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Sheet1Cost ($)Cost ($)Wagner-Whitin258Wagner-Whitin258Part Period Balancing286Least Unit Cost328Silver Meal258Least Unit Cost328EOQ418

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Sheet1Cost ($)Cost ($)Wagner-Whitin258Wagner-Whitin258Part Period Balancing286EOQ418Silver Meal258Least Unit Cost328EOQ418

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Sheet1Cost ($)Cost ($)Wagner-Whitin258Wagner-Whitin258Part Period Balancing286Silver Meal258Silver Meal258Least Unit Cost328EOQ418

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