Supply Chain Management Formulas
NEWSVENDOR MODEL
Too Much/Too Little Problem
Maximize Expected Profit
STEP 1: overage/underage costs
Co = overage cost per unit
Co = Variable Cost – Salvage value
Cu = underage cost per unit
Cu = Price – Cost (+ Future Cost)
STEP 2: Find Critical Ratio F(Q*) = Probability demand < Q.
Cu /Cu+ C0 = critical ratio/srvc level
STEP 3: Calculate z from table. φ(Ζ) = Critical ratio
STEP 4: Calculate Q*
= optimal order quantity Ζ= from above (table) μ = mean σ = standard deviation aka measure of uncertainty
~~~~~~~~~~~~~~~~~~~~~
NEWSVENDOR VARIATIONS
(Co/Cu) Ratio Given
1. Critical Ratio
F(Q) =
2. Find φ(Ζ) from table
3. then
Service Level is given.
1. Find φ(Ζ) for service level given, 2.
Finding SERVICE LEVEL given Q.
1.
2. find φ(Ζ) (expressed as %)
Comparing Stocking Quantities
Actual costs not given.
Holding cost in 2d year:
Yr1 C – Yr2 C + %holding cost
e.g. C – C + 0.25C
Salvage costs in 2d year:
Cost (C)– % Salvage value
e.g. C - 0.75C ECONOMIC ORDER QUANTITY (EOQ MODEL)
How much to Order Problem
TC = total annual inventory cost
D = annual demand (units/year)
Q = order quantity (units)
K = cost of placing an order or setup cost ($) h = annual inventory carrying cost ($/unit/year) may include: warehousing cost avg rtn for working capital
P = price of goods ($/unit)
STEP 1: Convert in D, h, K into same time units (mo, yr, etc…)
STEP 2: Determine EOQ, Q* Optimal quantity
EOQ =
STEP 3: Find total annual inventory cost (ordering + holding) annual ordering cost (D/Q)*K annual holding cost (Q/2)*h annual purchasing cost P*D annual inventory cost TC(Q)
STEP 4: Other Measures
# of Orders per year = D/Q*
Length of Order Cycle T= Q*/D
(Time between two orders)
~~~~~~~~~~~~~~~~~~~~~
EOQ VARIATIONS
Take new quantity discount?
(new Q* & new purchase cost)
1. Calculate original TC
2. Calculate new TC w/ new Q*
Too Much/Too Little Problem
Maximize Expected Profit
STEP 1: overage/underage costs
Co = overage cost per unit
Co = Variable Cost – Salvage value
Cu = underage cost per unit
Cu = Price – Cost (+ Future Cost)
STEP 2: Find Critical Ratio F(Q*) = Probability demand < Q.
Cu /Cu+ C0 = critical ratio/srvc level
STEP 3: Calculate z from table. φ(Ζ) = Critical ratio
STEP 4: Calculate Q*
= optimal order quantity Ζ= from above (table) μ = mean σ = standard deviation aka measure of uncertainty
~~~~~~~~~~~~~~~~~~~~~
NEWSVENDOR VARIATIONS
(Co/Cu) Ratio Given
1. Critical Ratio
F(Q) =
2. Find φ(Ζ) from table
3. then
Service Level is given.
1. Find φ(Ζ) for service level given, 2.
Finding SERVICE LEVEL given Q.
1.
2. find φ(Ζ) (expressed as %)
Comparing Stocking Quantities
Actual costs not given.
Holding cost in 2d year:
Yr1 C – Yr2 C + %holding cost
e.g. C – C + 0.25C
Salvage costs in 2d year:
Cost (C)– % Salvage value
e.g. C - 0.75C ECONOMIC ORDER QUANTITY (EOQ MODEL)
How much to Order Problem
TC = total annual inventory cost
D = annual demand (units/year)
Q = order quantity (units)
K = cost of placing an order or setup cost ($) h = annual inventory carrying cost ($/unit/year) may include: warehousing cost avg rtn for working capital
P = price of goods ($/unit)
STEP 1: Convert in D, h, K into same time units (mo, yr, etc…)
STEP 2: Determine EOQ, Q* Optimal quantity
EOQ =
STEP 3: Find total annual inventory cost (ordering + holding) annual ordering cost (D/Q)*K annual holding cost (Q/2)*h annual purchasing cost P*D annual inventory cost TC(Q)
STEP 4: Other Measures
# of Orders per year = D/Q*
Length of Order Cycle T= Q*/D
(Time between two orders)
~~~~~~~~~~~~~~~~~~~~~
EOQ VARIATIONS
Take new quantity discount?
(new Q* & new purchase cost)
1. Calculate original TC
2. Calculate new TC w/ new Q*