C723 | QUANTITATIVE ANALYSIS FOR BUSINESS
C723 Worked Revision and Formula Guide
Decision models inventory optimization critical paths spreadsheets
Research checked 1 November 2026. Original independent practice material. Not an official WGU OA or PA and
not endorsed by WGU.
Course coverage and current status
The November 2026 WGU catalog confirms C723 and BUS 3100 for Quantitative Analysis for Business. Its public
description covers decision models, numerical and graphical analysis, inventory, project scheduling, uncertainty,
crash costs and spreadsheets. [S1] The public guidebook adds competency-level detail. [S2] A private
assessment blueprint and a separate 2027 revision were not verified. Forecasting and extra statistics here
support the quantitative methods rather than claiming additional official domains.
Choose the method before calculating
Business task Method First check
Choose among uncertain payoffs Expected value or decision tree States and probabilities agree
Choose order size EOQ Demand and H use the same annual basis
Decide when to order Reorder point Lead time and demand units match
Allocate limited resources Linear programming All constraints and nonnegativity included
Schedule dependent work Critical Path Method Predecessors and durations are complete
Compare historical values Chart or numerical summary Scale and denominator are suitable
Formula reference
Expected payoff
EMV = sum of probability × payoff
Use signed net payoffs; minimize expected cost when the objective is cost.
Opportunity loss
Regret in a state = best payoff in that state − chosen payoff
For cost tables reverse the subtraction against the lowest cost.
Perfect information
EVPI = expected best payoff with perfect information − best current EMV
Use the best action in each state before probability weighting.
Inventory order quantity
EOQ = sqrt(2DS/H)
D is units/year; S is dollars/order; H is dollars/unit/year.
Inventory annual relevant cost
RC(Q) = DS/Q + HQ/2
Basic cycle model only; add H×safety stock and purchase cost when relevant.
Independent study resource • 1
, C723 | QUANTITATIVE ANALYSIS FOR BUSINESS
Inventory trigger
ROP = daily demand × lead time in days + safety stock
Continuous-review trigger normally uses inventory position.
Inventory position
IP = on hand + on order − backorders
Compare IP with ROP, not on-hand inventory alone.
Production contribution
Z = sum of unit contribution × units produced
Contribution is revenue less variable cost; it is not necessarily net profit.
Forward scheduling pass
ES = maximum predecessor EF; EF = ES + duration
An activity waits for every predecessor.
Backward scheduling pass
LF = minimum successor LS; LS = LF − duration
Anchor the finish to the baseline project duration.
Total float
TF = LS − ES = LF − EF
Standard unconstrained baseline network without imposed deadline anomalies.
Crash cost slope
Slope = (crash cost − normal cost)/(normal time − crash time)
Check available crash days and all critical paths after each step.
PERT approximation
Expected time = (a+4m+b)/6; variance = ((b−a)/6)^2
For independent fixed-path activities, add variances then take a square root.
Break even
Quantity = fixed cost/(price − unit variable cost)
Requires positive contribution; round up for a whole-unit threshold.
Descriptive calculations
Mean = sum/n; population variance = squared deviations/N
Sample variance uses n−1. Standard deviation is the square root of variance.
Supplementary forecasts
SMA = latest k actual values/k; new F = alpha×latest actual + (1−alpha)×prior F
MAD averages absolute errors over a common evaluation window.
Worked decision table
A retailer chooses a small or large launch. Values below are net profit in thousands of dollars; high demand
probability is 0.4 and low demand is 0.6. Assume a risk-neutral profit objective. [S3]
Action Low demand High demand EMV
Independent study resource • 2
C723 Worked Revision and Formula Guide
Decision models inventory optimization critical paths spreadsheets
Research checked 1 November 2026. Original independent practice material. Not an official WGU OA or PA and
not endorsed by WGU.
Course coverage and current status
The November 2026 WGU catalog confirms C723 and BUS 3100 for Quantitative Analysis for Business. Its public
description covers decision models, numerical and graphical analysis, inventory, project scheduling, uncertainty,
crash costs and spreadsheets. [S1] The public guidebook adds competency-level detail. [S2] A private
assessment blueprint and a separate 2027 revision were not verified. Forecasting and extra statistics here
support the quantitative methods rather than claiming additional official domains.
Choose the method before calculating
Business task Method First check
Choose among uncertain payoffs Expected value or decision tree States and probabilities agree
Choose order size EOQ Demand and H use the same annual basis
Decide when to order Reorder point Lead time and demand units match
Allocate limited resources Linear programming All constraints and nonnegativity included
Schedule dependent work Critical Path Method Predecessors and durations are complete
Compare historical values Chart or numerical summary Scale and denominator are suitable
Formula reference
Expected payoff
EMV = sum of probability × payoff
Use signed net payoffs; minimize expected cost when the objective is cost.
Opportunity loss
Regret in a state = best payoff in that state − chosen payoff
For cost tables reverse the subtraction against the lowest cost.
Perfect information
EVPI = expected best payoff with perfect information − best current EMV
Use the best action in each state before probability weighting.
Inventory order quantity
EOQ = sqrt(2DS/H)
D is units/year; S is dollars/order; H is dollars/unit/year.
Inventory annual relevant cost
RC(Q) = DS/Q + HQ/2
Basic cycle model only; add H×safety stock and purchase cost when relevant.
Independent study resource • 1
, C723 | QUANTITATIVE ANALYSIS FOR BUSINESS
Inventory trigger
ROP = daily demand × lead time in days + safety stock
Continuous-review trigger normally uses inventory position.
Inventory position
IP = on hand + on order − backorders
Compare IP with ROP, not on-hand inventory alone.
Production contribution
Z = sum of unit contribution × units produced
Contribution is revenue less variable cost; it is not necessarily net profit.
Forward scheduling pass
ES = maximum predecessor EF; EF = ES + duration
An activity waits for every predecessor.
Backward scheduling pass
LF = minimum successor LS; LS = LF − duration
Anchor the finish to the baseline project duration.
Total float
TF = LS − ES = LF − EF
Standard unconstrained baseline network without imposed deadline anomalies.
Crash cost slope
Slope = (crash cost − normal cost)/(normal time − crash time)
Check available crash days and all critical paths after each step.
PERT approximation
Expected time = (a+4m+b)/6; variance = ((b−a)/6)^2
For independent fixed-path activities, add variances then take a square root.
Break even
Quantity = fixed cost/(price − unit variable cost)
Requires positive contribution; round up for a whole-unit threshold.
Descriptive calculations
Mean = sum/n; population variance = squared deviations/N
Sample variance uses n−1. Standard deviation is the square root of variance.
Supplementary forecasts
SMA = latest k actual values/k; new F = alpha×latest actual + (1−alpha)×prior F
MAD averages absolute errors over a common evaluation window.
Worked decision table
A retailer chooses a small or large launch. Values below are net profit in thousands of dollars; high demand
probability is 0.4 and low demand is 0.6. Assume a risk-neutral profit objective. [S3]
Action Low demand High demand EMV
Independent study resource • 2
