Fall 2012 – MGT 3110
Exam 3 Formulas
Chapter 12 Inventory Management
ROP Models
Discrete Probability model
Total cost = Annual Holding cost + Annual stock-out cost
Annual Holding cost = Safety stock x H
Annual stock-out cost = Expected stock out per cycle x N x Cs
Where, Expected stock-out =  (Stock-out x Probability)
N = No. of orders per year = D/Q
Cs = Cost of stock-out per unit
Reorder point model with Normal distribution:
Reorder point (ROP) = Average demand during lead time + Safety stock
i.e. ROP = d x L + Z dLT
where, d = Demand rate per period
L = Lead time
Z = Normal table value for the given service level
dLT= Standard deviation of demand during lead time (as give in table below)
Lead time is constant
Lead time is variable
Demand is constant
𝜎dLT = 0
𝜎dLT = d𝜎𝐿
Demand is variable
𝜎dLT = d√𝐿
𝜎dLT = √𝐿𝜎𝑑2 + 𝑑 𝜎𝐿2
2
Single-Period model
𝐶
Service level = 𝐶 +𝑠𝐶 , where Cs = Cost of shortage, Co = cost of overage
𝑠
𝑜
Cs = Lost profit = Selling price per unit – Cost per unit
Co = Cost/unit – salvage value/unit
Order quantity =  + Z, where  = mean demand,  = standard deviation of demand
Stock-out risk= 1 - service level
Chapter 13 Aggregate Planning
Production rate/day/worker = Hours per day/ Standard hours
Production rate/period/worker = Production rate/day/worker x No. of days per period
Wage/worker/day = Wage rate/hour x hours/day
Wage/worker/period = Wage rate/worker/day x days per period
OT cost/unit = Standard hours x OT wage per hour
No. of workers needed = Production Required ÷ Production per worker
Cost summary for aggregate planning:
Cost summary
Regular wages
OT cost
SC cost
Hiring cost
Firing cost
Carrying cost
Total cost
No. of workers x no. of periods x wage rate per period per worker
OT quantity x OT rate/unit (Only for mixed strategy)
SC quantity x SC rate/unit (Only for mixed strategy)
Workers or units hired x hiring cost
Workers or units fired x firing cost
Sum of ending inventory x inventory carrying cost/unit/period
Chase:
Production 1st period = Forecasted Demand - (Initial inventory - Safety stock)
Production for all other periods = Forecasted demand
Month
Demand
Production
Days
(if different)
Production
rate
Workers
Hire
Fire
Level:
(Sum of demand−(Initial inventory−Safety stock)
Initial estimate of production rate =
Number of periods or days
Number of workers = Production rate/Production rate per worker – round up
Month
Demand
Days
(if different)
Production
Ending
inventory
Mixed:
Production Capacity= workers * production/worker/period
RT production = Minimum{Requirement, Capacity}
Shortage = Requirement – RT production
OT Capacity = OT Limit % x RT Capacity
OT production = Minimum{Shortage, OT Capacity}
SC production = Shortage - OT production
Month
Demand/
Requirement
Capacity
Days
(if different)
Production
Shortage
OT
Capacity
OT
SC
Chapter 14 Material Requirements Planning
Gross requirement:
= Number of units required per unit of Parent (from BOM) x MPS quantity if parent
is at Level zero of BOM
or
= Number of units required per unit of Parent (from BOM) x Planned Order Release
(PORL, the last row) if parent is at an intermediate Level of
BOM
Projected on-hand for week t+1
= Project on-hand for week t + Scheduled Receipt for week t – Gross Requirement for week t
After the first net requirement, = Planned order receipt for week t – Net requirement for week t
(Projected on-hand is never negative)
Net requirement
= If Projected on-hand for week t+1 is negative, then
Net requirement = (Projected on-hand + Scheduled Receipt) - Gross
requirement
Lot sizing: Lot-for-lot:
Total cost = No. of setups x Setup cost + Total ending inventory x Holding cost/week
EOQ:
Q
2dS
H / week
d = Average demand per week
S = Setup cost
H = Holding cost per week
Total cost/week = (d/Q)S + (Q/2)*Holding cost per week
Total cost for n weeks = Total cost/week x n
Part-period balancing:
EPP = S/H, where EPP = Economic part periods, S = Setup cost, H = holding cost
Periods
combined
(Lot size)
Quantities
combined
Periods brought
forward for the
last quantity
Total cost = Total setup cost + Total carrying cost
i.e. = No. of lots x S + Sum of Part-periods in the lots x H
New Partperiods
(Lot PP)
Total combined partperiods