MGT 3110 - Exam 2 Formulas
Chapter 12 Inventory Management
ABC Classification rule:
Class A: ~15% of items, 70-80% annual $ usage
Class B: ~30% of items, 15-25% annual $ usage
Class C: ~55% of items, 5% annual $ usage
Item
$ Usage
% of $ usage
Basic EOQ Model
2 DS
Q* 
H
Cumulative % of $
Cumulative % of no. of items
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
Expected number of orders (N) = D/Q
Expected time between orders (T) = (Q/D) No. of days per year = Q/d
Annual ordering cost = NS = (D/Q)S
Annual carrying cost = (Q/2)H
Total annual cost (TC) = (D/Q)S + (Q/2)H
POQ Model
Q 
*
p
2 DS
H (1  d / p )
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
p = Daily production rate
d = Daily demand rate = D/No. of working days
Length of production run (t) = Q/p
Rate of increase of inventory during production = (p - d)
Maximum inventory = Imax = (Q/p)(p-d)
Average inventory = Imax/2
Expected number of batches (N) = D/Q
Expected time between orders (T) = (Q/D) or No. of days per year = Q/d
Annual setup cost = NS = (D/ Q)S
Annual carrying cost = (Imax/2)H
Total annual cost (TC) = (D/Q)S + (Imax /2)H
Quantity discount model
Q
2 DS
IP
where, D = Demand per year
S = Ordering cost for each order
IP = H = Holding (carrying) cost per unit per year
I = Holding cost as a % of item cost
P = Item cost per unit
Class
Step 1: Determine Candidate Q
a. Compute Formula-Q for each price break price.
b. If Formula Q < Lower limit for price, then Candidate Q = Lower limit
If Formula Q is within the limits for the price, then Candidate Q = Formula Q
If Formula Q > Upper limit for price, then no candidate Q, ignore the Formula Q
Q-Range
Price
Holding cost/unit = % x P
Formula Q
Adjusted Q
Step 2: Compute total annual cost (TC) for each valid candidate Q and select the candidate Q with least
cost as EOQ.
Total annual cost = Annual holding cost + Annual ordering cost + Annual item cost
i.e. = (Q/2)H + (D/Q)S + PD, where P = cost of the item per unit
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/ Labor hours per unit
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 (Rounded up)
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 hired x hiring cost per worker
Workers fired x firing cost per worker
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
Period
Demand
Production
Workers
Hire
Fire
Hire/fire cost may be based on production rate changes or number of workers hired/fired.
Level:
(Sum of demand−(Initial inventory−Safety stock)
Initial estimate of production rate =
Number of periods
Number of workers = Production rate/Production rate per worker
Period
Demand
Production
Ending inventory
Mixed:
Production Capacity = number of workers * production rate/worker/period
Regular time production = Minimum{Requirement, Capacity}
Shortage = Requirement – Regular time production
Over time capacity = OT Limit % x Regular time capacity
Over time production = Minimum{Shortage, Over time Capacity}
Subcontracting production = Shortage – Over time production
Period
Demand
Requirement
Capacity
RT
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
POHt+1 = POHt + SRt – GRt
POH is always > Safety stock, if not there is net requirement
Net requirement
If POHt+1 < Safety stock, then NRt = GRt – (POHt + SRt)
POHt = Projected on hand for week t
POHt+1 = Projected on hand for week t+1
SRt = Scheduled Receipt for week t
GRt = Gross requirement for week t
NRt = Net requirement for week t
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
Periodic Order Quantity
POQ interval = EOQ/Average weekly demand rounded to whole number
Chapter 15 Short-term Scheduling
Input Output Control Chart
Cumulative deviation of input = Previous cumulative deviation + actual input – planned input
Cumulative deviation of output = Previous cumulative deviation + actual output – planned output
Cumulative backlog = Previous backlog + Actual input – Actual output
Job due date = Days till due date = Due date – Today’s date
Completion time (Flowtime) of a job = Completion time of the previous job + processing time
Average completion (flowtime) time =
Sum of total flow time
Number of jobs
Average job lateness =
Total late days
Number of jobs
Average number of jobs in the system =
Utilization =
Sum of total flow time
Total job processing time
Total job processing time
Critical Ratio =
Sum of totl flow time
Time remaining
Workdays remaining
=
Days till due date
Work time remaining in days