MGT 3110 Exam 2 Formulas
Chapter 11 Aggregate Planning
Workers needed = Regular time Production Required ÷ Production per worker (ROUND UP)
Available inventory = Beginning inventory + Total output
Ending inventory = Maximum{0, Available inventory – (Forecast + Previous backlog)}
Average inventory = (Beginning inventory + Ending inventory)/2
Backlog = Maximum{0, (Forecast + Previous backlog) - Available inventory}
Cost summary for aggregate planning:
Regular time cost
Overtime
Subcontracting cost
Hiring cost
Firing cost
Inventory carrying cost
Backorder cost
Regular time output x cost per unit for regular time
Overtime output x Overtime cost/unit
Subcontracting quantity x SC cost/unit
Workers hired x hiring cost per worker
Workers fired x firing cost per worker
Average inventory x inventory carrying cost/unit/period
Backorder units x Backorder cost per unit
Chase:
Regular time output = Minimum(Forecast, Capacity)
Level:
Required production = Average forecasted demand per period
Number of workers = Required Production/period/Production rate/ worker/period
Chapter 12 Material Requirements Planning
GR
Planned-order releases of “parents” x No. required per unit
SR
Given
POH
POH of previous period + SR + PORT – GR , (POH cannot be negative)
NR
GR – (POH + SR + PORT) if positive, otherwise zero
PORT
NR in the case of Lot for Lot
PORL
PORT offset by lead time
Chapter 13 Inventory Management
ABC Classification rule:
Class A: 10 to 20% of items, 60 to 70% annual $ usage
Class B: Intermediate
Class C: 50 to 60% of items, <= 15% annual $ usage
Item $ Usage
% of $ usage
Cumulative % of $
Cumulative % of no. of items
Class
Basic EOQ Model
Q0 = √
2𝐷𝑆
𝐻
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
Length of order cycle = Q/D in years = Q/u in days where u = demand rate/day
Number of orders per year = D/Q
Annual ordering cost = (D/Q)S
Annual carrying cost = (Q/2)H
Total annual cost (TC) = (D/Q)S + (Q/2)H
EPQ Model
Qp = √
2𝐷𝑆
𝐻
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
p = Production or delivery rate
u = Usage rate
𝑝
√𝑝−𝑢
Cycle time = (Qp/u)
Run time = Qp/p
Rate of increase of inventory during production = (p - u)
Maximum inventory = Imax = (Q/p)(p-u)
Average inventory = Imax/2
Number of batches per year = D/Q
Annual setup cost = (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
Step 1: Determine Candidate Q
1. Compute Formula-Q for each price break price.
2. 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 this price
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 (TC) = (D/Q)S + (Q/2)H + PD
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
Reorder point model with Normal distribution:
Reorder point (ROP) = Average demand during lead time + Safety stock
̅̅̅ + Z dLT
i.e. ROP = d̅ x ̅LT
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 = d𝜎𝐿𝑇
Demand is variable
𝜎dLT = d√𝐿𝑇
2
𝜎dLT = √𝐿𝑇𝜎𝑑2 + 𝑑 𝜎𝐿𝑇
2
where, d = Demand rate per period, d̅ = average demand rate
̅̅̅̅ = average lead time
LT = Lead time, LT
d = Standard deviation of demand per period
LT = Standard deviation of lead time in periods
Z = Normal table value for the given service level
Annual Service Level
E(n) = E(z)dLT
where E(n) = Expected number of units short per cycle
E(z) = Standardized number of units shorts (Table 13.3, page 583)
dLT= Standard deviation of demand during lead time
𝐷
E(N) = E(n)(𝑄 )
SLannual = 1 -
𝐸(N)
D
where E(N) = Expected number of units short per year
=1-
E(N) = (1 – SLannual)D
𝐸(𝑧)𝜎𝑑𝐿𝑇
𝑄
where SLannual = Annual service level
Fixed Order Interval Model
Q = 𝑑̅(OI + LT) + zd√OI + LT - A
where Q = Amount of order
OI = Order interval (length of time between orders)
A = Amount on hand at reorder time
Single-Period model
𝐶
SL = Service level = 𝐶 +𝑠𝐶 , where Cs = Cost of shortage, Ce = cost of excess
𝑠
𝑒
Cs = Lost profit = Revenue – Cost per unit
Ce = Original cost/unit – Salvage value/unit
Uniform distribution for demand:
S0 = a + SL (b – a)
where a = lower limit for demand, b = upper limit for demand
Normal distribution
S0 =  + Z, where  = mean demand,  = standard deviation of demand