BMGT 583: Chapter 15 –Inventory Management
Independent versus dependent demand items:

Independent demand items are items whose demand does not depend upon the demand
of other items. Finished goods are independent demand items.

Dependent demand items are items whose demand depends upon the demand of other
items. WIP and raw-materials inventory are dependent demand items.
Types of inventory:
Cycle inventory:
The portion of the total inventory that varies directly with lot size.
Average inventory = Q/2
Safety stock:
Surplus inventory that protects against uncertainties in demand, lead time, and supply.
Anticipation inventory:
Stockpiling inventory during periods of low demand anticipating future peaks in demand.
Pipeline inventory:
Orders that have been placed, but not yet received. Also, it can be estimated as average
demand during lead time ( D L ). Note, D L = dL, where d = average demand per period and L
= Lead time in periods.
Inventory costs
Holding cost:
Costs associated with holding or “carrying” inventory over time. Part of holding cost
include, (i) interest/opportunity cost, (ii) storage and handling cost, (iii) taxes, insurance, and
shrinkage costs.
Ordering cost (for vendor orders)/ Setup cost (for production orders):
Cost of preparing a vendor order, such as cost of supplies, labor, order processing, etc., or
cost of preparing a machine to process a lot of items, such as labor, tools, cleaning, etc.
Item cost:
Purchase price of the item. Unless quantity discounts are available, item cost (= demand x
price per unit) is independent of inventory related decisions. Hence, if quantity discount is
not available, item cost need not be considered.
Stock out cost:
Cost of stock out per unit.
ABC Analysis
Class A
Class B
Class C
About 15% of items
About 30% of items
About 55% of items
About 70 to 80% of annual $ usage
About 15 to 25% of annual $ usage
About 5% of annual $ usage
Procedure:
1. Collect and prepare the following data: Item stock number, annual volume, and unit cost.
2. Compute annual dollar volume for each item
3. Sort the items in descending order of annual dollar volume
4. Classify the items into A, B, and C using the above rule.
Basic EOQ Model
Assumptions:
1. Demand is constant, known, and independent
2. Lead time is known and constant
3. Receipt of inventory is instantaneous
4. No quantity discounts
5. Only holding cost and ordering cost are variable
6. No stock-out
2 DS
Q 
H
*
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 (TBO) = (Q/D) x No. of days per year
Annual ordering cost = NS = (D/Q)S
Annual carrying cost = (Q/2)H
Total annual cost (TC) = (D/Q)S + (Q/2)H
Inventory Control Systems
1. Continuous Review (Q) System (Reorder Point System)
(Assume, demand follows normal distribution, and lead time is constant)
ROP = R = Average demand during lead time + Safety stock = R = dL + z L,
where, d = average demand per period
L = lead time in periods
z = Standard normal table value for a given service level,
L= Standard deviation of demand during lead time
L= t√L where, t= Standard deviation of demand per period
Ordering rule: If inventory position (IP) = ROP, place an order for EOQ.
IP = OH + SR – BO,
where, OH = On-hand inventory, SR = Scheduled receipts, and BO = backorders
Total Cost of ROP system = Annual cycle inventory holding cost + Annual ordering cost +
Annual safety stock holding cost
i.e. = (Q/2)H + (D/Q)S + (zL)H
(If lead time is not constant or demand does not follow normal distribution, use simulation)
2. Periodic Review (P) System
(Assume, demand follows normal distribution, and lead time is constant)
Time between orders (TBO) is fixed. Order quantity varies.
Order quantity (Q) = T – IP
where, T = Target inventory, and IP = Inventory position
T = Average demand during protection interval + Safety stock for protection interval
Protection interval = P + L, where P = TBO, and L = Lead time
Average demand during protection interval = d(P+L)
Safety stock for protection interval = z P+L, where = P+L= t P  L 
Therefore, T = d(P+L) + z P+L
Total Cost of P system = Annual cycle inventory holding cost + Annual ordering cost +
Annual safety stock holding cost
i.e. = (dP/2)H + (D/dP)S + (zP+L)H
(If lead time is not constant, or demand does not follow normal distribution use simulation)
3. Optional replacement system
Like P system. But order is placed only if IP falls below a minimum value and for quantities
rounded to predetermined values. For example, if T = 100, minimum is 30 and orders are
placed rounded to the nearest 10’s, then if IP is 37 no order will be placed; however, if IP =
28, Q = 100 – 28 = 72, rounded to 70.
4. Base stock System
One-for-one replacement - if one is shipped to customer from stock, a replacement for one
unit is immediately ordered.
OM Solver:
Inventory System Designer
Input: Lead time, service Level, demand, standard deviation of Demand/Day, Working
days per year, holding Cost, Order Cost
Output: EOQ, ROP and total cost for Q system; TBO, Target inventory and total cost for P
system
Demand During Protection Interval Simulator
Input: Probability distribution for demand and lead time, and P for periodic system
Output: Average demand and demand distribution for protection interval
Q System Simulator
Input: Probability distribution for demand and lead time
Holding cost, setup cost, and stock-out cost
Order quantity, Reorder point, and initial inventory
Output: Average of total cost per week
Economic Lot Size (ELS) Model
ELS 
2 DS
H
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
p = Production rate
d = Demand rate
p
pd
Length of production run (t) = Q/p
Maximum inventory = Imax = (Q/p)(p-d) = Q(1-d/p)
Average inventory = Imax/2
Expected number of batches (N) = D/ Q
Expected time between orders (TBO) = (Q/D) No. of days per year = Q/d
Annual setup cost = NS = (D/ Q)S
Annual carrying cost = (Imax/2)H
Total annual cost (C) = (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
Steps
1. Compute Q for each price break price.
2. Compare Q computed in step 1 with the quantity range for each price break. If it is
greater than the upper limit, skip this price break. If it is within the lower and upper
limit, keep the Q as is. If it is smaller than the lower limit, adjust the Q to the lower
limit.
3. Compute the total cost (TC) for each Q determined in step 2. TC = (Q/2)H + (D/Q)S + PD
4. Select the Q that with the lowest total cost computed in step 3 as the Q*.