2. ADVANTAGES OF JOINT
REPLENISHMENT
• Savings on Unit Purchase Costs
If many items are bought from the same vendor, a
quantity discount if the total order is > breakpoint qty is
realized
When a order is placed to a vendor, certain fixed cost is
incurred but adding a line item to order incurs a smaller
fixed cost
Vendor - imposed minimum qty like 5000, 10000 units
etc
It doesn’t make sense to buy a single item to avail
discount, so it is necessary to coordinate several items
3. ADVANTAGES OF
COORDINATION
• Savings on Unit Transportation Costs
Grouping items to achieve a carload or container load
on a ship
Pool the items till the container is full to avail the
discount on full container load
• Savings on Ordering Costs
In case fixed cost of ordering is high, then it makes
sense to order several of these at once
In case of coordinated production, mfg set-up cost is
high
4. ADVANTAGES OF COORDINATION
• Ease of Scheduling
Scheduling of buyer time, receiving and inspection and
etc would be easy
5. Assumptions
Demand rate of each item is constant and deterministic
Replenishment qty need not be an integer
The unit variable cost doesn’t depend on qty (no
discounts)
Replenishment lead time is zero
No shortages allowed
The entire order quantity is delivered at the same time
6. Few Notations
S = major Setup cost
si = minor setup cost i.e. Item dependent marginal cost of
placing an order
A$ = annual rupee value of all items in the group ordered
A$i = annual rupee value of item i in the group ordered
Ci = unit cost of an item i
Di = annual demand of item i in number of units
Q$ = total rupee value of all items ordered during a cycle
Q$i = rupee value of item i ordered during a cycle
7. Total Relevant Cost
Number of orders N = D/Q = A$ / Q$ = a$ / Q$i
Total Relevant Costs = Ordering cost + Inventory carrying cost
Ordering cost involves a major setup ‘S’ (ordering) cost + si
minor setup ‘si’ (ordering) cost for any item i. So, Total cost of
placing an order for a group of items will be [S + ∑si] i = 1....n.
Inventory carrying cost would be I*(Q$/2)
So, TRC = Ordering cost + Inventory Carrying cost = N. [S +
∑si] + I*(Q$/2) = A$/Q$ * [S + ∑si] + I*(Q$/2)
Differentiate TRC w.r.t Qv and equate it with ‘0’
8. Total Relevant Cost
Q$ = SQRT[(2.[S + ∑si].A$)/I]
Q$i = Q$ * (a$i / A$)
Qi = Q$i / Ci
Iowa Abe Sporting Goods Company order five different
tennis racquets from a major distributor. The annual
demand, cost and other data are shown in the table
below. The major setup (order) cost with group of items
is Rs.75 per order and the annual inventory carrying %
‘r’ is 15% of the cost of items. Find EOQ in rupee value
‘Qivi’ and units of all items ‘Q’.
9. Total Relevant Cost
Item
No.
Annual
Demand Dv
Unit
Cost v
1
2
3
4
5
Total
5000
4000
10000
18000
1000
38000
5
8
10
12
20
Order Size
si
Rupees (Qivi)
Qi
5
5
8
8
10
36
Find Number of orders per year N, Time between orders
‘T’, Annual Cost of Ordering (Setup) and Average Annual
Inventory Carrying Costs.
10. The Decision Rule
TEOQ = √2S/hD = √2S/h*A$
S/A$ - An item with high S and low A$ value will have
high TEOQ meaning less no. of replenishments than an
item with low S and high A$ (in which case TEOQ is small)
Inventory policy is to consider the use of time interval (T)
between replenishments of a family and a set of mi’s, the
number of T intervals that replenishment quantity of item
i will last
M15 = 4 means that 15th item should be included every 4th
replenishment of the family, with a replenishment
quantity sufficient to last a time interval of duration 4T
11. BROWN’S ALGORITHM
Calculate T
Then calculate ‘mi’ = 1/T * SQRT [(2 * si)/(I * a$i)]
•Then
calculate revised value of T using:
T = SQRT [ (2 * [S + (∑si/mi)] / (I * ∑mi.a$i)]
Q$i = mi . a$i. T
12. SILVER’S ALGORITHM
Find minimum [si/a$i] and let that be m1 = 1 and let this
be item j
Then calculate ‘mi’ = SQRT [(si/a$i) * (a$j / (S + sj))]
•Then
calculate revised value of T using:
T = SQRT [ (2 * [S + (∑si/n)] / (I * ∑mi . a$i)]
Q$i = mi . a$i . T
