Page 252 - DMGT501_OPERATIONS_MANAGEMENT

Operations Management

Notes Max. Number of backorders (S*) = Q EOQ (r*v/(r*v + b)
= 33* (0.20*50/((0.20*50) +12) = 15 units
2
Total Annual Cost (with backorders permitted) = [(Q-S) *v*r /2Q ] + A* (D/Q) + S* *b/2* Q EOQ
2
2
= [(33 -15) *(0.20*50) / (2*33)] + (600*5)/33 + 15*15*12/ (2*33)
= 181
If stock outs and backorders are not permitted, the economic order quantity is:

Q = Q EOQ = √2*A*D/r*v
= √ 2*600*5/ (0.20*50) = 24.5 units
TC = Ordering Cost + Ave. Holding Cost = [D*A/ Q EOQ ] + Q EOQ * r*v/2
= [600*5/ 24.5)] + 24.5*0.20*50/2 = 254.00

Therefore, additional cost when backordering is not allowed = 254.00 – 181.00
= 64.00

10.1.2 Fixed-time Period Models

In many retail merchandising systems, a fixed-time period system is used. Sales people make

routine visits to customers and take orders for their complete line of products. Inventory,
therefore, is counted only at particular times, such as every week or every month or when the
supplier’s visit is due. Sometimes, this is also resorted to in order to combine orders to save
transportation costs.
Fixed-time period models generate order quantities that vary from period to period, depending

on the usage rates. A Fixed-Period Quantity system is shown in figure 17.6. These generally

require a higher level of safety stock than fixed-order quantity systems, which require continual
tracking of inventory on hand and replenishing stock when the reorder point is reached. In

contrast, the standard fixed-time period models assume that inventory is counted only at the
time specified for review.

The risk associated with this system is that it is possible that some large demand will draw the
stock down to zero right after an order is placed. There is no remedy for such a situation and the
condition could go unnoticed until the next review period. Even after placement of new orders,
the item may still take time to arrive.
This highlights the high probability of being out of stock throughout the entire review period and
order lead time. Safety stock, therefore, is an extremely important requirement for these systems
and is used to effectively protect against the high probability of stock outs.

10.1.3 Fixed-time Period Model with Safety Stock

Continuing our discussions on Fixed-time Period models, it is essential that ‘safety stock’ is a
consideration in model building. We will discuss below a fixed-time period system with safety

stock.
The notations that will be used in the model are given below:
q = Quantity to be ordered

T = Number of days between reviews
L = Lead time in days (time between placing an order and receiving it)

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