Finding the EOQ with shortages and the replenishment of inventory is at a finite rate
Model 4
Finding
the EOQ with shortages and the replenishment of inventory is at a finite rate
An Illustration: Consider the example, which is
given in the Model 1. Assume
that you are requiring Rs. 100 per day and in a month your demand is Rs. 3000/-
to manage your requirements. Again, you may get your required amount
immediately. Only the change is, instead of giving your demand Rs. 3000/- in a
single stroke, your parents decided to give the sum in such a way that first 20
days, you will be given with Rs. 150/-per day out of which Rs. 100/- per day is
incurred and every day you have to save Rs. 50/- for the first twenty days, and
you will not be given any amount after 20th. The remaining days in the month,
you will start using the ‘savings’.
Assume that on every 22nd your room mate/ close friend use to borrow Rs. 500
from you. You will run out of money after 25th, which you are in a position to
manage through borrowings from local firms at a nominal rate. (Indirectly you
are paying a penalty by way of interest for the shortages.)
If we consider companies such as Hyundai, Maruti
and other bigger automobiles, they use to follow this kind of ‘constant rate of
replenishment’ instead of instantaneous replenishment. If a truck manufacturer
who is placing an order of 10,000 Tyres would appreciate the concept of finite
rate of fulfilling the orders rather than getting all the 10,000 Tyres in a
single stroke. He may save a lot in keeping smaller warehouse(s), capital
locked in inventory is minimal. For the supplier also, he finds it convenient
to sending the quantities in batches rather than bulk dispatches. But all these
relaxation have a binding such that the quantities should be supplied on
specified date and time, any violation should dealt very severally by levying
large penalties.
Solution Let us have the following
assumptions: 1. Demand is
known and uniform. Let ‘r’ be the rate of demand for one unit of time.
2.
Let ‘k’
be the rate of replenishment per unit of time. 3. Shortages
are permitted and let C2 be the shortage cost per unit per unit of time.
4.
Lead-time
is zero. 5.
Let C1 be
the holding cost per unit of inventory per unit of time. 6.
Let Cs be
the set up cost per production run or ordering cost per cycle. Assume that each production run of length‘t’
consists of 2 parts say t1 and t2. In turn, they are sub divided into t11, t12
and t21, t22 as shown in the figure.
Example The demand for an item in a company is 12000 per
year and the company can produce the item at the rate of 3000 per month. The
cost of one set up is Rs. 500 and the holding cost of one unit per month is Rs
0.15. The shortage cost of one unit is Rs. 20 per year. Determine the optimum
manufacturing quantity and the # of production runs and time between the
production runs? Solution The given quantities can be
summarized in the following table.
Tags : Operations Management - Transportation / Assignment & Inventory Management
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