#!/usr/local/bin/perl -W
$K = 10; # ordering/setup cost
$D = 100; # demand rate
$F = 1; # holding cost
# T = cycle length
$P = 150; # production rate
$x = $D/$P; # \frac {D}{P}
# Q = order quantity
$EPQ = sqrt ( 2*$K*$D/($F*(1-$x)) );
print "The order/lot of production must be $EPQ\n";
$time_prod = $EPQ/$P;
print "Time in production = $time_prod\n";
$max_stock = ($P-$D) * $time_prod;
print "The maximun stock is $max_stock\n";
$time_cons = $max_stock / $D;
print "Time for consumption = $time_cons\n";
$time_cycl = $time_prod + $time_cons;
print "That is, ",100*$time_prod/$time_cycl,"% for production\n";
print "and ", 100*$time_cons/$time_cycl, "% for consumption only\n";
__END__
This script is stupid since I don't know in wich firm could be applied
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Economic production quantity
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Economic Production Quantity model (also known as the EPQ model)
determines the quantity a company or retailer should order to minimize
the total inventory costs by balancing the inventory holding cost and
average fixed ordering cost. The EPQ model was developed by E.W. Taft
in 1918. This method is an extension of the Economic Order Quantity
model (also known as the EOQ model). The difference between these two
methods is that the EPQ model assumes the company will produce its own
quantity or the parts are going to be shipped to the company while they
are being produced, therefore the orders are available or received in
an incrementally manner while the products are being produced. While
the EOQ model assumes the order quantity arrives complete and
immediately after ordering, meaning that the parts are produced by
another company and are ready to be shipped when the order is placed.
In some literature Economic Manufacturing Quantity model (EMQ) is used
for Economic Production Quantity model (EPQ). Similar to the EOQ model,
EPQ is a single product lot scheduling method. A multiproduct extension
to these models is called Product Cycling Problem.
Contents
* 1 Overview
* 2 Assumptions
* 3 Variables
* 4 Derivation of EPQ Formula
* 5 EPQ Formula
* 6 Inventory Cost Graph
* 7 Relevant Formulas
* 8 See also
* 9 References
[edit] Overview
EPQ only applies where the demand for a product is constant over the
year and that each new order is delivered/produced incrementally when
the inventory reaches zero. There is a fixed cost charged for each
order placed, regardless of the number of units ordered. There is also
a holding or storage cost for each unit held in storage (sometimes
expressed as a percentage of the purchase cost of the item).
We want to determine the optimal number of units of the product to
order so that we minimize the total cost associated with the purchase,
delivery and storage of the product
The required parameters to the solution are the total demand for the
year, the purchase cost for each item, the fixed cost to place the
order and the storage cost for each item per year. Note that the number
of times an order is placed will also affect the total cost, however,
this number can be determined from the other parameters
[edit] Assumptions
1. Demand for items from inventory is continuous and at a constant
rate
2. Production runs to replenish inventory are made at regular
intervals
3. During a production run, the production of items is continuous and
at a constant rate
4. Production set-up/ordering cost is fixed (independent of quantity
produced)
5. The lead time is fixed
6. The purchase price of the item is constant i.e. no discount is
available
7. The replenishment is made incrementally
[edit] Variables
* K = ordering/setup cost
* D = demand rate
* F = holding cost
* T = cycle length
* P = production rate
* x = \frac {D}{P}
* Q = order quantity
[edit] Derivation of EPQ Formula
Holding Cost per Year = \frac{Q} {2} F(1-x)
Where \frac{Q} {2} is the average inventory level, and F(1-x) is the
average holding cost. Therefore multiplying these two results in the
Holding cost per Year.
Ordering Cost per Year = \frac{D} {Q} K
Where \frac{D} {Q} are the orders placed in a year, multiplied by K
results in the Ordering Cost per Year.
We can notice from the equations above that the total ordering cost
decreases as the production quantity increases. Inversely, the total
holding cost increases as the production quantity increases. Therefore
in order to get the optimal production quantity we need to set holding
cost per year equal to ordering cost per year and solve for quantity
(Q), which is the EPQ formula mentioned below. Ordering this quantity
will result in the lowest total inventory cost per year.
[edit] EPQ Formula
EPQ = Q* = \sqrt {\frac {2KD}{F(1-x)}}
[edit] Inventory Cost Graph
This figure graphs the Holding Cost and Ordering Cost per year
equations. The third line is the addition of these two equations, which
generates the Total Inventory Cost per year. This graph should give you
a better understanding of the derivation of the optimal ordering
quantity equation, i.e., the EPQ equation.
* EPQ Graph
[edit] Relevant Formulas
Average holding cost per unit time:
\frac{1} {2} FD(1-x)*T
Average ordering and holding cost as a function of time:
x(T) = \frac {1} {2} FD(1-x)T+ \frac {K} {T}
[edit] See also
Classical Newsvendor problem
[edit] References
* Gallego, G. "IEOR4000: Production Management" (Lecture 2), Columbia
(2004). [1]
* Stevenson, W. J. "Operations Management" PowerPoint slide 19, The
McGraw-Hill Companies (2005). [2]
* Kroeger, D. R. "Determining Economic Production in a Continuous
Process" IIE Process Industries Webinar, IIE (2009). [3]
* Cárdenas-Barrón, L. E. "The Economic Production Quantity derived
Algebraically" International Journal of Production Economics,
Volume 77, Issue 1, (2002).
* Blumenfeld, D. "Inventory" Operations Research Calculations
Handbook, Florida (2001)
* Harris, F.W. "How Many Parts To Make At Once" Factory, The Magazine
of Management, 10(2), 135-136, 152 (1913).
Retrieved from
"http://en.wikipedia.org/w/index.php?title=Economic_production_quantity
&oldid=496286790"
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