Penalty costs can be assessed only against the number of units of demand that cannot be satisfied, or against the number of units weighted by the amount of time thatan order stays on the books. Consider the following history of supply and demandtransactions for a particular part:Number of Items Demand duringMonth Received MonthJanuary 200 520February 175 1,640March 750 670April 950 425May 500 280June 2,050 550Assume that starting inventory at the beginning of January is 480 units.a. Determine the ending inventory each month. Assume that excess demands areback-ordered.b. Assume that each time a unit is demanded that cannot be supplied immediately,a one-time charge of $10 is made. Determine the stock-out cost incurred duringthe six months (1) if excess demand at the end of each month is lost, and (2) ifexcess demand at the end of each month is back-ordered.c. Suppose that each stock-out costs $10 per unit per month that the demandremains unfilled. If demands are filled on a first-come, first-served basis, whatis the total stock-out cost incurred during the six months using this type of costcriterion? (Assume that the demand occurs at the beginning of the month forpurposes of your calculation.) Notice that you must assume that excessdemands are back-ordered for this case to make any sense.d. Discuss under what circumstances the cost criterion used in part (b) might beappropriate and under what circumstances the cost criterion used in part (c)might be appropriate.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Penalty costs can be assessed only against the number of units of demand that cannot be satisfied, or against the number of units weighted by the amount of time that
an order stays on the books. Consider the following history of supply and demand
transactions for a particular part:
Number of Items Demand during
Month Received Month
January 200 520
February 175 1,640
March 750 670
April 950 425
May 500 280
June 2,050 550
Assume that starting inventory at the beginning of January is 480 units.
a. Determine the ending inventory each month. Assume that excess demands are
back-ordered.
b. Assume that each time a unit is demanded that cannot be supplied immediately,
a one-time charge of $10 is made. Determine the stock-out cost incurred during
the six months (1) if excess demand at the end of each month is lost, and (2) if
excess demand at the end of each month is back-ordered.
c. Suppose that each stock-out costs $10 per unit per month that the demand
remains unfilled. If demands are filled on a first-come, first-served basis, what
is the total stock-out cost incurred during the six months using this type of cost
criterion? (Assume that the demand occurs at the beginning of the month for
purposes of your calculation.) Notice that you must assume that excess
demands are back-ordered for this case to make any sense.
d. Discuss under what circumstances the cost criterion used in part (b) might be
appropriate and under what circumstances the cost criterion used in part (c)
might be appropriate.

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