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Hillier and Lieberman §18.3: economic order quantity for the television speakers

ToolInventory Policy
SourceHillier, F. S., and Lieberman, G. J. (2010). Introduction to Operations Research, 9th ed. McGraw-Hill, New York. Section 18.3, speaker example.
LevelUndergraduate

Problem

A television manufacturer produces its own speakers for 8,000 sets a month; a production run costs $12,000 to set up, the unit cost is $10 and holding a speaker costs $0.30 per month. How many speakers should each run produce, how often, and what is the resulting variable cost per month? What does a rounded lot of 25,000 cost?

Inputs to Enter

  • Model EOQ (default), period month: demand 8,000, order cost 12,000, unit cost 10, holding cost 0.30 per unit-month
  • Evaluate Q = 25,000
Open the Inventory Policy tool (loaded with this example)

Answers

  • Q* = √(2 × 8,000 × 12,000/0.30) = 25,298; cycle t* = Q*/D = 3.162 months; 0.3162 runs per month
  • Ordering cost DK/Q* = 3,794.7 = holding cost hQ*/2; total variable cost √(2DKh) = 7,589.5 per month
  • Lot 25,000: ordering 3,840, holding 3,750, ratio to the optimum 1.00007; a lot of 2Q* or Q*/2 costs 25 % more

Notes

The tool's default inputs are this example; press Submit. The printed results are quoted in the CRAN SCperf manual, which cites the book.

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