Effect of Setup Reduction on EOQ and Inventory Cost What is the effect of reducing setup time on economic batch size and total inventory costs in Example 25.3 in the previous chapter? In that example, annual demand = 15,000 pc/yr, unit cost = $20, holding cost rate = 18%/yr, setup time = 5 hr, and

Question

Effect of Setup Reduction on EOQ and Inventory Cost
What is the effect of reducing setup time on economic batch size and total inventory costs in Example 25.3 in the previous chapter? In that example, annual demand = 15,000 pc/yr, unit cost = $20, holding cost rate = 18%/yr, setup time = 5 hr, and cost of downtime during setup = $150/hr. Suppose it were possible to reduce setup time from 5 hr to 5 min (this kind of reduction is not so far-fetched, given the data in Table 26.4).

Table 26.4 Examples of Setup Time Reductions in Japanese and U.S. Industries

Industry	Equipment Type	Setup Time Before	Setup Time After	Reduction (%)
Japanese automotive	1,000-ton press	4 hr	3 min	98.7
Japanese diesel	Transfer line	9.3 hr	9 min	98.4
U.S. power tool	Punch press	2 hr	3 min	97.5
Japanese automotive	Machine tool	6 hr	10 min	97.2
U.S. electric appliance	45-ton press	50 min	2 min	96.0

Determine (a) the economic batch quantity and (b) total inventory cost for this new situation.

Accepted Answer

First, recall the results of the earlier example. Setup cost [latex]C_{su} = (5 hr) (\$150) = \$750[/latex] and holding cost [latex]C_{h} = 0.18(\$20) = \$3.60[/latex]. Using these values, the economic batch quantity was computed as follows:

[latex]EOQ = \sqrt{\frac{2(15,000)(750)}{3.60} }= 2,500[/latex] units

The corresponding total inventory costs were computed as

[latex]TIC = \frac{2,500(3.60)}{2} + \frac{750(15,000)}{2,500}= \$9,000[/latex]

(a) Reducing the setup time to 5 min reduces the setup cost to [latex]C_{su} = (5/60 hr) (\$150) = \$12.50[/latex]. Holding cost remains the same, and the new economic batch quantity is

[latex]EOQ = \sqrt{\frac{2(15,000)(12.50)}{3.60} }= 323[/latex] units

This is a significant reduction from the 2,500 pc batch size when setup time was 5 hr.
(b) Total inventory costs are also reduced, as follows:

[latex]TIC = \frac{323(3.60)}{2} + \frac{12.50(15,000)}{323}= \$1,161[/latex]

This is an 87% cost reduction from the previous value.

Question 26.1: Effect of Setup Reduction on EOQ and Inventory Cost What is ...

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