Determining the number of attendants in a storeroom

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In designing a new manufacturing plant, questions have arisen regarding the number of support personnel required. In the process of analyzing each area of the plant to determine the number required, a dispute has occurred regarding the storeroom. Manufacturing wants enough attendants so that machine operator will seldom have to wait to be served; in fact, they are lobbying for five attendants to be assigned full-time to the storeroom. The manufacturing engineer argues that such a solution will be cost prohibitive.

Table 10.38 Determining the Number of Servers to Provide in a Storeroom
c	[latex]L_{q}[/latex]	VC(c)
2	1.92857	$116.79
3	0.23684	$55.66
4	0.04475	$60.40
5	0.00863	$75.39

The engineer and manufacturing manager have agreed that the costs involved are [latex]C_{1}[/latex] [latex]=\$ 45 /[/latex] hour and [latex]C_{3}=\$ 15 /[/latex] hour. It is estimated that [latex]\lambda=30 /[/latex] hour and [latex]\mu=20 /[/latex] hour. From Table [latex]10.38[/latex], we see that the optimum number of attendants for the storeroom is three.

Interestingly, with [latex]\lambda / \mu=1.5, c^{*}=3[/latex] for [latex]\$ 8.865 /[/latex] hour [latex]\leq C_{1} \leq \$ 78.13 /[/latex] hour when [latex]C_{3}=[/latex] [latex]\$ 15 /[/latex] hour. Hence, the optimum number of servers is relatively insensitive to the cost of machine operators waiting for service.

Question 10.72: Determining the number of attendants in a storeroom

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