Designing an aircraft repair and refurbishment facility

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A regional aircraft repair and refurbishing facility for a major airline company is to be located at the Northwest Arkansas Regional Airport in Highfill, Arkansas. Decisions must be made regarding the number of repair stations and crews [latex](c)[/latex] and the size of the hangar and apron space [latex](N)[/latex] for airplanes.

Requests for repair and refurbishment occur at a Poisson rate of 25 per month. The time required to perform the repair and refurbishment is exponentially distributed with a mean of [latex]0.125[/latex] month. Hence, [latex]\lambda=25[/latex] arrivals per month and [latex]\mu=8[/latex] repair and refurbishments per month. If requests are received and there is no space available for arriving jets, they will go to either another region or a private contractor's facility. Having repair stations and crews sitting idle, waiting to perform the required work, costs [latex]\$ 10,000[/latex] per month for each station and crew. When the stations and crews are busy, the cost is [latex]\$ 20,000[/latex] per month per station and crew. Hangar and apron space costs [latex]\$ 2,500[/latex] per airplane position per month. Having jets sitting, waiting to be served, incurs an additional cost of protecting and sheltering the planes; it is estimated to be [latex]\$ 500[/latex] per airplane per month waiting to be served.

When the system is full and business has to be diverted to other facilities, an opportunity cost of [latex]\$ 25,000[/latex] is incurred per lost job.

Based on the cost data available, the following expected cost per month is to be minimized:

[latex]\begin{aligned}T C(c, N)=& \$ 500 L_{q}+\$ 20,000\left(L-L_{q} ight)+\$ 10,000\left(c-L+L_{q} ight) \&+\$ 2,500 N+\$ 25,000(25) P_{N}\end{aligned}[/latex]

Table [latex]10.40[/latex] provides the results of an enumeration of [latex]c[/latex] and [latex]N[/latex].

As seen, the optimum number of crews and repair stations is five, and the optimum size of the facility, measured in number of jets it can handle, including those waiting for repair and refurbishment, is 10 . As with the previous example, the optimum solution is not especially sensitive to the cost parameters.

For example, if the opportunity cost is [latex]\$ 15,000[/latex], then the optimum solution is [latex]\left(c^{*}, N^{*} ight)=[/latex] [latex](5,9)[/latex]; likewise, if the opportunity cost is [latex]\$ 35,000[/latex], then the optimum solution is [latex]\left(c^{*}, N^{*} ight)=[/latex] [latex](5,11) .[/latex] What if demand changes? For [latex]C_{6}=\$ 25,000[/latex] and [latex]\lambda=20,\left(c^{*}, N^{*} ight)=(4,9) ;[/latex] likewise, if [latex]\lambda=30[/latex], then [latex]\left(c^{*}, N^{*} ight)=(6,11) .[/latex]

Table 10.40 Determining the Number of Aircraft Repair and Refurbishment Stations and Crews and the Number of Spaces for Aircraft in the Hangar and on the Service Apron
c	N
c	4	5	6	7	8	9	10	11	12	13	14
4	$203,501.03	$163,707.95	$140,915.59	$127,009.12	$118,298.79	$112,864.22	$109,607.09	$107,854.19	$107,170.65	$107,263.90	$107,930.75
5		$152,375.71	$125,749.36	$112,040.25	$105,086.95	$101,922.41	[latex]\fbox {\$100,972.94}[/latex]	$101,351.66	$102,539.29	$104,224.35	$106,217.12
6			$124,511.32	$110,127.17	$104,229.73	$102,458.56	$102,761.35	$104,124.45	$106,034.41	$108,227.71	$110,568.16
7				$114,695.36	$108,875.01	$107,722.29	$108,603.92	$110,383.98	$112,563.12	$114,920.02	$117,356.17
8					$116,480.57	$115,448.98	$116,577.20	$118,542.61	$120,834.01	$123,252.57	$125,720.76
9						$124,489.67	$125,678.81	$127,724.48	$130,066.85	$132,512.14	$134,993.15
10							$135,329.67	$137,397.78	$139,762.90	$142,220.76	$144,707.60
11								$147,292.63	$149,664.52	$152,128.13	$154,617.80
12									$159,632.40	$162,097.87	$164,588.88

Question 10.74: Designing an aircraft repair and refurbishment facility

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