EPQ Model for Trended Demand with Rework and Random Preventive Machine Time

Table 1

Sensitivity analysis of 𝑇_1𝑎 and total cost when preventive maintenance time is uniformly and exponentially distributed.

Parameter	Percentage change	Uniform distribution		Exponential distribution 𝜆=20
		𝑇1𝑎	TCT	𝑇1𝑎	TCT
𝐴	−40%	0.1118836	2217.023407	0.165363168	3105.82179
	−20%	0.1127598	2396.444313	0.168010377	3225.883231
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1145095	2751.208003	0.173362159	3460.599558
	40%	0.1153831	2926.585673	0.176064945	3575.33395
𝑃	−40%	0.119	0.224	0.873011973	3769.650118
	−20%	0.116	0.220356527	0.280588937	3224.896639
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.0784111	2671.944386	0.123903512	3421.121046
	40%	0.0598742	2748.060997	0.09758743	3473.297234
𝑃1	−40%	0.1252239	2840.779326	0.179184671	3667.154126
	−20%	0.117738	2670.650277	0.17374104	3462.440106
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1110459	2512.591082	0.168712009	3266.965218
	40%	0.1093473	2469.539689	0.167344624	3212.637461
a	−40%	0.0468611	2285.690117	0.081365729	2483.982152
	−20%	0.0736194	2419.311543	0.118822843	2928.274545
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1801641	2784.239588	0.248801609	3743.389279
	40%	0.313401	3147.605249	0.385620567	4166.830717
b	−40%	0.1133496	2572.975288	0.170020919	3336.335153
	−20%	0.113492	2573.73768	0.170347969	3340.233353
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1137789	2575.262185	0.171008033	3348.022553
	40%	0.1139235	2576.024314	0.1713411	3351.913594
𝑥	−40%	0.1075459	2440.729188	0.165578265	3180.040146
	−20%	0.1105098	2506.778232	0.168074836	3261.520565
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1169347	2644.037111	0.173391457	3427.954424
	40%	0.1204229	2715.549502	0.176225505	3513.094599
𝑥1	−40%	0.1131507	2451.633648	0.170247776	3220.242525
	−20%	0.1133924	2513.000758	0.170462207	3282.119979
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1138787	2636.131758	0.17089215	3406.270464
	40%	0.1141232	2697.89656	0.171107662	3468.544359
ℎ	−40%	0.1163864	2035.802579	0.196138784	2497.162768
	−20%	0.114993	2306.766649	0.18157314	2935.554059
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1123112	2839.068303	0.162020977	3729.597492
	40%	0.11102	3100.535386	0.15486872	4096.262909
ℎ1	−40%	0.113733	2555.165605	0.171388527	3315.223296
	−20%	0.113684	2564.8349	0.171031253	3329.691775
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1135862	2584.160837	0.170325715	3358.53567
	40%	0.1135373	2593.817484	0.169977356	3372.911591
𝑆	−40%	0.1119752	2570.475444	0.15263831	3147.25954
	−20%	0.1129966	2572.958931	0.162618107	3255.743808
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1140719	2575.549497	0.1774544	3418.940914
	40%	0.1143897	2576.310317	0.183312722	3483.929611
𝑆𝑐	−40%	0.113643	2453.561123	0.170776446	3223.952673
	−20%	0.113639	2514.030563	0.170726744	3284.041215
	0	0.1136351	2574.499976	0.170676999	3344.12915
	20%	0.1136311	2634.969362	0.17062721	3404.216467
	40%	0.1136271	2695.438718	0.170577378	3464.303169