Probabilistic multi-item inventory model with varying mixture shortage cost under restrictions

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Table 4 The optimal values of \(Q^{} ,r^{}\) and min E (TC) at different values of β

β	Item 1					Item 2					Item 3
β	\(\lambda_{1}^{*}\)	\(\lambda_{2}^{*}\)	\(Q^{*}\)	\(r^{*}\)	min E (TC1)	\(\lambda_{1}^{*}\)	\(\lambda_{2}^{*}\)	\(Q^{*}\)	\(r^{*}\)	min E (TC2)	\(\lambda_{1}^{*}\)	\(\lambda_{2}^{*}\)	\(Q^{*}\)	\(r^{*}\)	min E (TC3)
0.1	0.02	0.021	3635.43	10,543	39,538	0.001	0.012	3758	1161	36,431	0.14	0.012	3322	9282	159,060
0.2	0.024	0.025	3786.93	10,635	40,586	0.001	0.021	3926	11,699	37,443	0.13	0.18	3430	9323	161,426
0.3	0.025	0.027	3931.32	10,727	41,582	0.002	0.022	4071	11,789	38,400	0.13	0.19	3584	9364	164,554
0.4	0.032	0.034	4083.49	10,819	42,467	0.002	0.027	4210	11,879	39,256	0.13	0.19	3717	9384	166,737
0.5	0.039	0.040	4246	10,888	43,302	0.004	0.042	4404	11,857	39,603	0.12	0.19	3852	9384	168,639
0.6	0.042	0.043	4413.04	10,934	44,124	0.005	0.052	4554	11,992	40,902	0.12	0.19	3990	9384	170,104
0.7	0.043	0.044	4554.17	11,003	44,886	0.008	0.063	4719	12,069	41,634	0.12	0.19	4124	9405	172,461
0.8	0.048	0.046	4730.91	11,026	45,598	0.01	0.068	4881	12,104	42,323	0.12	0.19	4261	9405	174,186
0.9	0.049	0.048	4876.67	11,026	45,865	0.01	0.071	5056	12,149	43,008	0.13	0.19	4455	9364	175,779