A modelling framework for the acquisition and remanufacturing of used products

Figures & data

Figure 1 The states of the PAS.

Table 1 Characteristics and description of the various quality levels of returned cell phones.

Quality level	Description
6	Pass a functional and electrical test and with minimal cleaning look like brand new. Phones show no physical damage and have a good antenna, display, lens, keypad and a working charging system.
5	Pass a functional and electrical test and with cleaning and buffing look almost as if they were brand new. Phones show no physical damage and have a good antenna, display, lens, keypad and a working charging system. Keypad and plastic may show some fading.
4	Pass a functional and electrical test but will require rework to make these phones usable. Phones have a good display and working keypad, but may have some physical damage and may show signs of wear that will require the replacement of some parts.
3	Phones have the same physical appearance as the quality level 6 phones, but failed the test or did not power up and their lens may have some scratches. Many of these phones can be repaired with some technical knowledge.
2	Phones have the same physical appearance as a quality level 5 phones, but failed the test or did not power up. Many of these phones can be repaired with some technical knowledge.
1	Phones have failed the test or did not power up. Phones can be used for part salvage.

Table 2 Parameters values for states 3 and 4 of the PAS.

States 3 and 4
Parameter	Examined values	Parameter	Examined values	Parameter	Examined values
K	6	p s ($)	U (125, 145)	c r,4 ($)	U (30, 31.5)
i	1 to	P e ($)	U (4, 13)	c r,5 ($)	U (20, 21)
L	6	c r,1 ($)	U (45, 47.25)	c r,6 ($)	U (5, 5.25)
j	1 to	c r,2 ($)	U (40, 42)	c s ($)	U (7.5, 33.5)
D (cell phones)	U (10, 5000)	c r,3 ($)	U (35, 36.75)	W ($)	A very large value
State 3
	Examined values
Parameter	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6
f i (j) for ∀ i	The types of suppliers arise randomly	Every type of supplier appears once	The types of suppliers arise randomly	Every type of supplier appears once	The types of suppliers arise randomly	Every type of supplier appears once
A i for ∀ i (cell phones)	U (0, 0.8√D)	U (0, 0.8√D)	U (0, 1.1√D)	U (0, 1.1√D)	U (0, 5000)	U (0, 5000)
State 4
Parameter	Examined values
c a,i ($)	For	For	For	For	For	For
	U (60, 63)	U (70, 73.5)	U (80, 84)	U (90, 94.5)	U (95, 99.75)	U (100, 105)
A i for ∀ i (cell phones)	for every j, where A i refers to the batch size of state 3
Note: Information on prices and costs was valid in 2004. Today, there might be significant differentiations.

Table 3 Percentages f _i(j) of the various types of suppliers.

Type of supplier	Percentages f i (j)
I
II
III
IV
V
VI

Table 4 Indicative sets of size and quality of offered batches.

	State 3									State 4
D	i	A i	Type of supplier	f i (1)	f i (2)	f i (3)	f i (4)	f i (5)	f i (6)	j	A 1	A 2	A 3	A 4	A 5	A 6
1133	1	702	I	0	0	0.2414	0.2586	0.2993	0.2007	1	251.64
	2	614	II	0.0848	0.1621	0.3079	0.2921	0.1379	0.0152	2		293.19
	3	682	III	0	0	0	0	0.4720	0.5280	3			533.85
	4	760	IV	0.2540	0.2460	0.2231	0.2769	0	0	4				987.24
	5	1236	V	0	0	0	0.3365	0.3602	0.3034	5					1061.80
	6	19	VI	0.3442	0.3502	0.3056	0	0	0	6						885.27
1700	1	1251	II	0.0691	0.1955	0.3413	0.2587	0.1045	0.0309	1	510.97
	2	136	II	0.0972	0.1512	0.3186	0.2814	0.1488	0.0028	2		709.71
	3	1033	IV	0.2868	0.2132	0.2061	0.2939	0	0	3			1095.25
	4	1349	II	0.0853	0.1663	0.3054	0.2946	0.1337	0.0147	4				1410.73
	5	1094	III	0	0	0	0	0.5026	0.4974	5					1214.56
	6	1061	V	0	0	0	0.3279	0.3143	0.3579	6						982.78
2029	1	68	I	0	0	0.2071	0.2929	0.2385	0.2615	1	0
	2	1854	I	0	0	0.2595	0.2405	0.2712	0.2288	2		0
	3	1227	V	0	0	0	0.3541	0.3100	0.3359	3			984.98
	4	2109	I	0	0	0.2323	0.2677	0.2005	0.2995	4				2089.32
	5	1304	V	0	0	0	0.3657	0.3370	0.2973	5					1896.53
	6	415	V	0	0	0	0.3551	0.3248	0.3201	6						2006.17

Table 5 Minimum values of c _a,i s and c _r,j s, for a used Nokia 5100, depending on its quality level.

j	1	2	3	4	5	6
min c a,i	60	70	80	90	95	100
min c r,j	45	40	35	30	20	5

Table 6 Simulated parameters values and solution of the versions of the MIP model for states 3 and 4 of the PAS, for the second (highlighted) set of A _i and f _i (j) values of Table 4.

Parameters values for both states 3 and 4
p s	p e	c r,1	c r,2	c r,3	c r,4	c r,5	c r,6	c s
128.75	6.29	46.22	41.25	36.28	30.64	20.59	5.16	27.80

Table 7 Analysis of results of all simulated sets (20,000 per examined scenario).

	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6
Percentage (number) of sets where C 3 < 0 (%)	0 (0)	0.02 (4)	0 (0)	0.005 (1)	16.52 (3304)	16.57 (3314)
Percentage (number) of sets where C 4 < 0 (%)	0.06 (12)	0.02 (4)	0.35 (70)	0.005 (1)	18.06 (3611)	20.80 (4159)
Percentage of sets where ΔQ 4>0 (%)	88.89	90.91	81.05	86.61	68.73	70.83
Average ΔQ 4 (%)	17.37	17.84	16.56	19.34	46.21	9.49
Maximum ΔQ 4 (%)	500.62	914.49	306.83	545.89	147,832.80	180,820.45
Minimum ΔQ4 (%)	− 175.60	− 37.22	− 234.22	− 65.92	− 212,684.21	− 80,471.09

Figure 2 Relative frequencies of the percentage profit increase .

Parameters values for state 3						Parameters values for state 4
c a,1	c a,2	c a,3	c a,4	c a,5	c a,6	c a,1	c a,2	c a,3	c a,4	c a,5	c a,6
83.94	84.02	77.30	84.31	99.65	97.82	60.92	71.16	83.43	93.44	95.27	104.07

Solution of the version of the MIP model for state 3
y 1	y 2	y 3	y 4	y 5	y 6	C 3	A	R	R 1		R 2	R 3	R 4	R 5		R 6
0	1	0	1	0	0	9929.45	1485	1485	128.24		244.87	455.32	435.68	200.63		20.26
x 1,1	x 1,2	x 1,3	x 1,4	x 1,5	x 1,6	x 2,1	x 2,2	x 2,3	x 2,4	x 2,5	x 2,6	x 3,1	x 3,2	x 3,3	x 3,4	x 3,5	x 3,6
0	0	0	0	0	0	1	1	1	1	1	1	0	0	0	0	0	0
x 4,1	x 4,2	x 4,3	x 4,4	x 4,5	x 4,6	x 5,1	x 5,2	x 5,3	x 5,4	x 5,5	x 5,6	x 6,1	x 6,2	x 6,3	x 6,4	x 6,5	x 6,6
1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0

Solution of the version of the MIP model for state 4
y 1	y 2	y 3	y 4	y 5	y 6	C 4	A	R	x 1	x 2	x 3	x 4	x 5	x 6
0	1	0	0	0	1	30,561.99	1692.50	1692.50	0	1	0	0	0	1

Table 8 Sensitivity analysis results.

State 3 of the PAS
Parameter	A i ∼U (0,0.8 · D) for ∀ i			A i ∼U (0,1.1 · D) for ∀ i			A i ∼U (0,5000) for ∀ i
pk
D	258,763,383	1,082,154,241	0.761	249,572,475	1,080,533,105	0.769	358,669,007	1,449,807,024	0.752
p s	779,692,298	1,111,688,993	0.299	742,674,849	1,053,212,235	0.295	1,184,331,686	1,443,883,475	0.180
c r,l	1,005,355,673	1,107,093,637	0.092	978,309,736	1,074,738,905	0.090	1,335,099,947	1,476,648,192	0.096
p e	966,423,504	1,076,390,633	0.102	990,370,778	1,093,970,751	0.095	1,220,606,022	1,367,246,360	0.107
A 1	992,941,324	1,108,368,535	0.104	965,640,030	1,067,453,614	0.095	1,317,229,625	1,465,259,837	0.101
c s	981,608,690	1,083,460,186	0.094	994,308,866	1,121,898,848	0.114	1,315,678,443	1,469,309,489	0.105
c a,1	994,128,215	1,097,968,916	0.095	926,580,868	1,058,031,262	0.124	1,348,510,094	1,474,993,274	0.086
f 1 (1)	1,027,458,816	1,118,222,793	0.081	996,277,426	1,115,125,018	0.107	1,265,413,351	1,446,481,406	0.125
State 4 of the PAS
D	308,533,125	1,400,620,596	0.780	345,769,300	1,430,516,877	0.758	421,860,626	1,799,455,068	0.766
p s	1,050,585,023	1,362,280,021	0.229	1,086,742,658	1,414,279,087	0.232	1,396,072,048	1,750,699,754	0.203
c r,l	1,182,036,654	1,322,757,713	0.106	1,219,267,454	1,371,204,625	0.111	1,527,408,214	1,684,166,299	0.093
p e	1,237,974,191	1,396,584,295	0.114	1,291,006,353	1,442,749,324	0.105	1,532,141,662	1,700,168,011	0.099
A 1	1,258,830,823	1,387,059,062	0.092	1,289,017,532	1,434,714,469	0.102	1,523,152,641	1,678,719,323	0.093
c s	1,262,408,580	1,406,859,253	0.103	1,274,173,372	1,408,864,239	0.096	1,444,289,156	1,615,289,036	0.106
c a,1	1,219,522,421	1,357,697,529	0.102	1,248,086,922	1,380,093,339	0.096	1,604,543,173	1,820,829,228	0.119