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The inventory replenishment planning and staggering problem: a bi-objective approach

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Abstract

To the best of our knowledge, this paper is the first one to suggest formulating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions.

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Acknowledgements

This research work was partially supported by Grant OPG0036509 from the National Science and Engineering Research Council of Canada (NSERC) and Grant 96139 from “Université Laval.” This support is gratefully acknowledged. We also thank the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Centre interuniversitaire de recherché sur les réseaux d’entreprises, la logistique et le transport (CIRRELT), Faculté des sciences de l’administration, Université Laval, Quebec City, Canada

    Fayez F. Boctor & Marie-Claude Bolduc

Authors
  1. Fayez F. Boctor
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  2. Marie-Claude Bolduc
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Corresponding author

Correspondence to Fayez F. Boctor.

Appendix

Appendix

Results for the 20-item instances

Instance

Number of solutions on the OPF

EM

TPEA 200

TPEA 500

TPEA/EM

Method obtained the compromise solution

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

1

78

8

0

4

165

44

458

30

94

TPEA500

2

73

2

0

29

260

26

642

19

111

TPEA200

3

71

4

0

8

128

47

303

15

71

TPEA500

4

72

11

0

8

185

35

421

29

98

EM and TPEA/EM

5

77

2

0

10

320

46

848

22

159

TPEA500

6

71

4

0

6

187

44

494

20

86

TPEA500

7

75

5

0

7

158

55

395

14

83

TPEA500

8

66

3

0

12

405

38

1021

16

158

TPEA500

9

67

4

1

8

502

44

1105

14

207

TPEA500

10

91

8

0

13

248

44

600

34

101

TPEA200

11

64

0

0

3

185

52

444

9

99

TPEA500

12

81

2

0

4

295

59

758

18

184

TPEA500

13

66

13

1

7

298

22

624

37

128

EM and TPEA/EM

14

82

11

0

6

270

53

616

23

138

EM and TPEA/EM

15

72

11

1

9

439

19

1154

44

241

TPEA/EM

Instance

Number of solutions on the OPF

EM

TPEA 200

TPEA 500

TPEA/EM

Method obtained the compromise solution

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

16

67

5

0

4

422

36

1000

27

182

TPEA500

17

68

6

0

5

329

40

893

23

169

TPEA/EM

18

84

8

1

3

162

35

370

46

80

EM and TPEA/EM

19

66

2

0

8

203

34

461

25

80

TPEA/EM

20

76

1

0

16

402

45

974

16

194

TPEA200

21

61

1

0

4

286

38

758

19

145

TPEA500

22

88

4

0

11

229

43

599

34

117

TPEA500

23

68

1

0

28

275

25

800

16

150

TPEA200

24

70

16

1

4

458

27

1347

39

213

EM and TPEA/EM

25

71

1

0

9

201

41

567

21

117

TPEA500

26

70

9

0

14

388

26

971

30

176

TPEA500

27

61

8

0

4

175

29

502

27

118

TPEA/EM

28

95

3

0

22

364

55

791

18

185

TPEA500

29

63

6

0

6

328

28

876

30

161

TPEA/EM

30

87

1

0

12

274

52

700

23

135

TPEA500

Average

73.37

5.33

0.17

9.47

284.70

39.40

716.40

24.60

139.33

 

Minimum

61

0

0

3

128

19

303

9

71

 

Maximum

95

16

1

29

502

59

1347

46

241

 

Results for the 50-item instances

Instance

Number of solutions on the OPF

EM

TPEA 500

TPEA/EM

Method obtained the compromise solution

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

1

92

30

5

12

9240

80

1309

TPEA/EM

2

99

35

4

4

7573

95

1182

EM and TPEA/EM

3

100

36

4

10

6018

90

775

EM and TPEA/EM

4

87

32

4

3

9819

83

1395

EM and TPEA/EM

5

89

21

3

24

3466

65

584

TPEA/EM

6

96

31

4

3

9605

93

1378

EM and TPEA/EM

7

82

27

4

1

8775

81

1267

TPEA/EM

8

75

15

4

21

8070

54

1101

TPEA/EM

9

86

37

6

3

11,028

83

1499

EM and TPEA/EM

10

98

34

4

3

9058

95

1277

TPEA/EM

11

70

17

4

5

8046

65

1204

TPEA/EM

12

81

27

4

1

8190

80

1458

EM and TPEA/EM

13

92

31

4

3

8853

89

1389

EM and TPEA/EM

14

84

27

4

6

8742

78

1396

EM and TPEA/EM

15

89

27

4

8

9183

81

1482

TPEA/EM

Instance

Number of solutions on the OPF

EM

TPEA 500

TPEA/EM

Method obtained the compromise solution

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

Number of solutions on the OPF

Computation time (s)

16

77

29

3

4

7577

73

1219

TPEA/EM

17

84

18

4

1

8456

83

1166

TPEA/EM

18

88

35

4

7

8178

81

1622

EM and TPEA/EM

19

103

36

5

7

8961

95

1275

EM and TPEA/EM

20

92

26

4

12

9199

80

1337

EM and TPEA/EM

21

84

31

4

7

8229

77

1770

EM and TPEA/EM

22

102

42

5

4

11,589

98

1400

TPEA/EM

23

83

31

6

5

8084

78

1390

EM and TPEA/EM

24

105

36

6

7

8429

98

1485

TPEA/EM

25

88

40

6

7

9622

81

1350

EM and TPEA/EM

26

93

34

8

4

10,644

89

1605

EM and TPEA/EM

27

93

43

5

3

8543

90

1201

EM and TPEA/EM

28

98

40

5

10

8721

88

1438

EM and TPEA/EM

29

78

25

3

6

6984

72

1151

EM and TPEA/EM

30

98

34

6

4

9663

94

1402

TPEA/EM

Average

89.53

30.90

4.53

6.50

8 618.17

82.97

1316.90

 

Minimum

70

15

3

1

3466

54

584

 

Maximum

105

43

8

24

11,589

98

1770

 

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Boctor, F.F., Bolduc, MC. The inventory replenishment planning and staggering problem: a bi-objective approach. 4OR-Q J Oper Res 16, 199–224 (2018). https://doi.org/10.1007/s10288-017-0362-2

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