no. 1
Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model
Benkherouf, Lakdere1 ; Omar, Mohamed2
1 Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait.
2 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 173-187

This paper proposes a finite-horizon and time-varying demand rate function formulations for the optimal manufacturing batch size model with rework. The basic model is found in [Jamal et al. Comput. Ind. Eng. 47 (2004) 77–89.]. Two policies 1 and 2 are considered. In Policy 1 defective items produced in a given period are remanufactured within thesame period while Policy 2 accumulates the defective items until the last period. The search for the optimal manufacturing batch size for policies 1 and 2 is shown to reduce to the problem of determining the number of manufacturing-rework periods as well as their starting and finishing times. This leads to the examination of two mixed integer non-linear programming problem which are completely solved by appealing to some established techniques proposed in [Al-Khamis et al. Int. J. Syst. Sci. 45 (2014) 2196–2202]. Numerical results are also presented for illustration.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016011
Classification : 90B05
Keywords: Inventory control, finite horizon problem, mixed integer non-linear programming, optimization

Benkherouf, Lakdere 1 ; Omar, Mohamed 2

1 Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait.
2 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia. 
@article{RO_2017__51_1_173_0,
     author = {Benkherouf, Lakdere and Omar, Mohamed},
     title = {Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {173--187},
     year = {2017},
     publisher = {EDP Sciences},
     volume = {51},
     number = {1},
     doi = {10.1051/ro/2016011},
     mrnumber = {3597665},
     zbl = {1358.90006},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2016011/}
}
TY  - JOUR
AU  - Benkherouf, Lakdere
AU  - Omar, Mohamed
TI  - Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2017
SP  - 173
EP  - 187
VL  - 51
IS  - 1
PB  - EDP Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2016011/
DO  - 10.1051/ro/2016011
LA  - en
ID  - RO_2017__51_1_173_0
ER  - 
%0 Journal Article
%A Benkherouf, Lakdere
%A Omar, Mohamed
%T Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2017
%P 173-187
%V 51
%N 1
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/ro/2016011/
%R 10.1051/ro/2016011
%G en
%F RO_2017__51_1_173_0
Benkherouf, Lakdere; Omar, Mohamed. Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 173-187. doi: 10.1051/ro/2016011

T. Al-Khamis, L. Benkherouf and M. Omar, Optimal policies for a finite-horizon batching inventory model. Int. J. Syst. Sci. 45 (2014) 2196–2202. | MR | Zbl | DOI

A.O. Alsuwainea, L. Benkherouf and S.P. Sethi, Optimal batch ordering over a finite-horizon batching inventory model. Int. J. Oper. Res. 19 (2014) 385–406. | MR | Zbl | DOI

L. Benkherouf and B.H. Gilding, On a class of optimization problems for finite time horizon inventory models. SIAM J. Control Optim. 48 (2009) 993–1030. | MR | Zbl | DOI

P. Biswas and B.R. Sarker, Optimal batch quantity for a lean production system with in-cycle rework and scrap. Int. J. Prod. Res. 46 (2008) 6585–6610. | DOI

L.E. Cárdenas-Barrón, On Optimal manufacturing batch size with rework process in a single-stage production system. Comput. Ind. Eng. 53 (2007) 196–198. | DOI

L.E. Cárdenas-Barrón, Optimal manufacturing batch size with rework in a single-stage production system – A simple derivation. Comp. Ind. Eng. 55 (2008) 758–765. | DOI

L.E. Cárdenas-Barrón, On optimal batch-sizing in a multi-production system with rework consideration. Eur. J. Oper. Res. 196 (2009) 1238–1244. | MR | Zbl | DOI

S.D.P. Flapper, J.C. Fransoo, R.A.C.M. Broekmeulen and K. Inderfurth, Planning and control of rework in the process industries: a review. Prodution Planning and Control 43 (2002) 1355–1374.

M. Fleishmann, H.R. Krikke, R. Dekker and S.D. Flapper, A characterisation of logistic networks for product recovery. Omega 28 (2000) 653–666. | DOI

R.M. Hill, Batching policies for linearly increasing demand with a finite input rate. Int. J. Prod. Econ. 43 (1996) 149–154. | DOI

R.M. Hill, M. Omar and D.K. Smith, Stock replenishment policy for deterministic linearly increasing demand with a finite input rate. J. Sains 8 (2000) 977–986.

A.M.M. Jamal, B.R. Sarker and S. Mondal, Optimal manufacturing batch size with rework in a single-stage production system. Comput. Ind. Eng. 47 (2004) 77–89. | DOI

I. Konstantaras and S. Papachristos, A note on: Developing an exact solution for an inventory system with product recovery. Int. J. Prod. Econ. 111 (2008) 707–712. | DOI

I. Konstantaras, S.K. Goyal and S. Papachristos, Economic ordering policy for an item with imperfect quality subject to the in-house inspection. Int. J. Syst. Sci. 38 (2007) 473–482. | Zbl | DOI

N. Liu, Y., Kim and H. Hwang, An optimal operating policy for the production system with rework. Comput. Ind. Eng. 56 (2009) 874–888. | DOI

S. Nahmias and H. Reviera, A deterministic model for repairable item inventory systems with a finite repair rate. Int. J. Prod. Res. 17 (1979) 215–221. | DOI

M. Omar and D.K. Smith, An optimal batch size for a production system under linearly increasing-time varying demand process. Comput. Ind. Eng. 42 (2002) 35–42. | DOI

M. Omar and I. Yeo, A model for a production repair system under a time-varying demand process. Int. J. Prod. Econ. 119 (2009) 17–23. | DOI

M. Omar and I. Yeo, A production-repair inventory model time-varying demand and multiple setups. Int. J. Prod. Econ. 155 (2014) 398–405. | DOI

H. Rau and B.C. Ou Yang, A general and optimal approach to three inventory models with a linear trend in demand. Comput. Ind. Eng. 52 (2007) 521–532. | DOI

B.R. Sarker, A.M.M. Jamal and S. Mondal, On optimal batch-sizing in a multi-production system with rework consideration. Eur. J. Oper. Res. 184 (2008) 915–929. | MR | Zbl | DOI

D.A. Schrady, A deterministic inventory model for repairable items. Naval Res. Logistic 48 (1967) 484–495.

R.H. Teunter, Lot-sizing with product recoovery. Comput. Ind. Eng. 46 (2004) 431–441. | DOI

A.A. Taleizadeh, L.E. Cárdenas-Barrón, J. Biabani and R. Nikousokhan, Multi products single machine EPQ model with immediate rework process. Int. J. Ind. Eng. Comput. 3 (2012) 93–102.

M. Ullah and C.W. Kang, Effect of rework, rejects and inspection on lot size with work-in-process inventory. Int. J. Prod. Res. 52 (2014) 2448–2460. | DOI

H.M. Wee, W.T. Wang and L.E. Cárdenas-Barrón, An alternative analysis and solution procedure for the EPQ model with rework process at a single-stage manufacturing system with planned backorders. Comput. Ind. Eng. 64 (2013) 748–755. | DOI

G.A. Widyadana and H.M. Wee, An economic production quantity model for deteriorating items with multiple production setups and rework. Int. J. Prod. Econ. 138 (2012) 62–67. | DOI

Cité par Sources :