This research work deals with an imperfect production system considering the purchasing of raw materials in order to study the economic production quantity (EPQ). This manufacturing system produces perfect and defective finished products; defectives are considered as scrap. A single product is manufactured from multiple raw materials which are purchased from outside suppliers. In the integrated procurement-production-inventory (IPPI) model, one of the principal decisions, in addition to determining the optimal lot size to produce, is to define the number of optimal orders of each raw material with respect to rate of consumption in the manufacturing of finished product. Two cases are considered: without shortage (first model) and with shortage (backordering, second model). In the first model, the purpose is to determine jointly the optimal lot size to manufacture and the optimal number orders of each raw material in order to minimize the total cost. The second model obtains the optimal number of orders of each raw material, the optimal lot size to manufacture and the optimal shortage level with aim to minimize the total cost. This research also shows that both of the proposed inventory models are a convex programming problem, so exact algorithms to solve these inventory problems are proposed.
Accepté le :
DOI : 10.1051/ro/2017067
Mots-clés : Economic production quantity, imperfect production system, shortage, lot sizingo, ptimization
@article{RO_2018__52_3_755_0,
author = {Nobil, Amir Hossein and C\'ardenas{\textendash}Barr\'on, Leopoldo Eduardo and Nobil, Erfan},
title = {Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {755--778},
publisher = {EDP-Sciences},
volume = {52},
number = {3},
year = {2018},
doi = {10.1051/ro/2017067},
zbl = {1405.90017},
mrnumber = {3868444},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2017067/}
}
TY - JOUR AU - Nobil, Amir Hossein AU - Cárdenas–Barrón, Leopoldo Eduardo AU - Nobil, Erfan TI - Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 755 EP - 778 VL - 52 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2017067/ DO - 10.1051/ro/2017067 LA - en ID - RO_2018__52_3_755_0 ER -
%0 Journal Article %A Nobil, Amir Hossein %A Cárdenas–Barrón, Leopoldo Eduardo %A Nobil, Erfan %T Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 755-778 %V 52 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2017067/ %R 10.1051/ro/2017067 %G en %F RO_2018__52_3_755_0
Nobil, Amir Hossein; Cárdenas–Barrón, Leopoldo Eduardo; Nobil, Erfan. Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 3, pp. 755-778. doi : 10.1051/ro/2017067. http://archive.numdam.org/articles/10.1051/ro/2017067/
[1] , , , and , A century of evolution from Harris basic lot size model: Survey and research agenda. Int. J. Prod. Econ. 155 (2014) 16–38 | DOI
[2] and , Integrated production and quality model under various preventive maintenance policies. J. Oper. Res. Soc. 49 (1998) 840–853 | DOI | Zbl
[3] , The economic production lot–sizing problem with imperfect production processes and imperfect maintenance. Int. J. Prod. Econ. 76 (2002) 257–264 | DOI
[4] , and , Optimal batch production with rework process for products with time–varying demand over finite planning horizon. In Operations Research, Engineering, and Cyber Security. Springer International Publishing (2017) 57–68 | MR | Zbl
[5] and , Multi–item imperfect production inventory model in bi–fuzzy environments. OPSEARCH 54 (2017) 260–282 | DOI | MR | Zbl
[6] , The economic production quantity without backlogging derived with algebra, in: Sixth International Conference of the Decision Sciences Institute, Chihuahua, Mexico (2001a)
[7] , The economic production quantity (EPQ) with shortage derived algebraically. Int. J. Prod. Econ. 70 (2001b) 289–292 | DOI
[8] , On optimal manufacturing batch size with rework process at single–stage production system. Comput. Ind. Eng. 53 (2007) 196–198 | DOI
[9] , Optimal manufacturing batch size with rework in a single–stage production system–a simple derivation. Comput. Ind. Eng. 55 (2008) 758–765 | DOI
[10] , The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra. Appl. Math. Model. 35 (2011) 2394–2407 | DOI | MR | Zbl
[11] , and , Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris. Int. J. Prod. Econ. 155 (2014) 1–7 | DOI
[12] , , and , A constrained multi-products EPQ inventory model with discrete delivery order and lot size. Appl. Math. Comput. 230 (2014) 359–370 | MR | Zbl
[13] , Scheduling for batch production. Instit. Prod. Eng. J. 36 (1957) 549–570 and 582
[14] and , Analysis of inventory systems with deteriorating items. Int. J. Prod. Res. 21 (1983) 449–460 | DOI | Zbl
[15] , , and , The integrality of the lot size in the basic EOQ and EPQmodels: applications to other production-inventory models. Appl. Math. Comput. 216 (2010) 1660–1672 | MR | Zbl
[16] , An integrated inventory model for a single supplier-single customer problem. Int. J. Prod. Res. 15 (1977) 107–111 | DOI
[17] , , Integrated procurement-production systems: a review. Eur. J. Oper. Res. 62 (1992) 1–10 | DOI | Zbl
[18] and , An integrated production–inventory–marketing model for deteriorating items. Comput. Ind. Eng. 28 (1995) 755–762 | DOI
[19] , and , Production lot sizing with machine breakdowns. Manag. Sci. 38 (1992) 104–123 | DOI | Zbl
[20] , Material requirements planning and manufacturing resource planning, edited by . International Encyclopedia of Business and Management, Routledge, London (1996)
[21] and , Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs, NJ (1963) | Zbl
[22] , , and , Lot sizing with non-zero setup times for rework. J. Syst. Sci. Sys. Eng. 17 (2008) 230–240 | DOI
[23] , How many parts to make at once. Factory: The Magazine of Manag. 10 (1913) 135–136 and 152
[24] and , Production lot sizing with the reworking of imperfect quality items produced. Prod. Plann. Control 12 (2001) 584–590 | DOI
[25] and , An optimal algorithm for integrating raw materials inventory in a single–product manufacturing system. Eur. J. Oper. Res. 59 (1992) 313–318 | DOI | Zbl
[26] , and , Optimal manufacturing batch size with rework process at a single-stage production system. Comput. Ind. Eng. 47 (2004) 77–89 | DOI
[27] and , in Production Planning, Scheduling and Inventory Model, Wiley (1974)
[28] , and , An inventory model under development cost–dependent imperfect production and reliability–dependent demand. J. Manag. Anal. 4 (2017) 258–275
[29] and , An integrated inventory model for a single product and its raw materials. Int. J. Prod. Res. 25 (1987) 627–634 | DOI | Zbl
[30] and , A production and maintenance planning model with restoration cost dependent on detection delay. IIE Trans. 21 (1989) 368–375 | DOI
[31] and , Economic production quantity model for randomly failing production process with minimal repair and imperfect maintenance. Int. J. Prod. Econ. 130 (2011) 118–124 | DOI
[32] , A production–inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments. J. Intell. Manuf . 28 (2017) 883–897 | DOI
[33] , , and , An EPQ model with promotional demand in random planning horizon: population varying genetic algorithm approach. To appear in: J. Intell. Manuf. (2016). DOI | DOI
[34] , and , Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand. Comput. Ind. Eng. 104 (2017) 9–22 | DOI
[35] , , and , Optimizing integrated manufacturing and products inspection policy for deteriorating manufacturing system with imperfect inspection. J. Manuf. Sys. 37 (2015) 299–315 | DOI
[36] , A summary of imperfect preventive maintenance policies with minimal repair. Revue Française D’automatique, D’informatique et de Recherche Opérationnelle. RAIRO: OR 14 (1980) 249–255 | DOI | Numdam | MR | Zbl
[37] , and , A multi–machine multi–product EPQ problem for an imperfect manufacturing system considering utilization and allocation decisions. Expert Sys. Appl. 56 (2016) 310–319 | DOI
[38] , and , Some observations to: Lot sizing with non–zero setup times for rework. Int. J. Appl. Comput. Math. (Suppl. 1) 3 (2017) 1511–1517 | DOI | MR
[39] , An integrated production–inventory model for decaying raw materials. Int. J. Sys. Sci. 14 (1983) 801–806 | DOI
[40] , , and , A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost. Int. J. Prod. Econ. 169 (2015) 203–214 | DOI
[41] and , A genetic algorithm approach to optimize a multi–products EPQ model with discrete delivery orders and constrained space. Appl. Math. Comput. 195 (2008) 506–514 | MR | Zbl
[42] , and , The deterministic EPQ with partial backordering: a new approach. Omega 37 (2009) 624–636 | DOI
[43] , Joint determination of production quantity, inspection schedule, and control chart design. IIE Trans. 26 (1994) 2–11 | DOI
[44] and , A generalized economic model for joint determination of production run, inspection schedule and control chart design. Int. J. Prod. Res. 36 (1998) 277–289 | DOI | Zbl
[45] , A production–inventory model for decaying raw materials and a decaying single finished product system. Int. J. Sys. Sci. 16 (1985) 1039–1044 | DOI | Zbl
[46] , and , Joint determination of process mean, production run size and material order quantity for a container–filling process. Int. J. Prod. Econ. 63 (2000) 303–317 | DOI
[47] and , Economic production cycles with imperfect production processes. IIE Trans. 18 (1986) 48–55 | DOI
[48] , A computational approach to the economic lot scheduling problem. Manag. Sci. 4 (1958) 264–291 | DOI
[49] and , Economic production quantity model for items with imperfect quality. Int. J. Prod. Econ. 64 (2000) 59–64 | DOI
[50] , A constrained integrated imperfect manufacturing–inventory system with preventive maintenance and partial backordering. Ann. Oper. Res. 261 (2017) 303–337 | DOI | MR | Zbl
[51] , and , A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process. Int. J. Prod. Econ. 150 (2014) 9–27 | DOI
[52] , and , Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments. Top 24 (2016) 143–155 | DOI | MR | Zbl
[53] , and , Multiproduct single–machine production system with stochastic scrapped production rate, partial backordering and service level constraint. J. Comput. Appl. Math. 233 (2010) 1834–1849 | DOI | MR | Zbl
[54] , The most economical production lot. Iron Age 101 (1918) 1410–1412
[55] and , A multi-product EPQ model with discrete delivery order: a Langrangean solution approach. In Global Perspective for Competitive Enterprise, Economy and Ecology. Springer, London (2009) 601–608 | DOI
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