An economic production quantity model with backlogging and imperfect rework process for uncertain demand

This paper deals with a lot-sizing problem in the economic production quantity model with imperfect production processes and failure in repair where a Brownian motion process governs the inventory level variation. We assume that the unsatisfied demand is fully backlogged. In addition, we assume that all imperfect items produced are stocked separately and then reworked. Reworking and shortage costs are included in the proposed mathematical modelling and analysis. The aim of this research is to determine the optimal production lot size and backorder level such that the long-run total expected cost of the system is minimised. For the proposed model, we prove closed-form expressions for the inventory process and for the backlog costs. Moreover, a computer code using software package for the numerical work is furnished to derive the optimal solution. Some numerical examples and sensitivity analysis are provided to illustrate the validity of the proposed model.

[1]  Abolfazl Gharaei,et al.  An integrated multi-product, multi-buyer supply chain under penalty, green, and quality control polices and a vendor managed inventory with consignment stock agreement: The outer approximation with equality relaxation and augmented penalty algorithm , 2019, Applied Mathematical Modelling.

[2]  Hsien-Jen Lin,et al.  Two-echelon stochastic inventory system with returns and partial backlogging , 2015, Int. J. Syst. Sci..

[3]  L. Ouyang,et al.  An arithmetic-geometric mean inequality approach for determining the optimal production lot size with backlogging and imperfect rework process , 2016 .

[4]  Saeed Zolfaghari,et al.  A review of the extensions of a modified EOQ model for imperfect quality items , 2011 .

[5]  Walid W. Nasr,et al.  Production lot sizing with quality screening and rework , 2016 .

[6]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .

[7]  Seyed Ashkan Hoseini Shekarabi,et al.  Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decomposition , 2020, International Journal of Systems Science: Operations & Logistics.

[8]  G. Gallego.  Scheduling the production of several items with random demands in a single facility , 1990 .

[9]  Biswajit Sarkar,et al.  Easy and Improved Algorithms to Joint Determination of the Replenishment Lot Size and Number of Shipments for an Epq Model with Rework , 2013 .

[10]  Peter W. Glynn,et al.  Managing Capacity and Inventory Jointly in Manufacturing Systems , 2002, Manag. Sci..

[12]  Y. Chiu.  Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging , 2003 .

[13]  Singa Wang Chiu,et al.  Production lot size problem with failure in repair and backlogging derived without derivatives , 2008, Eur. J. Oper. Res..

[14]  Walid W. Nasr,et al.  Economic production quantity with maintenance interruptions under random and correlated yields , 2017, Int. J. Prod. Res..

[15]  Leopoldo Eduardo Cárdenas-Barrón,et al.  An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments , 2013 .

[16]  L. Cárdenas-Barrón,et al.  Multi products single machine EPQ model with immediate rework process , 2012 .

[17]  K. S. Chaudhuri,et al.  Maximising profits for an EPQ model with unreliable machine and rework of random defective items , 2013, Int. J. Syst. Sci..

[18]  J. Sicilia,et al.  Optimal lot size for a production–inventory system with partial backlogging and mixture of dispatching policies , 2014 .

[19]  Salwa Hanim Abdul-Rashid,et al.  Economic order quantity models for items with imperfect quality and emission considerations , 2018 .

[20]  R. Vickson.  A Single Product Cycling Problem Under Brownian Motion Demand , 1986 .

[21]  Ata Allah Taleizadeh,et al.  An improved solution to replenishment lot size problem with discontinuous issuing policy and rework, and the multi-delivery policy into economic production lot size problem with partial rework , 2012, Expert Syst. Appl..

[22]  Monami Das Roy,et al.  An economic production lot size model for defective items with stochastic demand, backlogging and rework , 2014 .

[23]  Ata Allah Taleizadeh,et al.  Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments , 2016 .

[24]  Anja Walter,et al.  Introduction To Stochastic Calculus With Applications , 2016 .

[25]  Manoranjan Maiti,et al.  A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints , 2008, Eur. J. Oper. Res..

[26]  Hui-Ming Wee,et al.  Multi-product production quantity model with repair failure and partial backordering , 2010, Comput. Ind. Eng..

[27]  L. Cárdenas-Barrón,et al.  Learning and screening errors in an EPQ inventory model for supply chains with stochastic lead time demands , 2017, Int. J. Prod. Res..

[28]  Chao Deng,et al.  Selective maintenance scheduling under stochastic maintenance quality with multiple maintenance actions , 2018, Int. J. Prod. Res..

[29]  Hui-Ming Wee,et al.  An economic production quantity model with non-synchronized screening and rework , 2014, Appl. Math. Comput..

[30]  A. H. Nobil,et al.  Economic production quantity model considering warm-up period in a cleaner production environment , 2018, Int. J. Prod. Res..

[31]  Allen H. Tai.  Economic production quantity models for deteriorating/imperfect products and service with rework , 2013, Comput. Ind. Eng..

[32]  S. T. A. Niaki,et al.  A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost , 2015 .

[33]  Shib Sankar Sana,et al.  A mathematical model on EPQ for stochastic demand in an imperfect production system , 2013 .

[34]  Hsien-Jen Lin,et al.  Two-critical-number control policy for a stochastic production inventory system with partial backlogging , 2017, Int. J. Prod. Res..

[35]  Ata Allah Taleizadeh,et al.  Determining Replenishment Lot Size and Shipment Policy for an EPQ Inventory Model with Delivery and Rework , 2015 .

[36]  Adriana Leiras,et al.  Economic production quantity (EPQ) model with partial backordering and a discount for imperfect quality batches , 2018, Int. J. Prod. Res..

[37]  P. A. Hayek,et al.  Production lot sizing with the reworking of imperfect quality items produced , 2001 .

[38]  L. Ouyang,et al.  Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging , 2013 .

[39]  Jia-Tzer Hsu,et al.  Economic production quantity (EPQ) models under an imperfect production process with shortages backordered , 2016, Int. J. Syst. Sci..

[40]  Hsien-Jen Lin.  A collaborating inventory system in a supply chain under Brownian motion demand and imperfect quality , 2014 .

[41]  Rezg Nidhal,et al.  Joint optimisation of maintenance and production policies considering random demand and variable production rate , 2012 .

[42]  Shib Sankar Sana,et al.  A production-inventory model in an imperfect production process , 2010, Eur. J. Oper. Res..

[43]  B. Bidanda,et al.  Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging , 2018, Int. J. Prod. Res..

[44]  Singa Wang Chiu,et al.  Mathematical modeling for production system with backlogging and failure in repair , 2006 .

[45]  J. Bather.  A continuous time inventory model , 1966, Journal of Applied Probability.

[46]  Dacheng Yao.  Joint pricing and inventory control for a stochastic inventory system with Brownian motion demand , 2016, 1608.03033.

[47]  Shib Sankar Sana,et al.  An economic production lot size model in an imperfect production system , 2010, Eur. J. Oper. Res..

[48]  Gad Allon,et al.  Global Dual Sourcing: Tailored Base-Surge Allocation to Near- and Offshore Production , 2010, Manag. Sci..

[49]  Michael Trott.  The Mathematica GuideBook for Numerics , 2005 .