The modern marketing environment involves variability and randomness within the numerous parties of any supply chain network. Thus, formation of a supply chain model including multiple buyers and variable production rate is more acceptable than assuming a single-buyer with constant production rate model. This paper considers a supply chain network, where a single-vendor manufactures products in a batch production process and supplies them to a set of buyers over multiple times. Instead of assuming a fixed production rate, as commonly used in the literature, a variable production rate is introduced by the vendor and the production cost of the vendor is treated as a function of production rate. The continuous review inventory model is applied for multiple buyers to inspect inventory levels and a crashing cost is incurred by all buyers to reduce their lead times. The lead time demand follows a normal distribution. The unsatisfied demands at the buyers end are partially backordered. A model is formulated to minimize the joint expected cost of the vendor-buyers supply chain system. A classical optimization technique is utilized to solve the model. An improved algorithm is developed to obtain the numerical solution of the model. Finally, numerical examples are given to illustrate the model.
Mots clés : Supply chain model, single-setup multi-delivery (SSMD) policy, controllable lead time reduction, variable production rate
@article{RO_2018__52_3_943_0,
author = {Majumder, Arunava and Jaggi, Chandra K. and Sarkar, Biswajit},
title = {A multi-retailer supply chain model with backorder and variable production cost},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {943--954},
publisher = {EDP-Sciences},
volume = {52},
number = {3},
year = {2018},
doi = {10.1051/ro/2017013},
zbl = {1405.90015},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2017013/}
}
TY - JOUR AU - Majumder, Arunava AU - Jaggi, Chandra K. AU - Sarkar, Biswajit TI - A multi-retailer supply chain model with backorder and variable production cost JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 943 EP - 954 VL - 52 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2017013/ DO - 10.1051/ro/2017013 LA - en ID - RO_2018__52_3_943_0 ER -
%0 Journal Article %A Majumder, Arunava %A Jaggi, Chandra K. %A Sarkar, Biswajit %T A multi-retailer supply chain model with backorder and variable production cost %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 943-954 %V 52 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2017013/ %R 10.1051/ro/2017013 %G en %F RO_2018__52_3_943_0
Majumder, Arunava; Jaggi, Chandra K.; Sarkar, Biswajit. A multi-retailer supply chain model with backorder and variable production cost. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 3, pp. 943-954. doi : 10.1051/ro/2017013. http://www.numdam.org/articles/10.1051/ro/2017013/
[1] and , Reducing lost-sales rate in (T, R, L) inventory model with controllable lead time. Appl. Math. Modell. 34 (2010) 3465−3477 | DOI | Zbl
[2] , A joint economic-lot-size model for purchaser and vendor. Decision Sci. 17 (1986) 292−311 | DOI
[3] and , A coordinated order-up-to inventory control policy for a single supplier and multiple buyers using electronic data interchange. Int. J. Prod. Econom. 35 (1994) 85−91 | DOI
[4] and , Coordinated versus independent inventory replenishment policies for a vendor and multiple buyers. Int. J. Prod. Econom. 35 (1994) 215−222 | DOI
[5] and , Inventory models involving lead time as a decision variable. J. Oper. Res. Soc. 45 (1994) 579−582 | DOI | Zbl
[6] , and , Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris. Int. J. Prod. Econom. 155 (2014) 1−7 | DOI
[7] and , A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams’ initiatives. Int. J. Prod. Econom. 155 (2014) 249−258 | DOI
[8] and , An optimal solution to a three echelon supply chain network with multi-product and multi-period. Appl. Math. Modell. 38 (2014) 1911−1918 | DOI | Zbl
[9] and , Multi-item EOQ inventory model in a two-layer supply chain while demand varies with a promotional effort. Appl. Math. Modell. 39 (2015) 6725−6737 | DOI | Zbl
[10] , , and , An economic manufacturing quantity model for a two-stage assembly system with imperfect processes and variable production rate. Comput. Industrial Eng. 63 (2012) 285−293 | DOI
[11] , An easy method to derive the integrated vendor-buyer production-inventory model with backordering using cost-difference rate comparison approach. Math. Comput. Modell. 57 (2013) 632−640 | DOI | Zbl
[12] and , The drilling problem: a stochastic modeling and control example in manufacturing. IEEE Tran. Auto. Cont. 32 (1987) 947−958 | DOI | Zbl
[13] , and , Lead time and ordering cost reductions in budget and storage space restricted probabilistic inventory models with imperfect items. RAIRO: OR 49 (2015) 215−242 | DOI | Numdam | Zbl
[14] and , Computational aspects of an extended EMQ model with variable production rate. Comput. Oper. Res. 32 (2005) 3143−3161 | DOI | Zbl
[15] and , The effect of forward integration on a single-vendor multi-retailer supply chain under retailer competition. Int. J. Prod. Econom. 164 (2015) 179−192 | DOI
[16] , An integrated inventory model for a single supplier-single customer problem. Int. J. Prod. Res. 15 (1976) 107−111
[17] , Economic ordering policy for deteriorating items over an infinite time horizon. Eur. J. Oper. Res. 28 (1987) 298−301 | DOI | Zbl
[18] , A joint economic-lot-size model for purchaser and vendor: a comment. Deci. Sci. 19 (1988) 236−241 | DOI
[19] and , Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies. Comput. Oper. Res. 38 (2011) 1294–1304 | DOI | Zbl
[20] and , Implementation of JIT purchasing: an integrated approach. Prod. Plan. Cont. 8 (1997) 152−157 | DOI
[21] , Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain. Eur. J. Oper. Res. 188 (2008) 811−825 | DOI | Zbl
[22] and , Two-echelon supply chain inventory model with controllable lead time and service level constraint. Comput. Industrial Eng. 57 (2009) 1096−1104 | DOI
[23] and , Economic production lot size model with variable production rate and imperfect quality. J. Oper. Res. Soc. 45 (1994) 1405−1417 | DOI | Zbl
[24] and , An analytical determination of lead time with normal demand. Int. J. Oper. Prod. Manag. 11 (1991) 72−78 | DOI
[25] , and , Min-max distribution free continuous review model with a service level constraint and variable lead time, Appl. Math. Comput. 229 (2014) 310−315 | Zbl
[26] , and , Mixture inventory model with backorders and lost sales for variable lead time. J. Oper. Res. Soc. 47 (1996) 829−832 | DOI | Zbl
[27] , and , Integrated vendor-buyer cooperative models with stochastic demand in controllable lead time. Int. J. Prod. Econom. 92 (2004) 255−266 | DOI
[28] and , A study of an integrated inventory with controllable lead time. Int. J. Prod. Res. 40 (2002) 1263−1273 | DOI | Zbl
[29] , A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Appl. Math. Modell. 37 (2013) 3138−3151 | DOI | Zbl
[30] and , Integrated vendor-buyer supply chain model with vendor’s setup cost reduction. Appl. Math. Comput. 224 (2013) 362−371 | Zbl
[31] and , Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process. Int. J. Prod. Econom. 155 (2014) 2014−2013 | DOI
[32] , , and , An economic production quantity model with random defective rate, rework process and backorders for a single stage production system. J. Manufact. Syst. 33 (2014) 423−435 | DOI
[33] and , Periodic review fuzzy inventory models with variable lead time and fuzzy demand. Int. Tran. Oper. Res. 24 (2017) 1197–227 | DOI | Zbl
[34] , and , Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level. J. Manufact. Syst. 34 (2015) 74−82 | DOI
[35] , and , Quality improvement and backorder price discount under controllable lead time in an inventory model. J. Manufact. Syst. 35 (2015) 26−36 | DOI
[36] , Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Math. Prob. Eng. 2016 (2016) 6318737 | DOI | Zbl
[37] , , , and , Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction. J. Indus. Manag. Optim. 13 (2017) 1085−1104 | DOI | Zbl
[38] , and , Coordination of a single-manufacturer/multi-buyer supply chain with credit option. Int. J. Prod. Econom. 111 (2008) 676−685 | DOI
[39] , , and , Controllable lead time, service level constraint, and transportation discounts in a continuous review inventory model. RAIRO-Oper. Res. 50 (2015) 921−934 | DOI | Numdam | Zbl
[40] and , Optimal strategy for an integrated inventory system involving variable production and defective items under retailer partial trade credit policy. Deci. Supp. Syst. 54 (2012) 235−247 | DOI
[41] , Optimal times of price reductions for an inventory model with partial backorder and vertical shift demand. RAIRO: OR 41 (2007) 35−47 | DOI | Numdam | Zbl
Cité par Sources :
