April  2017, 13(2): 1085-1104. doi: 10.3934/jimo.2016063

Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction

1. 

Department of Industrial & Management Engineering, Hanyang University, Ansan Gyeonggi-do, 426 791, South Korea

2. 

Department of Basic Science And Humanities, Techno India College of Technology, Rajarhat, Kolkata 700 156, India

3. 

Department of Mathematics & Statistics, Banasthali Vidyapith, Banasthali, Rajasthan, 304 022, India

4. 

New Jersey Institute of Technology University Heights, Newark, NJ 07102-1982, USA

* Corresponding author: mitalisarkar.ms@gmail.com(Mitali Sarkar), Phone Number-010-7490-1981, Fax No +82-31-436-8146

Received  September 2015 Revised  August 2016 Published  October 2016

For quality improvement purposes often times, a manufacturing unit has to change certain parts of equipment. Any such changes in the assembly line manufacturing system or production process involves a cost known as the setup cost. Minimizing the setup cost and improving the product quality is of prime importance in today's competitive business arena. This paper develops the effects of setup cost reduction and quality improvement in a two-echelon supply chain model with deterioration. The objective is to minimize the total cost of the entire supply chain model (SCM) by simultaneously optimizing setup cost, process quality, number of deliveries, and lot size. Numerical examples are provided to illustrate the model.

Citation: Biswajit Sarkar, Arunava Majumder, Mitali Sarkar, Bikash Koli Dey, Gargi Roy. Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1085-1104. doi: 10.3934/jimo.2016063
References:
[1]

M. AsghariS. J. Abrishami and F. Mahdavi, Reverse logistic network design with incentive-dependent return, Industrial Engineering & Management Systems, 13 (2014), 383-397.  doi: 10.7232/iems.2014.13.4.383.  Google Scholar

[2]

A. Banerjee, A joint economic-lot-size model for purchaser and vendor, Decision Sciences, 17 (1986), 292-311.  doi: 10.1111/j.1540-5915.1986.tb00228.x.  Google Scholar

[3]

M. Ben-Daya and A. Raouf, Inventory models involving lead time as decision variable, The Journal of the Operational Research Society, 45 (1994), 579-582.   Google Scholar

[4]

S. Bylka, Competitive and cooperative policies for the vendor-buyer system, International Journal of Production Economics, 81/82 (2003), 533-544.  doi: 10.1016/S0925-5273(02)00273-6.  Google Scholar

[5]

L. E. Cárdenas-Barrón, Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note, Transportation Research Part E: Logistics and Transportation Review, 43 (2007), 647-654.   Google Scholar

[6]

L. E. Cárdenas-Barrón, The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra, Applied Mathematical Modelling, 35 (2011), 2394-2407.  doi: 10.1016/j.apm.2010.11.053.  Google Scholar

[7]

R. P. Covert and G. C. Philip, An EOQ model for items with Weibull distribution deterioration, A I I E Transactions, 5 (1973), 323-326.   Google Scholar

[8]

P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.   Google Scholar

[9]

A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with shortages and a linear trend in demand, The Journal of the Operational Research Society, 42 (1991), 1105-1110.   Google Scholar

[10]

S. K. Goyal, An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 15 (2007), 107-111.  doi: 10.1080/00207547708943107.  Google Scholar

[11]

S. K. Goyal, Economic ordering policy for deteriorating items over an infinite time horizon, European Journal of Operational Research, 28 (1987), 298-301.  doi: 10.1016/S0377-2217(87)80172-8.  Google Scholar

[12]

S. K. Goyal, A joint economic-lot-size model for purchaser and vendor: A comment, Decision Sciences, 19 (1988), 236-241.  doi: 10.1111/j.1540-5915.1988.tb00264.x.  Google Scholar

[13]

M. Hariga and M. Ben-Daya, Some stochastic inventory models with deterministic variable lead time, European Journal of Operational Research, 113 (1999), 42-51.  doi: 10.1016/S0377-2217(97)00441-4.  Google Scholar

[14]

R. M. Hill, The single-vendor single-buyer integrated production-inventory model with a generalised policy, European Journal of Operational Research, 97 (1997), 493-499.  doi: 10.1016/S0377-2217(96)00267-6.  Google Scholar

[15]

J. D. Hng and J. C. Hayya, Joint investment in quality improvement and setup reduction, Computers & Operations Research, 22 (1995), 567-574.   Google Scholar

[16]

H. HwangD. B. Kim and Y. D. Kim, Multiproduct economic lot size models with investments costs for setup reduction and quality improvement, International Journal of Production Research, 31 (1993), 691-703.  doi: 10.1080/00207549308956751.  Google Scholar

[17]

G. Keller and H. Noori, Impact of investing in quality improvement on the lot size model, OMEGA, 16 (1988), 595-601.  doi: 10.1016/0305-0483(88)90033-3.  Google Scholar

[18]

G. Keller and H. Noori, Justifying new technology acquisition through its impact on the cost of running an inventory policy, IIE Transactions, 20 (1988), 284-291.  doi: 10.1080/07408178808966182.  Google Scholar

[19]

E. Kusukawa and S. Alozawa, Optimal operation for green supply chain with quality of recyclable parts and contract for recycling activity, Industrial Engineering & Management Systems, 14 (2015), 248-274.  doi: 10.7232/iems.2015.14.3.248.  Google Scholar

[20]

C. J. Liao and C. H. Shyu, An analytical determination of lead time with normal demand, International Journal of Operations & Production Management, 11 (1991), 72-80.  doi: 10.1108/EUM0000000001287.  Google Scholar

[21]

R. B. Misra, Optimum production lotsize model for a system with deteriorating inventory, International Journal of Production Research, 13 (1975), 495-505.   Google Scholar

[22]

I. Moon, Multiproduct economic lot size models with investments costs for setup reduction and quality improvement: review and extensions, International Journal of Production Research, 32 (1994), 2795-2801.  doi: 10.1080/00207549408957100.  Google Scholar

[23]

I. Moon and S. Choi, A note on lead time and distributional assumptions in continuous review inventory models, Computers and Operations Research, 25 (1998), 1007-1012.  doi: 10.1016/S0305-0548(97)00103-2.  Google Scholar

[24]

L. Y. OuyangN. C. Yeh and K. S. Wu, Mixture inventory model with backorders and lost sales for variable lead time, The Journal of the Operational Research Society, 47 (1996), 829-832.   Google Scholar

[25]

M. J. PaknejadF. Nasri and J. F. Affisco, Defective units in a continuous review (s, Q) system, International Journal of Production Research, 33 (1995), 2767-2777.  doi: 10.1080/00207549508904844.  Google Scholar

[26]

C. Park, Partial backordering inventory model under purchase dependence, Industrial Engineering & Management Systems, 14 (2015), 275-288.   Google Scholar

[27]

E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144.  doi: 10.1287/opre.34.1.137.  Google Scholar

[28]

E. L. Porteus, Investing in reduced setups in the EOQ model, Management Science, 31 (1985), 998-1010.  doi: 10.1287/mnsc.31.8.998.  Google Scholar

[29]

F. Raafat, Survey of literature on continuously deteriorating inventory model, The Journal of the Operational Research Society, 42 (1991), 27-37.   Google Scholar

[30]

M. J. Rosenblatt and H. L. Lee, Economic production cycles with imperfect production processes, IIE Transactions, 18 (1986), 48-55.  doi: 10.1080/07408178608975329.  Google Scholar

[31]

B. Sarkar, An EOQ model with delay in payments and time varying deterioration rate, Mathematical and Computer Modelling, 55 (2012), 367-377.  doi: 10.1016/j.mcm.2011.08.009.  Google Scholar

[32]

B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Applied Mathematical Modelling, 37 (2013), 3138-3151.  doi: 10.1016/j.apm.2012.07.026.  Google Scholar

[33]

B. SarkarK. Chaudhuri and I. Moon, Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint, Journal of Manufacturing Systems, 34 (2015), 74-82.   Google Scholar

[34]

B. R. Sarker and E. R. Coates, Manufacturing setup cost reduction under variable lead times and finite opportunities for investment, International Journal of Production Economics, 49 (1997), 237-247.  doi: 10.1016/S0925-5273(97)00010-8.  Google Scholar

[35]

B. SarkarB. Mandal and S. Sarkar, Quality improvement and backorder price discount under controllable lead time in an inventory model, Journal of Manufacturing Systems, 35 (2015), 26-36.  doi: 10.1016/j.jmsy.2014.11.012.  Google Scholar

[36]

B. Sarkar and I. Moon, Improved quality, set up cost reduction and variable backorder costs in an imperfect production process, International Journal of Production Economics, 155 (2014), 204-213.   Google Scholar

[37]

B. SarkarS. Saren and H. M. Wee, An inventory model with variable demand, component cost and selling price for deteriorating items, Economic Modelling, 30 (2013), 306-310.  doi: 10.1016/j.econmod.2012.09.002.  Google Scholar

[38]

B. Sarkar and S. Sarkar, An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand, Economic Modelling, 30 (2013), 924-932.  doi: 10.1016/j.econmod.2012.09.049.  Google Scholar

[39]

B. Sarkar and S. Sarkar, Variable deterioration and demand-a inventory model, Economic Modelling, 31 (2013), 548-556.  doi: 10.1016/j.econmod.2012.11.045.  Google Scholar

[40]

Y. K. Shah, An order-level lot-size inventory model for deteriorating items, A I I E Transactions, 9 (1977), 108-112.  doi: 10.1080/05695557708975129.  Google Scholar

[41]

E. A. Silver, Changing the givens in modelling inventory problems: The example of just-in-time systems, International Journal of Production Economics, 26 (1992), 347-351.  doi: 10.1016/0925-5273(92)90086-M.  Google Scholar

[42]

E. A. Silver, D. F. Pyke and R. Peterson, Inventory Management and Production Planning and Scheduling, Wiley, New York, 1998. Google Scholar

[43]

K. Skouri and S. Papachristos, Four inventory models for deteriorating items with time varying demand and partial backlogging: A cost comparison, Optimal Control Applications and Methods, 24 (2003), 315-330.  doi: 10.1002/oca.734.  Google Scholar

[44]

K. SkouriI. KonstantarasS. Papachristos and I. Ganas, Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate, European Journal of Operational Research, 192 (2009), 79-92.  doi: 10.1016/j.ejor.2007.09.003.  Google Scholar

[45]

J. T. TengL. E. Cárdenas-BarrónK. R. Lou and H. M. Wee, Optimal economic order quantity for buyer-distributor-vendor supply chain with backlogging without derivatives, International Journal of Systems Science, 44 (2013), 986-994.  doi: 10.1080/00207721.2011.652226.  Google Scholar

[46]

A. Villa, Introducing some supply chain management problems, International Journal of Production Economics, 73 (2001), 1-4.  doi: 10.1016/S0925-5273(01)00090-1.  Google Scholar

[47]

S. Viswanathan, Optimal strategy for the integrated vendor-buyer inventory model, European Journal of Operational Research, 105 (1998), 38-42.  doi: 10.1016/S0377-2217(97)00032-5.  Google Scholar

[48]

N. Watanable and E. Kusukawa, Optimal ordering policy in dual-sourcing supply chain considering supply disruptions and demand information, Industrial Engineering & Management Systems, 14 (2015), 129-158.   Google Scholar

[49]

W. Wisittipanich and P. Hengmeechai, A multi-objective differential evolution for just-in-time door assignment and truck scheduling in multi-door cross docking problems, Industrial Engineering & Management Systems, 14 (2015), 299-311.  doi: 10.7232/iems.2015.14.3.299.  Google Scholar

[50]

P. C. Yang and H. M. Wee, An arborescent inventory model in a supply chain system, Production Planning & Control: The Management of Operations, 12 (2001), 728-735.  doi: 10.1080/09537280010024063.  Google Scholar

show all references

References:
[1]

M. AsghariS. J. Abrishami and F. Mahdavi, Reverse logistic network design with incentive-dependent return, Industrial Engineering & Management Systems, 13 (2014), 383-397.  doi: 10.7232/iems.2014.13.4.383.  Google Scholar

[2]

A. Banerjee, A joint economic-lot-size model for purchaser and vendor, Decision Sciences, 17 (1986), 292-311.  doi: 10.1111/j.1540-5915.1986.tb00228.x.  Google Scholar

[3]

M. Ben-Daya and A. Raouf, Inventory models involving lead time as decision variable, The Journal of the Operational Research Society, 45 (1994), 579-582.   Google Scholar

[4]

S. Bylka, Competitive and cooperative policies for the vendor-buyer system, International Journal of Production Economics, 81/82 (2003), 533-544.  doi: 10.1016/S0925-5273(02)00273-6.  Google Scholar

[5]

L. E. Cárdenas-Barrón, Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note, Transportation Research Part E: Logistics and Transportation Review, 43 (2007), 647-654.   Google Scholar

[6]

L. E. Cárdenas-Barrón, The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra, Applied Mathematical Modelling, 35 (2011), 2394-2407.  doi: 10.1016/j.apm.2010.11.053.  Google Scholar

[7]

R. P. Covert and G. C. Philip, An EOQ model for items with Weibull distribution deterioration, A I I E Transactions, 5 (1973), 323-326.   Google Scholar

[8]

P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.   Google Scholar

[9]

A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with shortages and a linear trend in demand, The Journal of the Operational Research Society, 42 (1991), 1105-1110.   Google Scholar

[10]

S. K. Goyal, An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 15 (2007), 107-111.  doi: 10.1080/00207547708943107.  Google Scholar

[11]

S. K. Goyal, Economic ordering policy for deteriorating items over an infinite time horizon, European Journal of Operational Research, 28 (1987), 298-301.  doi: 10.1016/S0377-2217(87)80172-8.  Google Scholar

[12]

S. K. Goyal, A joint economic-lot-size model for purchaser and vendor: A comment, Decision Sciences, 19 (1988), 236-241.  doi: 10.1111/j.1540-5915.1988.tb00264.x.  Google Scholar

[13]

M. Hariga and M. Ben-Daya, Some stochastic inventory models with deterministic variable lead time, European Journal of Operational Research, 113 (1999), 42-51.  doi: 10.1016/S0377-2217(97)00441-4.  Google Scholar

[14]

R. M. Hill, The single-vendor single-buyer integrated production-inventory model with a generalised policy, European Journal of Operational Research, 97 (1997), 493-499.  doi: 10.1016/S0377-2217(96)00267-6.  Google Scholar

[15]

J. D. Hng and J. C. Hayya, Joint investment in quality improvement and setup reduction, Computers & Operations Research, 22 (1995), 567-574.   Google Scholar

[16]

H. HwangD. B. Kim and Y. D. Kim, Multiproduct economic lot size models with investments costs for setup reduction and quality improvement, International Journal of Production Research, 31 (1993), 691-703.  doi: 10.1080/00207549308956751.  Google Scholar

[17]

G. Keller and H. Noori, Impact of investing in quality improvement on the lot size model, OMEGA, 16 (1988), 595-601.  doi: 10.1016/0305-0483(88)90033-3.  Google Scholar

[18]

G. Keller and H. Noori, Justifying new technology acquisition through its impact on the cost of running an inventory policy, IIE Transactions, 20 (1988), 284-291.  doi: 10.1080/07408178808966182.  Google Scholar

[19]

E. Kusukawa and S. Alozawa, Optimal operation for green supply chain with quality of recyclable parts and contract for recycling activity, Industrial Engineering & Management Systems, 14 (2015), 248-274.  doi: 10.7232/iems.2015.14.3.248.  Google Scholar

[20]

C. J. Liao and C. H. Shyu, An analytical determination of lead time with normal demand, International Journal of Operations & Production Management, 11 (1991), 72-80.  doi: 10.1108/EUM0000000001287.  Google Scholar

[21]

R. B. Misra, Optimum production lotsize model for a system with deteriorating inventory, International Journal of Production Research, 13 (1975), 495-505.   Google Scholar

[22]

I. Moon, Multiproduct economic lot size models with investments costs for setup reduction and quality improvement: review and extensions, International Journal of Production Research, 32 (1994), 2795-2801.  doi: 10.1080/00207549408957100.  Google Scholar

[23]

I. Moon and S. Choi, A note on lead time and distributional assumptions in continuous review inventory models, Computers and Operations Research, 25 (1998), 1007-1012.  doi: 10.1016/S0305-0548(97)00103-2.  Google Scholar

[24]

L. Y. OuyangN. C. Yeh and K. S. Wu, Mixture inventory model with backorders and lost sales for variable lead time, The Journal of the Operational Research Society, 47 (1996), 829-832.   Google Scholar

[25]

M. J. PaknejadF. Nasri and J. F. Affisco, Defective units in a continuous review (s, Q) system, International Journal of Production Research, 33 (1995), 2767-2777.  doi: 10.1080/00207549508904844.  Google Scholar

[26]

C. Park, Partial backordering inventory model under purchase dependence, Industrial Engineering & Management Systems, 14 (2015), 275-288.   Google Scholar

[27]

E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144.  doi: 10.1287/opre.34.1.137.  Google Scholar

[28]

E. L. Porteus, Investing in reduced setups in the EOQ model, Management Science, 31 (1985), 998-1010.  doi: 10.1287/mnsc.31.8.998.  Google Scholar

[29]

F. Raafat, Survey of literature on continuously deteriorating inventory model, The Journal of the Operational Research Society, 42 (1991), 27-37.   Google Scholar

[30]

M. J. Rosenblatt and H. L. Lee, Economic production cycles with imperfect production processes, IIE Transactions, 18 (1986), 48-55.  doi: 10.1080/07408178608975329.  Google Scholar

[31]

B. Sarkar, An EOQ model with delay in payments and time varying deterioration rate, Mathematical and Computer Modelling, 55 (2012), 367-377.  doi: 10.1016/j.mcm.2011.08.009.  Google Scholar

[32]

B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Applied Mathematical Modelling, 37 (2013), 3138-3151.  doi: 10.1016/j.apm.2012.07.026.  Google Scholar

[33]

B. SarkarK. Chaudhuri and I. Moon, Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint, Journal of Manufacturing Systems, 34 (2015), 74-82.   Google Scholar

[34]

B. R. Sarker and E. R. Coates, Manufacturing setup cost reduction under variable lead times and finite opportunities for investment, International Journal of Production Economics, 49 (1997), 237-247.  doi: 10.1016/S0925-5273(97)00010-8.  Google Scholar

[35]

B. SarkarB. Mandal and S. Sarkar, Quality improvement and backorder price discount under controllable lead time in an inventory model, Journal of Manufacturing Systems, 35 (2015), 26-36.  doi: 10.1016/j.jmsy.2014.11.012.  Google Scholar

[36]

B. Sarkar and I. Moon, Improved quality, set up cost reduction and variable backorder costs in an imperfect production process, International Journal of Production Economics, 155 (2014), 204-213.   Google Scholar

[37]

B. SarkarS. Saren and H. M. Wee, An inventory model with variable demand, component cost and selling price for deteriorating items, Economic Modelling, 30 (2013), 306-310.  doi: 10.1016/j.econmod.2012.09.002.  Google Scholar

[38]

B. Sarkar and S. Sarkar, An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand, Economic Modelling, 30 (2013), 924-932.  doi: 10.1016/j.econmod.2012.09.049.  Google Scholar

[39]

B. Sarkar and S. Sarkar, Variable deterioration and demand-a inventory model, Economic Modelling, 31 (2013), 548-556.  doi: 10.1016/j.econmod.2012.11.045.  Google Scholar

[40]

Y. K. Shah, An order-level lot-size inventory model for deteriorating items, A I I E Transactions, 9 (1977), 108-112.  doi: 10.1080/05695557708975129.  Google Scholar

[41]

E. A. Silver, Changing the givens in modelling inventory problems: The example of just-in-time systems, International Journal of Production Economics, 26 (1992), 347-351.  doi: 10.1016/0925-5273(92)90086-M.  Google Scholar

[42]

E. A. Silver, D. F. Pyke and R. Peterson, Inventory Management and Production Planning and Scheduling, Wiley, New York, 1998. Google Scholar

[43]

K. Skouri and S. Papachristos, Four inventory models for deteriorating items with time varying demand and partial backlogging: A cost comparison, Optimal Control Applications and Methods, 24 (2003), 315-330.  doi: 10.1002/oca.734.  Google Scholar

[44]

K. SkouriI. KonstantarasS. Papachristos and I. Ganas, Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate, European Journal of Operational Research, 192 (2009), 79-92.  doi: 10.1016/j.ejor.2007.09.003.  Google Scholar

[45]

J. T. TengL. E. Cárdenas-BarrónK. R. Lou and H. M. Wee, Optimal economic order quantity for buyer-distributor-vendor supply chain with backlogging without derivatives, International Journal of Systems Science, 44 (2013), 986-994.  doi: 10.1080/00207721.2011.652226.  Google Scholar

[46]

A. Villa, Introducing some supply chain management problems, International Journal of Production Economics, 73 (2001), 1-4.  doi: 10.1016/S0925-5273(01)00090-1.  Google Scholar

[47]

S. Viswanathan, Optimal strategy for the integrated vendor-buyer inventory model, European Journal of Operational Research, 105 (1998), 38-42.  doi: 10.1016/S0377-2217(97)00032-5.  Google Scholar

[48]

N. Watanable and E. Kusukawa, Optimal ordering policy in dual-sourcing supply chain considering supply disruptions and demand information, Industrial Engineering & Management Systems, 14 (2015), 129-158.   Google Scholar

[49]

W. Wisittipanich and P. Hengmeechai, A multi-objective differential evolution for just-in-time door assignment and truck scheduling in multi-door cross docking problems, Industrial Engineering & Management Systems, 14 (2015), 299-311.  doi: 10.7232/iems.2015.14.3.299.  Google Scholar

[50]

P. C. Yang and H. M. Wee, An arborescent inventory model in a supply chain system, Production Planning & Control: The Management of Operations, 12 (2001), 728-735.  doi: 10.1080/09537280010024063.  Google Scholar

Figure 1.  Buyer's inventory model
Figure 2.  Supplier's inventory model (See for instance Sarkar [32])
Table 1.  Comparison between the contributions of different authors
Author(s) NameSetup cost reductionQuality improvementLot sizeDeteriorationSSMD
Goyal [10]$\surd$$\surd$$\surd$
Sarkar and Sarkar [48]$\surd$
Goswami and Chaudhuri [9]$\surd$
Sarker and Coates [44]$\surd$
Skouri and Papachristos [31]$\surd$$\surd$
Sarkar [37]$\surd$
Sarkar et al. [38]$\surd$
Sarkar and Sarkar [39]$\surd$
Sarkar [32]$\surd$$\surd$$\surd$
Porteus [27]$\surd$
Paknejad et al. [25]$\surd$
Hong and Hayya [34]$\surd$
Rosenblatt and Lee [30]$\surd$
This paper$\surd$$\surd$$\surd$$\surd$$\surd$
Author(s) NameSetup cost reductionQuality improvementLot sizeDeteriorationSSMD
Goyal [10]$\surd$$\surd$$\surd$
Sarkar and Sarkar [48]$\surd$
Goswami and Chaudhuri [9]$\surd$
Sarker and Coates [44]$\surd$
Skouri and Papachristos [31]$\surd$$\surd$
Sarkar [37]$\surd$
Sarkar et al. [38]$\surd$
Sarkar and Sarkar [39]$\surd$
Sarkar [32]$\surd$$\surd$$\surd$
Porteus [27]$\surd$
Paknejad et al. [25]$\surd$
Hong and Hayya [34]$\surd$
Rosenblatt and Lee [30]$\surd$
This paper$\surd$$\surd$$\surd$$\surd$$\surd$
Table 2.  Study for non-deterioration case
Total costLot sizeNumber of deliveriesSetup cost$\theta$
6297.311.17228.170.0021
Total costLot sizeNumber of deliveriesSetup cost$\theta$
6297.311.17228.170.0021
Table 3.  Study for SSSD case
Total costLot sizeNumber of deliveriesSetup cost$\theta$
6342.83 1.22 1 14.650.0041
Total costLot sizeNumber of deliveriesSetup cost$\theta$
6342.83 1.22 1 14.650.0041
Table 4.  Sensitivity analysis for key parameters
ParametersChanges of parameters (in %)TC(in %)
-50%-5.29
-25%-2.19
$C_o$+25%1.70
+50%3.09
-50%-7.47
-25%-3.31
s+25%3.73
+50%7.47
-50%-1.67
-25%-0.83
A+25%0.82
+50%1.64
-50%-18.73
-25%-8.74
F+25%7.88
+50%15.12
-50%-0.01
-25%-0.007
d+25%0.007
+50%0.01
-50%-0.007
-25%-0.003
$C_d$+25%0.003
+50%0.007
-50%-0.02
-25%-0.01
$H_s$+25%0.01
+50%0.02
-50%-0.32
-25%-0.16
V+25%0.16
+50%0.32
ParametersChanges of parameters (in %)TC(in %)
-50%-5.29
-25%-2.19
$C_o$+25%1.70
+50%3.09
-50%-7.47
-25%-3.31
s+25%3.73
+50%7.47
-50%-1.67
-25%-0.83
A+25%0.82
+50%1.64
-50%-18.73
-25%-8.74
F+25%7.88
+50%15.12
-50%-0.01
-25%-0.007
d+25%0.007
+50%0.01
-50%-0.007
-25%-0.003
$C_d$+25%0.003
+50%0.007
-50%-0.02
-25%-0.01
$H_s$+25%0.01
+50%0.02
-50%-0.32
-25%-0.16
V+25%0.16
+50%0.32
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