# American Institute of Mathematical Sciences

January  2012, 8(1): 141-162. doi: 10.3934/jimo.2012.8.141

## A common cycle approach for solving the economic lot and inspection scheduling problem

 1 Department of Transportation Technology and Management, National Chiao Tung University, Hsinchu, 30010, Taiwan 2 Department of Industrial Engineering and Management, Hsiuping University of Science and Technology, Taichung, 41280, Taiwan 3 Department of Information Management, Tunghai University, Taichung, 40704, Taiwan

Received  October 2010 Revised  July 2011 Published  November 2011

In this study, we consider an imperfect production system in which the manager not only faces the Economic Lot Scheduling Problem, but also needs to conduct multiple inspections during a production lot of any product. Inspection plays an important role in an imperfect production system since it saves the cost from producing and restoring defective items though it also incurs extra inspection cost at the same time. In this study, we employ the common cycle approach in which all the products share the same replenishment cycle, and adopt a consensus inspection policy. The focus of this study is to determine the optimal cycle time and an optimal production and inspection schedule that minimize the total cost per unit time. We formulate a mathematical model in which we take into accounts both the production capacity and inspection capacity constraints. Also, we conduct full theoretical analysis and propose an effective search algorithm for solving an optimal solution. Our numerical experiments demonstrate the effectiveness of the proposed search algorithm.
Citation: Ming-Jong Yao, Shih-Chieh Chen, Yu-Jen Chang. A common cycle approach for solving the economic lot and inspection scheduling problem. Journal of Industrial & Management Optimization, 2012, 8 (1) : 141-162. doi: 10.3934/jimo.2012.8.141
##### References:

show all references

##### References:
 [1] Fuying Jing, Zirui Lan, Yang Pan. Forecast horizon of dynamic lot size model for perishable inventory with minimum order quantities. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1435-1456. doi: 10.3934/jimo.2019010 [2] Antonio Sedeño-Noda, José M. Gutiérrez. Solving a constrained economic lot size problem by ranking efficient production policies. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021102 [3] Javad Taheri-Tolgari, Mohammad Mohammadi, Bahman Naderi, Alireza Arshadi-Khamseh, Abolfazl Mirzazadeh. An inventory model with imperfect item, inspection errors, preventive maintenance and partial backlogging in uncertainty environment. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1317-1344. doi: 10.3934/jimo.2018097 [4] Sankar Kumar Roy, Magfura Pervin, Gerhard Wilhelm Weber. Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 45-74. doi: 10.3934/naco.2019032 [5] Biswajit Sarkar, Bijoy Kumar Shaw, Taebok Kim, Mitali Sarkar, Dongmin Shin. An integrated inventory model with variable transportation cost, two-stage inspection, and defective items. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1975-1990. doi: 10.3934/jimo.2017027 [6] Jianjun Liu, Min Zeng, Yifan Ge, Changzhi Wu, Xiangyu Wang. Improved Cuckoo Search algorithm for numerical function optimization. Journal of Industrial & Management Optimization, 2020, 16 (1) : 103-115. doi: 10.3934/jimo.2018142 [7] Pedro Piñeyro, Omar Viera. Inventory policies for the economic lot-sizing problem with remanufacturing and final disposal options. Journal of Industrial & Management Optimization, 2009, 5 (2) : 217-238. doi: 10.3934/jimo.2009.5.217 [8] Tien-Yu Lin, Bhaba R. Sarker, Chien-Jui Lin. An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts. Journal of Industrial & Management Optimization, 2021, 17 (1) : 467-484. doi: 10.3934/jimo.2020043 [9] Ata Allah Taleizadeh, Solaleh Sadat Kalantari, Leopoldo Eduardo Cárdenas-Barrón. Determining optimal price, replenishment lot size and number of shipments for an EPQ model with rework and multiple shipments. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1059-1071. doi: 10.3934/jimo.2015.11.1059 [10] Leong-Kwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 193-207. doi: 10.3934/naco.2014.4.193 [11] Behrouz Kheirfam, Morteza Moslemi. On the extension of an arc-search interior-point algorithm for semidefinite optimization. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 261-275. doi: 10.3934/naco.2018015 [12] Kien Ming Ng, Trung Hieu Tran. A parallel water flow algorithm with local search for solving the quadratic assignment problem. Journal of Industrial & Management Optimization, 2019, 15 (1) : 235-259. doi: 10.3934/jimo.2018041 [13] Mohamed A. Tawhid, Ahmed F. Ali. An effective hybrid firefly algorithm with the cuckoo search for engineering optimization problems. Mathematical Foundations of Computing, 2018, 1 (4) : 349-368. doi: 10.3934/mfc.2018017 [14] Ming-Jong Yao, Tien-Cheng Hsu. An efficient search algorithm for obtaining the optimal replenishment strategies in multi-stage just-in-time supply chain systems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 11-32. doi: 10.3934/jimo.2009.5.11 [15] Abdel-Rahman Hedar, Ahmed Fouad Ali, Taysir Hassan Abdel-Hamid. Genetic algorithm and Tabu search based methods for molecular 3D-structure prediction. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 191-209. doi: 10.3934/naco.2011.1.191 [16] Sen Zhang, Guo Zhou, Yongquan Zhou, Qifang Luo. Quantum-inspired satin bowerbird algorithm with Bloch spherical search for constrained structural optimization. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020130 [17] Zheng Chang, Haoxun Chen, Farouk Yalaoui, Bo Dai. Adaptive large neighborhood search Algorithm for route planning of freight buses with pickup and delivery. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1771-1793. doi: 10.3934/jimo.2020045 [18] Yishui Wang, Dongmei Zhang, Peng Zhang, Yong Zhang. Local search algorithm for the squared metric $k$-facility location problem with linear penalties. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2013-2030. doi: 10.3934/jimo.2020056 [19] Y. K. Lin, C. S. Chong. A tabu search algorithm to minimize total weighted tardiness for the job shop scheduling problem. Journal of Industrial & Management Optimization, 2016, 12 (2) : 703-717. doi: 10.3934/jimo.2016.12.703 [20] Behrad Erfani, Sadoullah Ebrahimnejad, Amirhossein Moosavi. An integrated dynamic facility layout and job shop scheduling problem: A hybrid NSGA-II and local search algorithm. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1801-1834. doi: 10.3934/jimo.2019030

2020 Impact Factor: 1.801