Abstract
We consider the problem of optimizing the production planning with aggregation of operations and selection of their intensities for batch processing of a given family of products on a multi-position reconfigurable production system at specified (time) intervals under nonstationary deterministic demand. Backlog is allowed. Aggregation of operations is invariable for the entire planning period, the composition of the batch and intensities of processing operations are invariable within an interval, but can vary from interval to interval. As the objective function we use the planned profit. Investment costs are determined by the aggregation option. Time and material costs for the manufacturing of a batch of products during each interval depend on the aggregation of operations, intensities of their implementation, and costs of reconfiguring the equipment. Logistic costs include the cost of storing unclaimed products, lost added value, and penalties for unmet demand. We propose a three-level decomposition method for solving the problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alting, L. and Zhang, H., Computer Aided Process Planning: The State-of-the-Art Survey, Int. J. Prod. Res., 1989, vol. 27, no. 4, pp. 553–585.
Halevi, G., Process and Operation Panning, Dordrecht: Springer, 2003.
Bukchin, J. and Tzur, M., Design of Flexible Assembly Line to Minimize Equipment Cost, IIE Trans., 2000, vol. 32, pp. 585–598.
Burkov, V.N. and Novikov, D.A., Models and Methods of Multiprojects’ Management, Syst. Sci., 1999, vol. 256, no. 2, pp. 5–4.
Dolgui, A., Guschinsky, N., and Levin, G., Enhanced Mixed Integer Programming Model for a Transfer Line Design Problem, Comput. Ind. Eng., 2012, vol. 62, no. 2, pp. 570–578.
Levin, G.M. and Rozin, B.M., Modes Optimization for Parallel Multi-Tool Part Processing on Aggregate Equipment with Group Tool Change, Informatika, 2011, no. 3, pp. 33–47.
Levin, G.M. and Rozin, B.M., Optimization of Series-Parallel Execution of a Complex of Interrelated Operations, Vestsi NAS Belarusi, Ser. Fiz.-Mat. Navuk, 2013, no. 1, pp. 111–116.
Dolgui, A., Rozin, B., and Levin, G., Optimisation of Processing Conditions for Multi-Product Batch Production Lines with Series-Parallel Operations under Uncertainty on Demands for Finished Products, Proc. 18th APIEMS Conf. Ind. Eng. Manage. Syst., Bandung, Indonesia, 2017, pp. A2–7–A2–12.
Levin, G.M., Rozin, B.M., and Dolgui, A.B., Linear Approximation for the Optimization Problem for Intensities of Series-Parallel Execution of Intersecting Sets of Operations, Informatika, 2014, no. 3, pp. 44–51.
Karimi, B., Fatemi Ghomi, S.M.T., and Wilson, J.M., The Capacitated Lot Sizing Problem: A Review of Models and Algorithms, Omega, 2003, vol. 31, no. 5, pp. 365–378.
Ullah, H. and Parveen, S., A Literature Review on Inventory Lot Sizing Problems, Global J. Res. Eng., 2010, vol. 10, no. 5, pp. 21–36.
Chubanov, S. and Pesch, E., An FPTAS for the Single-Item Capacitated Economic Lot-Sizing Problem with Supply and Demand, Oper. Res. Lett., 2012, vol. 40, no. 6, pp. 445–449.
Absi, N. and Kedad-Sidhoum, S., The Multi-Item Capacitated Lot-Sizing Problem with Safety Stocks and Demand Shortage Costs, Comput. Oper. Res., 2009, vol. 36, no. 11, pp. 2926–2936.
Florian, M., Lenstra, J.K., and Kan, A.H.G.R., Deterministic Production Planning: Algorithms and Complexity, Manage. Sci., 1980, vol. 26, pp. 669–679.
Bitran, G.R. and Yanasse, H.H., Computational Complexity of the Capacitated Lot Size Problem, Manage. Sci., 1982, vol. 28, no. 10, pp. 1174–1186.
Chen, W.H. and Thizy, J.M., Analysis of Relaxations for the Multi-Item Capacitated Lot-Sizing Problem, Ann. Oper. Res., 1990, vol. 26, pp. 29–72.
Dixon, P.S. and Silver, E.A., A Heuristic Solution Procedure for the Multi-Item, Single Level, Limited Capacity, Lot Sizing Problem, J. Oper. Manage., 1981, vol. 21, no. 1, pp. 23–40.
Thizy, J.M. and Van Wassenhove, L.N., Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem: A Heuristic Implementation, IIE Trans., 1985, vol. 17, no. 4, pp. 308–313.
Gelders, L.F., Maes, J., and Van Wassenhove, L.N., A Branch and Bound Algorithm for the Multi Item Single Level Capacitated Dynamic Lotsizing Problem, in Multistage Production Planning and Inventory Control, Lecture Notes in Economics and Mathematical Systems, vol. 266, Axaster, S., Schneeweiss, C.H., and Silver, E., Eds., Berlin: Springer, 1986, pp. 92–108.
Wagelmans, A., Van Hoesel, S., and Kolen, A., Economic Lotsizing: An O(n log n) Algorithm that Runs in Linear Time in the Wagner–Whitin Case, Oper. Res., 1992, vol. 40, pp. 145–155.
Aggarwal, A. and Park, J.K., Improved Algorithms for Economic Lot-Size Problem, Oper. Res., 1993, vol. 41, no. 3, pp. 549–571.
Federgruen, A. and Tzur, M.A., A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in O(n log n) or O(n) Time, Manage. Sci., 1991, vol. 37, no. 8, pp. 909–925.
Levin, G.M., Rozin, B.M., and Dolgui, A.B., Optimizing the Output and the Intensities of Processing a Batch of Parts under Nonstationary Demand, Vestsi NAN Belarusi, Ser. Fiz.-Mat. Navuk, 2016, no. 3, pp. 102–109.
Levin, G.M. and Tanaev, V.S., Dekompozitsionnye metody optimizatsii proektnykh reshenii (Decomposition Methods for Optimizing Design Solutions), Minsk: Nauka i Tekhnika, 1978.
Author information
Authors and Affiliations
Corresponding authors
Additional information
This paper was recommended for publication by A. A. Lazarev, a member of the Editorial Board
Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 5, pp. 26–40.
Rights and permissions
About this article
Cite this article
Dolgui, A.B., Levin, G.M. & Rozin, B.M. Structural-Parametric Optimization of a Complex of Intersecting Sets of Operations under Nonstationary Demand. Autom Remote Control 81, 791–802 (2020). https://doi.org/10.1134/S0005117920050021
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117920050021