Minimizing total inventory cost on a single machine in just-in-time manufacturing

The just-in-time concept decrees not to accept ordered goods before their due dates in order to avoid inventory cost. This bounces the inventory cost back to the manufacturer: products that are completed before their due dates have to be stored. Reducing this type of storage cost by preclusion of early completion conflicts with the traditional policy of keeping work-in-process inventories down. This paper addresses a single-machine scheduling problem with the objective of minimizing total inventory cost, comprising cost associated with work-in-process inventories and storage cost as a result of early completion. The cost components are measured by the sum of the job completion times and the sum of the job earlinesses. This problem differs from more traditional scheduling problems, since the insertion of machine idle time may reduce total cost. The search for an optimal schedule, however, can be limited to the set of job sequences, since for any sequence there is a clear-cut way to insert machine idle time in order to minimize total inventory cost. We apply branch-and-bound to identify an optimal schedule. We present five approaches for lower bound calculation, based upon relaxation of the objective function, of the state space, and upon Lagrangian relaxation. Key Words and Phrases: just-in-time manufacturing, inventory cost, work-in-process inventory, earliness, tardiness, machine idle time, branch-and-bound algorithm, Lagrangian relaxation

Geometric and harmonic means based priority dispatching rules for single machine scheduling problems

[EN] This work proposes two new prority dispatching rules (PDRs) for solving single machine scheduling problems. These rules are based on the geometric mean (GM) and harmonic mean (HM) of the processing time (PT) and the due date (DD) and they are referred to as GMPD and HMPD respectively. Performance of the proposed PDRs is evaluated on the basis of five measures/criteria i.e. Total Flow Time (TFT), Total Lateness (TL), Number of Late Jobs (TNL), Total Earliness (TE) and Number of Early Parts (TNE). It is found that GMPD performs better than other PDRs in achieving optimal values of multiple performance measures. Further, effect of variation in the weight assigned to PT and DD on the combined performance of TFT and TL is also examined which reveals that for deriving optimal values of TFT and TL, weighted harmonic mean (WHMPD) rule with a weight of 0.105 outperforms other PDRs. The weighted geometric mean (WGMPD) rule with a weight of 0.37 is found to be the next after WHMPD followed by the weighted PDT i.e. WPDT rule with a weight of 0.76.Ahmad, S.; Khan, ZA.; Ali, M.; Asjad, M. (2021). Geometric and harmonic means based priority dispatching rules for single machine scheduling problems. International Journal of Production Management and Engineering. 9(2):93-102. https://doi.org/10.4995/ijpme.2021.15217OJS9310292Baharom, M. Z., Nazdah, W., &Hussin, W. (2015). Scheduling Analysis for Job Sequencing in Veneer Lamination Line. Journal of Industrial and Intelligent Information, 3(3). https://doi.org/10.12720/jiii.3.3.181-185Chan, F. T. S., Chan, H. K., Lau, H. C. W., & Ip, R. W. L. (2003). Analysis of dynamic dispatching rules for a flexible manufacturing system. Journal of Materials Processing Technology, 138(1), 325-331. https://doi.org/10.1016/S0924-0136(03)00093-1Cheng, T. C. E., &Kahlbacher, H. G. (1993). Single-machine scheduling to minimize earliness and number of tardy jobs. Journal of Optimization Theory and Applications, 77(3), 563-573. https://doi.org/10.1007/BF00940450da Silva, N. C. O., Scarpin, C. T., Pécora, J. E., & Ruiz, A. (2019). Online single machine scheduling with setup times depending on the jobs sequence. Computers & Industrial Engineering, 129, 251-258. https://doi.org/10.1016/j.cie.2019.01.038Doh, H.H., Yu, J.M., Kim, J.S., Lee, D.H., & Nam, S.H. (2013). A priority scheduling approach for flexible job shops with multiple process plans. International Journal of Production Research, 51(12), 3748-3764. https://doi.org/10.1080/00207543.2013.765074Dominic, Panneer D. D., Kaliyamoorthy, S., & Kumar, M. S. (2004). Efficient dispatching rules for dynamic job shop scheduling. The International Journal of Advanced Manufacturing Technology, 24(1), 70-75.Ðurasević, M., &Jakobović, D. (2018). A survey of dispatching rules for the dynamic unrelated machines environment. Expert Systems with Applications, 113, 555-569. https://doi.org/10.1016/j.eswa.2018.06.053Forrester, P. (2006). Operations Management: An Integrated Approach. International Journal of Operations & Production Management.Geiger, C. D., &Uzsoy, R. (2008). Learning effective dispatching rules for batch processor scheduling. International Journal of Production Research, 46(6), 1431-1454. https://doi.org/10.1080/00207540600993360Hamidi, M. (2016). Two new sequencing rules for the non-preemptive single machine scheduling problem. The Journal of Business Inquiry, 15(2), 116-127.Holthaus, O., & Rajendran, C. (1997). New dispatching rules for scheduling in a job shop-An experimental study. The International Journal of Advanced Manufacturing Technology, 13(2), 148-153. https://doi.org/10.1007/BF01225761Hussain, M. S., & Ali, M. (2019). A Multi-agent Based Dynamic Scheduling of Flexible Manufacturing Systems. Global Journal of Flexible Systems Management, 20(3), 267-290. https://doi.org/10.1007/s40171-019-00214-9Jayamohan, M. S., & Rajendran, C. (2000). New dispatching rules for shop scheduling: A step forward. International Journal of Production Research, 38(3), 563-586. https://doi.org/10.1080/002075400189301Kadipasaoglu, S. N., Xiang, W., &Khumawala, B. M. (1997). A comparison of sequencing rules in static and dynamic hybrid flow systems. International Journal of Production Research, 35(5), 1359-1384. https://doi.org/10.1080/002075497195371Kanet, J. J., & Li, X. (2004). A Weighted Modified Due Date Rule for Sequencing to Minimize Weighted Tardiness. Journal of Scheduling, 7(4), 261-276. https://doi.org/10.1023/B:JOSH.0000031421.64487.95Lee, D.K., Shin, J.H., & Lee, D.H. (2020). Operations scheduling for an advanced flexible manufacturing system with multi-fixturing pallets. Computers & Industrial Engineering, 144, 106496. https://doi.org/10.1016/j.cie.2020.106496Lu, C.C., Lin, S.W., & Ying, K.C. (2012). Robust scheduling on a single machine to minimize total flow time. Computers & Operations Research, 39(7), 1682-1691. https://doi.org/10.1016/j.cor.2011.10.003Krishnan, M., Chinnusamy, T. R., & Karthikeyan, T. (2012). Performance Study of Flexible Manufacturing System Scheduling Using Dispatching Rules in Dynamic Environment. Procedia Engineering, 38, 2793-2798. https://doi.org/10.1016/j.proeng.2012.06.327Munir, E. U., Li, J., Shi, S., Zou, Z., & Yang, D. (2008). MaxStd: A task scheduling heuristic for heterogeneous computing environment. Information Technology Journal, 7(4), 679-683. https://doi.org/10.3923/itj.2008.679.683Oyetunji, E. O. (2009). Some common performance measures in scheduling problems. Research Journal of Applied Sciences, Engineering and Technology, 1(2), 6-9.Pinedo, M. L. (2009). Planning and Scheduling in Manufacturing and Services (2nd ed.). Springer-Verlag. https://doi.org/10.1007/978-1-4419-0910-7Prakash, A., Chan, F. T. S., & Deshmukh, S. G. (2011). FMS scheduling with knowledge based genetic algorithm approach. Expert Systems with Applications, 38(4), 3161-3171. https://doi.org/10.1016/j.eswa.2010.09.002Rafsanjani, M. K., &Bardsiri, A. K. (2012). A New Heuristic Approach for Scheduling Independent Tasks on Heterogeneous Computing Systems. International Journal of Machine Learning and Computing, 371-376. https://doi.org/10.7763/IJMLC.2012.V2.147Tyagi, N., Tripathi, R. P., &Chandramouli, A. B. (2016). Single Machine Scheduling Model with Total Tardiness Problem. Indian Journal of Science and Technology, 9(37). https://doi.org/10.17485/ijst/2016/v9i37/97527Vinod, V., & Sridharan, R. (2008). Dynamic job-shop scheduling with sequence-dependent setup times: Simulation modeling and analysis. 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A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Integrating labor awareness to energy-efficient production scheduling under real-time electricity pricing : an empirical study

With the penetration of smart grid into factories, energy-efficient production scheduling has emerged as a promising method for industrial demand response. It shifts flexible production loads to lower-priced periods to reduce energy cost for the same production task. However, the existing methods only focus on integrating energy awareness to conventional production scheduling models. They ignore the labor cost which is shift-based and follows an opposite trend of energy cost. For instance, the energy cost is lower during nights while the labor cost is higher. Therefore, this paper proposes a method for energy-efficient and labor-aware production scheduling at the unit process level. This integrated scheduling model is mathematically formulated. Besides the state-based energy model and genetic algorithm-based optimization, a continuous-time shift accumulation heuristic is proposed to synchronize power states and labor shifts. In a case study of a Belgian plastic bottle manufacturer, a set of empirical sensitivity analyses were performed to investigate the impact of energy and labor awareness, as well as the production-related factors that influence the economic performance of a schedule. Furthermore, the demonstration was performed in 9 large-scale test instances, which encompass the cases where energy cost is minor, moderate, and major compared to the joint energy and labor cost. The results have proven that the ignorance of labor in existing energy-efficient production scheduling studies increases the joint energy and labor cost, although the energy cost can be minimized. To achieve effective production cost reduction, energy and labor awareness are recommended to be jointly considered in production scheduling. (C) 2017 Elsevier Ltd. All rights reserved

Mechanism design for decentralized online machine scheduling

Traditional optimization models assume a central decision maker who optimizes a global system performance measure. However, problem data is often distributed among several agents, and agents take autonomous decisions. This gives incentives for strategic behavior of agents, possibly leading to sub-optimal system performance. Furthermore, in dynamic environments, machines are locally dispersed and administratively independent. Examples are found both in business and engineering applications. We investigate such issues for a parallel machine scheduling model where jobs arrive online over time. Instead of centrally assigning jobs to machines, each machine implements a local sequencing rule and jobs decide for machines themselves. In this context, we introduce the concept of a myopic best response equilibrium, a concept weaker than the classical dominant strategy equilibrium, but appropriate for online problems. Our main result is a polynomial time, online mechanism that |assuming rational behavior of jobs| results in an equilibrium schedule that is 3.281-competitive with respect to the maximal social welfare. This is only lightly worse than state-of-the-art algorithms with central coordination

Scheduling aircraft landings - the static case

This is the publisher version of the article, obtained from the link below.In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways.J.E.Beasley. would like to acknowledge the financial support of the Commonwealth Scientific and Industrial Research Organization, Australia