adaptive due date deviation regulation using capacity and order release time adjustment

Available online at www.sciencedirect.com ScienceDirect Procedia CIRP 17 (2014) 398 – 403 Variety Management in Manufacturing Proceedings of the 47th CIRP Conference on Manufacturing Systems Adaptive Due Date Deviation Regulation Using Capacity and Order Release Time Adjustment I Falua, N Duffiea* a University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA * Corresponding author Tel.: +1-608-262-9457 ; fax: +1-608-265-2316 E-mail address: duffie@engr.wisc.edu Abstract A control-theoretic, order due date deviation regulation method is presented in this paper for work systems that can dynamically adjust their capacity and order release times The relationship between due date deviations and work system capacity is shown to be nonlinear and time varying, and a method is presented for characterizing the relationship quantitatively in real time and using this information in an adaptive capacity adjustment control law that maintains favorable dynamic behavior in the presence of the nonlinearities Control theoretic analyses are included in the paper for designing the dynamic behavior of due date deviations and work system capacity, and results of discrete event simulations driven by industrial data are used to illustrate dynamic behavior Conclusions are presented regarding the efficacy of combining scheduling and due date deviation regulation and the resulting tradeoffs between due date deviation and capacity © 2014 Elsevier B.V This is an open access article under the CC BY-NC-ND license © 2014 The Authors Published by Elsevier B.V (http://creativecommons.org/licenses/by-nc-nd/3.0/) Selection and peer-review under responsibility of the International Scientific Committee of “The 47th CIRP Conference on Manufacturing Selection in and responsibility of the International Scientific Committee of “The 47th CIRP Conference on Systems” thepeer-review person of theunder Conference Chair Professor Hoda ElMaraghy Manufacturing Systems” in the person of the Conference Chair Professor Hoda ElMaraghy” Keywords: Due Date; Control; Adaptive Introduction Meeting customers due dates is one of the most important metrics in scheduling and supply chain management [1] By completing orders after the due date a company might face penalties set by the customer or lose future business due to unreliability One solution is to set due dates far into the future but customers can demand discounts in exchange for the delay Also companies might be tempted to stock raw material or finished produce in order to accommodate future demand, but this will increase inventory cost [2] Centralized control planning and scheduling has been used to minimize the effects of demand and improve shop floor effectiveness [3], but high level planning typically does not have the ability to react in real time to unexpected disturbances [4] On the other hand, low level schedulers typically use centralized information to schedule the release time of orders, assume that there is enough capacity available at all times, and assume that changes in capacity can be made instantaneously [5] Changeable production capacity can significantly improve the ability to meet order due dates when there are fluctuations in demand; however, in order to be profitable, companies need to manage their resources efficiently It is desirable to minimize resources such as production capacity, yet customer requirements must be met [6,7] Duffie et al previously proposed a lead time regulation approach for adjusting production capacity to eliminate deviation between desired and actual lead time [8] In work described in this paper, the effects of adjustments in capacity on scheduling of the release times of orders to production, and the resulting deviations from due dates were investigated along with influence of delays in adjustment of capacity on deviation from due dates 2212-8271 © 2014 Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Selection and peer-review under responsibility of the International Scientific Committee of “The 47th CIRP Conference on Manufacturing Systems” in the person of the Conference Chair Professor Hoda ElMaraghy” doi:10.1016/j.procir.2014.01.073 I Falu and N Duffie / Procedia CIRP 17 (2014) 398 – 403 Previous research has been conducted in the regulation of Due Date Deviation (DDD), which here is the deviation of the time of completion of an order from the order due date Arakawa et al proposed a backward/forward simulation combined with a parameter space search improvement method, based on a shop floor model, for generating schedules to minimize DDD [9] Kuo et al used a time-buffer control using Theory of Constraints to regulate DDD, using first-infirst-out and earliest-due-date scheduling heuristics, illustrating improvements in on-time delivery rate and average DDD [10] Srirangacharyulu et al described an algorithm for minimizing mean square deviation by solving a completion time variance problem using dynamic programming; however, the method was computationally intensive for a large number of jobs [11] Sakuraba et al addressed the minimization of mean absolute deviation from a common due date in a twomachine shop; the authors used mixed integer linear programming to obtain optimal sequences [12] Control theoretic approaches have been proposed as a means for understanding fundamental work system dynamic properties in regulation of backlog, Work In Progress (WIP) and lead time Toshniwal et al used discrete event simulations to assess the fidelity of control theoretic models of the dynamics of WIP regulation and capacity adjustments [13] Duffie et al used control theoretic methods to coordinate modes of capacity adjustment [14], and Kim and Duffie used control theoretic methods to analyze and design WIP regulation for interacting multi-work-station production systems [15] From a strategic standpoint, there is an advantage in producing with an effective amount of resources while completing orders as close as possible to their due date In this paper, an adaptive due date deviation regulation system topology is first presented that incorporates both work system capacity and order release time adjustment For a group of orders, average absolute due date deviation is used as a metric for adjusting work system capacity, and a scheduler is used to adjust the release times of orders into the work system queue The system tends to eliminate the difference between planned average absolute due date deviation and actual average absolute due date deviation by adjusting both capacity and release order times First, a discrete system model is presented along with the equations used to regulate DDD and adjust capacity Then, the relationship between capacity and DDD, and control theoretic analysis is used to provide guidance for setting parameters in DDD regulation A discrete event simulation of DDD regulation driven by industrial data is described, and results obtained are used to illustrate the dynamic behavior of DDD regulation Finally, conclusions are presented regarding the efficacy of combining scheduling and DDD regulation and the resulting tradeoffs between DDD and capacity Due Date Deviation Regulation Figure shows a block diagram for due date deviation regulation In the diagram, the database contains incoming order information including name, due date and processing 399 time This information is sent to the scheduler where an appropriate algorithm is used to determine the release time for each order into the actual work system’s first-in-first-out queue and hence the order processing sequence A model of the work system within the scheduler is used, for a given set of order release times, to compute the predicted completion time ci(kT) for each order, the due date deviation for each order, and the average absolute due date deviation DDDa(kT) for all orders currently being scheduled, which is then used as the feedback for making capacity adjustments: m ∑ d − c (kT ) i DDDa (kT ) = i i=1 m (1) where di is the due date for order i, m is the total number of orders being scheduled, T is time period between capacity adjustments and k =0,1,2,3,… Average absolute value of due date deviation is used as a straightforward measure of contention of orders for the work system resource, where work has units of shop calendar days (scd) If DDDa(kT) is greater than the planned average absolute due date deviation DDDp, it is desirable to increase capacity in order to complete orders closer to their due dates On the other hand, if DDDa(kT) is less than the planned average absolute due date deviation DDDp, it is desirable to decrease capacity in order to increase due date deviation While obtaining zero average absolute due date deviation would be ideal, this is not possible if due dates are identical, and requires unrealistically large capacities depending upon the mix of processing times and due dates when no due dates are identical Therefore, a reasonable DDDp>0 is selected The work station’s production capacity Ca(kT) is adjusted using the following equation, which has an integrating effect: C f (kT ) = C f ((k -1)T ) + K c (DDD p − DDDa ((k − d)T ) (2) Ca (kT ) = C f (kT ) - Cd (kT ) (3) where Kc is an adjustable due date regulation gain, dT is a time delay in adjusting capacity (d is assumed to be a positive integer) and Cd(kT) is any unexpected capacity disturbance such as equipment failure or worker illness For a group of orders, the relationship between average absolute due date deviation DDDa(kT) and capacity Ca(kT) depends on the mix of individual order due dates and processing times Figure shows examples of this relationship for groups of orders due during two time periods in the data set used in simulation results presented in Section There is an inverse relationship between capacity and due date because, unless there is no contention for the work system resource, the average absolute due date deviation decreases as capacity is increase In general, increasing capacity beyond some value will not yield practical improvements in due date deviation 400 I Falu and N Duffie / Procedia CIRP 17 (2014) 398 – 403 + DDDp(kT) Kc z −d 1- z −1 - Cf(kT) + - Cd(kT) DDDa(kT) Ca(kT) Planning Scheduling Order Database Scheduler & Model Orders Queue Actual Work System Completed Orders Fig Dynamic model for due date deviation regulation for a given Kc work system response is slower and can be approximately characterized by time constant τ in: 25 160-165 scd DDDa (scd) 20 190-195 scd K c (kT )K s (kT ) = 1− e 15 ( τ) −T (7) 10 0 10 12 Ca (h/scd) 14 16 18 20 Fig Examples of the relationship between average absolute due date deviation and work system capacity For a given capacity Ca(kT), this relationship can be approximated using DDDa (kT ) ≈ K s (kT )Ca (kT ) + DDDs (kT ) (4) where DDDs(kT) is the vertical axis intercept and slope Ks(kT) can be approximated using K s (kT ) ≈ DDDa (Ca (kT ) + ΔCa ) − DDDa (Ca (kT ) − ΔCa ) 2ΔCa (5) where the production model in the scheduler is used to obtain predict average absolute due date deviations at two capacities separated from Ca(kT) by an incremental change in capacity ∆Ca Equations (2) through (5) lead to the following approximate characteristic equation for due date deviation regulation for a given value of Ks and d=0: z − (1− K c K s ) = (6) where Kc is a given value of due date deviation regulation gain At time kT, Kc(kT) can be computed from Ks(kT) to maintain desired approximate fundamental dynamic properties When d=0, Kc(kT)Ks(kT)=1 results in approximate work system response to order input fluctuations and disturbances that is a fast as possible and has no overcorrection On the other hand, when Kc(kT)Ks(kT)0.25, the work system response is fundamentally oscillatory and can be approximately characterized by damping ratio ζ