Application of the TOC FAL, IE, Seoul National University Eoksu

2/21 Contents General concepts and terms in TOC Recent domestic researches Formulation and solution of the drum-buffer-rope constraint scheduling problem(DBRCSP) Comment Reference list

3/21 General concepts and terms in TOC(1/3) What is the TOC? –A production control methodology that maximizes profits in a plant that has a demonstrated bottleneck. –A management philosophy developed by Eliyahu M.Goldratt which is useful in identifying core problems of an organization The TOC provides 5 step –Identifying the constraints –Deciding how to exploit the constraint –Subordinating all other activities to the constraint –Elevating the constraint –Continuous improvement step of admonishing against managerial inertia

4/21 General concepts and terms in TOC(2/3) Theory of Constraints Logistics Problem solving/ thinking process Performance system DBR Buffer management Throughput dollar days Inventory dollar days Product mix Throughput Inventory Operating expense Five-Step focusing process Scheduling process V-A-T analysis ECE diagrams ECE audit Cloud diagrams Five-Step focusing process

5/21 General concepts and terms in TOC(3/3) Performance Measure under TOC –Throughput : the rate at which the system generates money through sales –Inventory: All the money that the system invests in purchasing things the system intends to sell –Operation expense : All the money the system spends in turning inventory into the throughput Several additional supporting measurement –Throughput = selling price - raw material –Net profit from production line = total throughput - the additional operation expense –ROI = net profit divided by the inventory

6/21 Recent domestic researches In IE conference on 30 th, Oct –Development of the TOC-based MPS component Using UML, COM like Mr. Yoon –Present conditions of the TOC

Formulation and solution of the drum- buffer-rope constraint scheduling problem(DBRCSP) Int. J. Prod. Res., 1996, Vol. 34, No. 9, J. V. Simons, Jr., W. P. Simpson, III, B. J. Carlson, S. W. James, C. A. Lettiere and B. A. Mediate, Jr. Graduate School of Logistics and Acquisition Management, Air Force Institute of Technology, Wright-Patterson AFB, OH , USA

8/21 Constraint scheduling in DBR systems Constraints –Bottleneck, temporary(wandering) bottleneck –In the TOC, a capacity constraint resource(CCR) is defined to be any resource which restricts throughput TOC’s five focusing steps and the idea of DBR production systems are typically focused on two primary problems –product mix : maximizes the overall system value –product flow : a schedule for each constraint This paper will focus on product flow, as determined constraint scheduling

9/21 The multiple constraint schedules cannot be generated in isolation from each other. - interactive constraints Goldratt introduced the notion of rods to deal with both interactive constraints and multiple constraint operations for a single job –Rods - required time lags b/w constraint operations time rods : rods b/w operations on different constraints batch rods : rods b/w operations on same constraints –The rod’s placement in the constraint schedule function of two factors: transfer batch size and the relative magnitude of the per unit processing time –Fig. 1 and Fig. 2

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11/21 Problem formulation - general job shop problem

12/21 Process batch vs. transfer batch –The net effect is a partial relaxation of the general job shop precedence constraint (2) The general job shop problem produces schedules for each machine. –DBR systems simplify the problem by requiring schedules only for the constraint(s). In the DBRCSP, rods(time lags) may be placed b/w operations on either the first part in a batch or the last, depending on whether the first constraint operation is faster or slower that the second.

13/21 Problem formulation - the general production scheduling problem(GPSP)

14/21 Equation 13 addresses the advantage gained by the use of single unit transfer batches Consideration of all three relationships in equation 13 is necessary to ensure the improvement in the schedule is achievable

15/21 Problem formulation - The drum-buffer-rope constraint scheduling problem(DBRCSP)

16/21 An evaluation of Goal System solutions Optimized Production Technology(OPT) , proprietary –1990 AGI - DISASTER –1994 TOC Center - the Goal System The GS is heuristic in nature and is organized consistently with the five focusing steps –Essentially, GS begins by assuming that job order due dates are the only constraints to be met Two aspects of the GS process are particularly noteworthy –whenever constraint schedules are produced, rods are inserted to protect either previously developed constraint schedule or intervening non-constraint operations –GS builds schedules for multiple constraints sequentially

17/21 Construct benchmark test problems(108 problems) –Resource criticality factor as a measure of the severity of the load placed on a resource –ten resources types, two resources(overloaded) –A plant, V plant, T plant Obtain multiple GS solutions –Total days late(TDL) for both the best and worst GS solution –Maximum tardy days(MTD) for both the best and worst GS solution –%difference b/w best and worst GS solutions for both TDL and MTD Obtain optimal solutions –we sought to evaluate the quality of GS solutions compared to solutions which optimally minimize maximum tardiness(B&B)

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19/21 Conclusion The sequence in which multiple constraints are scheduled can make a substantial difference in the quality of GS solutions Following the GS recommendation concerning which constraint to schedule first usually produces the best solution GS solution appear to do a good job of minimizing maximum tardiness, especially when GS is run more than once(scheduling different constraints first)and the best solution used

20/21 Comments TOC is not a really new concept. There are some areas that TOC can be applied. If you want to understand the Goldratt’s theory more easily, you can read the book “The Goal” which is located in our lab.

21/21 Reference Lists Demeulemeester, E. L. and Herroelen, W. S., 1992, A branch-and-bound procedure for the multiple resource- constrained project scheduling problem. Management Science, 38(12), Plenert, G., 1993, Optimizing theory of constraints when multiple constrained resources exist, EJOR, 70,