Variations in a supply chain; Kanban or CONWIP control, what to prefer!?

1. Variations in a supply chain; Kanban or CONWIP control, what to prefer!? • Anders Segerstedt • Professor Industriell logistik, Luleå tekniska universitet, Sverige • Professor II “Logistikk og styring av forsyningskjeder”, Høgskolen i Narvik, Norge

2. A small example Machine A Every machine takes exactly one hour! Machine B Zero space in buffers! Machine C Machine D Machine E Throughput rate [units/time unit]? Lead time [time units]? Work-in-Process [units]?

3. A small example cont. Machine A Every machine now takes between 0.5 hours and 1.5 hours! Machine B Still zero space in buffers! Machine C Machine D Machine E Throughput rate [units/time unit]? Lead time [time units]? (Little’s formula: LT=1/TR·WIP=P·WIP) Work-in-Process [units]?

4. Throughput rate WIP Lead time WIP

5. Lead time/Queue Low variation High variation 1.0 Utilisation

6. Kanban control = every queue (buffer) is restricted CONWIP control = only the total amount in the queues (buffers) and machines is restricted

7. Simulation results:

8. Observation I. The maximum throughput or minimum time between jobs out, from a given total maximum WIP comes from a situation where there is only a total restriction of WIP (CONWIP-control) and not a restriction on every inventory in the supply chain (Kanban-control). This is also in line with Tayur (1993). Observation II. An increase of one extra unit of WIP in the given total maximum WIP increases the throughput, decreases time between jobs out, despite if it is a CONWIP or Kanban control situation, and despite in a Kanban control situation in what inventory the extra unit WIP is put. (But with Kanban control the machines/stations should have the same capacity as in our test cases or the extra WIP unit should be put in the inventory before the bottleneck.) However, the effect of the extra unit WIP diminishes with higher total maximum WIP, and it reaches zero when the throughput reaches the bottleneck (in our test 60 minutes between jobs out).

9. Observation III. With a restriction on every inventory in the supply chain (Kanban control), with the same capacity and variations in operation times, the available WIP should be divided as even as possible. Any surplus should not be distributed in the beginning or in the middle; the possible surplus should be distributed in the end of the supply chain. The extra WIP in the end helps the jobs to leave the chain as soon as possible. Extra WIP in the beginning or middle increases the “capacity” just there because starving and blocking decreases around these machines, but the jobs are stuck, they can not continue because the end machines have largely the same starving and blocking as before. The chain is then not balanced, the average total WIP increase but the throughput rate does not improve as much as it should do if the extra WIP were put in the end.

10. Observation IV. The relative variation in lead-time, time in system, its coefficient of variation, increases with rising maximum WIP. The relative variation in time between jobs out decreases with increasing maximum WIP, but it reaches a limit, the relative variation in operation times for the last machine. (In our case the last machine is also the bottleneck, if we have a significant bottleneck elsewhere, the same would happen the relative variation in time between jobs out decreases with increasing maximum WIP, and it reaches a limit, dependent of the bottleneck and the relative variation in operation times for the last machine.)

11. Observation V. With the possible surplus maximum WIP placed in the end of the supply chain; the same average throughput rate is established from the same average WIP independent of a Kanban or CONWIP control (WIP restricted in every inventory or only as a total). However, CONWIP control needs a lower maximum WIP than Kanban control (Observation I). (cf. Figure 10 and 13) Observation VI. With the extra maximum WIP placed in the end of the supply chain; the same lead-time, average time in system, is established from the same average WIP independent of Kanban or CONWIP control (WIP restricted in every inventory or only as a total). However, CONWIP control needs a lower maximum WIP than Kanban control (Observation I) (cf. Figure 3, 11, 12 and 13)

12. Observation VII. The relative utilisation of maximum WIP is dependent of the control parameters, Kanban or CONWIP, and relatively independent of the variation in operation times. It could have been suspected that a higher variation in operation times would create more starving and blocking and therefore a lower utilisation of available max WIP. Instead maximum WIP is on average used more or less to the same extent independent of the variation in operation times. This confirms and agrees with Little’s formula; earlier it has been shown that higher variation in operation times create lower throughput rate and longer lead-times with the same average WIP. Consequently a maximum WIP creates almost the same average WIP independent of variations in operation times, but different throughput and lead-times. An important difference is that CONWIP control implies that a larger part of maximum WIP is used compared to Kanban control. (cf. Figure 13)

13. If we have a bottleneck!? If we have a machine with greater variation than the others!?

14. References:Silver E. A., Pyke D., Peterson R., 1998. Inventory Management and Production Planning and Scheduling (3 ed.), New York: WileyPettersen J.-A., Segerstedt A., 2009. Restricted Work-In-Process, A study of differences between Kanban and CONWIP, International Journal of Production Economics, 118, 1, 199-207