© C.Hicks, University of Newcastle ASAC06/1 Establishing the relationship between mean tardiness and the number of resources under close control for companies producing complex products with Beta distributed processing times Christian Hicks University of Newcastle upon Tyne, England

© C.Hicks, University of Newcastle ASAC06/2 Dispatching rule literature Majority of work has focused upon small problems. Work has focused upon the production of components, mostly in job shops. Minimum set-up, machining and transfer times have been neglected. Deterministic process times have been assumed. The same rules have been used for all resources

© C.Hicks, University of Newcastle ASAC06/3 Optimised Production Technology Resources are either bottlenecks, which constrain production or are non-bottlenecks that have excess capacity. All systems have at least one constraint – “anything that limits a system from achieving higher performance versus its goal” (Goldratt, 1988, p453). OPT software aims to fully utilise the bottlenecks and synchronise the non-bottlenecks.

© C.Hicks, University of Newcastle ASAC06/4 Capital goods companies Design, manufacture and construction of large products such as turbine generators, cranes and boilers. Complex product structures with many levels of assembly. Highly customised and produced in low volume on an engineer-to-order basis.

© C.Hicks, University of Newcastle ASAC06/5 Typical product

© C.Hicks, University of Newcastle ASAC06/6 Project Management MRP Lean

© C.Hicks, University of Newcastle ASAC06/7 Use of Beta distribution in planning Large complex projects are often planned using project management systems based upon the Project Evaluation and Review Technique (PERT). PERT models uncertainties using the Beta distribution based upon estimates of optimistic, pessimistic and most likely activity durations. The Probability Density Function for a Beta distribution can be uniform, symmetric or skewed.

© C.Hicks, University of Newcastle ASAC06/8

© C.Hicks, University of Newcastle ASAC06/9 Case Study 52 Machine tools. Three product families competing for resource (main product, spares and subcontract). Complex product structures.

© C.Hicks, University of Newcastle ASAC06/10

Load on machines in rank order

© C.Hicks, University of Newcastle ASAC06/13 Experimental design Processing times assumed to be Beta distributed with α = 2 and β = 3 (skewed to the right).

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© C.Hicks, University of Newcastle ASAC06/15

© C.Hicks, University of Newcastle ASAC06/16 Tardiness (T) = completion time – due time (for completion time > due time) Tardiness (T) = 0 (for completion time  due time) Performance Metric

© C.Hicks, University of Newcastle ASAC06/17 Figure 3 Mean tardiness (days) for products vs. number of resources under close control Products

© C.Hicks, University of Newcastle ASAC06/18 Figure 4 Mean tardiness (days) for components vs. number of resources under close control Components

© C.Hicks, University of Newcastle ASAC06/19 Figure 5 Minimum mean product tardiness vs. number of resources under close control. Second stage experiment Products

© C.Hicks, University of Newcastle ASAC06/20 Figure 6 Minimum mean component tardiness vs. number of resources under close control Components

© C.Hicks, University of Newcastle ASAC06/21 Conclusions Most dispatching rule research has focused upon job shops and has neglected other operational factors such as minimum setup, machining and transfer times and the data update period. Dispatching rule research has mainly investigated deterministic situations. This research has included complex assemblies, stochastic processing times and a multi-product environment. Mean tardiness for products reduces considerably when most highly utilised resources are placed under close control.

© C.Hicks, University of Newcastle ASAC06/22 Conclusions Most of the benefits arise with <= 10% of resources under close control. Mean tardiness for components relatively insensitive to number of resources under close control. “Best” dispatching rule varies according to level and product family. This research shows that the relative performance of the dispatching rules is also quite insensitive to the number of resources under close control.