Stochastic Models in Planning Complex Engineer-To-Order Products By: Dong-Ping Song Supervisors: Dr. Chris Hicks, Prof. Chris F. Earl Department of Mechanical, Materials and Manufacturing Engineering, University of Newcastle upon Tyne, UK, Oct. 2001

Objectives of Thesis Developing a series of effective methods for the planning of ETO manufacturing systems producing products with complex product structure and various uncertainties.

Engineer-To-Order System ETO – products are engineered and produced based on the specifications of the customer. Order tendering and engineering design are included. Characteristics – highly customised; low volume; complex product structure; uncertainties; two major stages.

Work-flow and Planning Levels of an ETO System

Special Issues in ETO Planning Product due date planning (-- level 1) Stage due date and activity start times planning (-- level 2) Production scheduling (-- level 3) Dynamic production scheduling (-- level 3)

Structure of Thesis Ch 1 & Ch 2 Ch 3 Ch 4 & Ch 5 Ch 6 Ch 7 Ch 9 Ch 8 high Ch 3 Product due date planning Ch 4 & Ch 5 Stage due date planning Activity start times planning Planning level Ch 6 Ch 7 Production scheduling Dynamic scheduling Ch 9 Ch 8 low Ch 10

Key Assumptions Probability distribution of operation processing times are available Products have specified structures of manufacturing and assembly operations

Product Due Date Planning Objective – find a better product due date using the information on processing time distributions of operations in a multistage product structure. Method – moment-based approximation. Possible application – quote reliable delivery date at order tendering stage.

Stage Due Date and Activity Start Time Planning Objective – planning due dates at each stage to meet specified service targets. Method – recursive procedure with moment-based approximation. Objective – planning activity start times with given product due date to minimise expected earliness and tardiness cost. Method – Perturbation Analysis Stochastic Approximation (PASA). Possible application – set good start and due dates for each stage in multistage assembly systems by taking into account the effects of uncertainty.

Production Scheduling In stochastic systems, a schedule must be capable of dealing with the situation, “when a resource finishes one operation, the next scheduled operation has not arrived but several other operations are queuing at this resource; which operation should the resource do next?” Choice I – Keeping original schedule  scheduling problem I Choice II – Applying a priority rule  scheduling problem II

Two Type Scheduling Problems Type-I scheduling problem – find optimal sequences and timings by minimising expected total earliness and tardiness cost, where the current operation sequence is followed when determining the cost of a particular candidate schedule during optimisation. Type- II scheduling problem – find the optimal operation timings directly by minimising expected total earliness and tardiness cost, where the operation sequences are unknown in advance due to uncertainty of operation durations (a priority rule is used).

Two-phase optimisation method to solve type-I scheduling problem

One-phase optimisation method to solve type-II scheduling problem Sn – a schedule. EPST – earliest planned start time

Production Scheduling – applicable situations Deterministic scheduling problems – using Heuristic, Simulated Annealing, Evolution Strategy methods in Ch 6. Stochastic timing scheduling with fixed sequences – using PASA, Simulated Annealing, Evolution Strategy methods in Ch 7. Type-I scheduling in stochastic situation – using two-phase optimisation method in Ch 8 based on Ch 6 and 7. Type-II scheduling in stochastic situation – using one-phase optimisation method in Ch 8.

Dynamic Production Scheduling Incremental planning – generate an incremental plan for the new order without affecting the production schedule for the existing orders. Regenerative planning – regenerate a plan for the new order and those unfinished existing orders. Assumption – deterministic operation times.

Dynamic Scheduling – methods Incremental Planning Regenerative Planning Forward incremental planning Backward incremental planning Evolution Strategy incremental planning Forward regenerative planning Evolution Strategy regenerative planning

Conclusions Developed a series of effective methods for the planning of stochastic ETO products. Investigated the effects of complex product structure and uncertainty in processing times. Examined the effects of dynamic arriving orders. Addressed specific planning problems such as product due date planning, stage due date and activity start time planning, production scheduling, dynamic incremental planning and rescheduling.

Limitations Distribution of processing times are required. Random variables in Ch 3~5 are assumed to be independent. Process planning is not considered and product structure is pre-specified. Set-up and transfer times are not explicitly considered.