Scheduling assembly job shop associated with multiple routings using particle swarm optimization approach

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Scheduling assembly job shop associated with multiple routings using particle swarm optimization approach

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Abstract

This paper addresses the scheduling model of a capital goods industry in which the components of different products are processed and assembled in an assembly job shop type environment associated with multiple routings. Assembly job shop scheduling problem (AJSP) is an extension of classical job shop scheduling problem (JSP) which is well known as NPhard. AJSP is a much more complex problem than the JSP as it has to satisfy the precedence relationship between the components and subassemblies at different levels in addition to the routing constraints between the operations of each component. To solve such NP-hard problems, heuristics are commonly preferred over the traditional mathematical approaches. A Particle Swarm Optimization (PSO) based heuristic has been proposed to solve this complex scheduling problem for the objective of minimization of total tardiness. The performance of the proposed PSO is evaluated using a constraint programming model solved using ILOG OPL Studio. The results reveal the effectiveness of PSO in solving AJSP.

Abstract
Introduction
Background of the scheduling model
Description of the model
1. Notations used
2. Problem environment
3. Assumptions
4. Objective
Description of the proposed algorithm
1. Input module
2. Initial swarm generation module
Performance comparison and results
1. Test problems
2. Performance comparison and results
Conclusion
References

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[...] DESCRIPTION OF THE PROPOSED PSO ALGORITHM The different modules of the PSO algorithm that is proposed to evolve simultaneously the route choice and schedule to the assembly job shop problem associated with multiple routings is outlined as flow chart given in Fig Data input module Initial swarm generation module Evaluation module Sorting module Kpijr (Tpijr) corresponding to route r r=1 r=2 r=3 TABLE III DETAILS OF ASSEMBLY OPERATIONS OF THE ILLUSTRATION PROBLEM Preceding operations p Dp Jp0 j apj Ep0j j')} 3 Input module: The following data pertaining to the problem are given as input: number of products number of components for each product number of machines in the shop number of operations Jpi of each component i of product p number of alternative machines (routes) Rpij for operation j of component i of product p Opij∈Lk), the machine number Kpijr corresponding to the route r of operation j of component i of product p along with its processing time Tpijr : Opij∈Lk), number of assembly operations Jp0 for each product assembling time for each assembly operation apj, precedence relationship Ep0j between assembly operations and components of each product p and due date for each product p. [...]

[...] The problem environment in the scheduling model presented in this paper has an assembly job shop type environment associated with multiple routings. There has been extensive research relating to the use of various priority dispatching rules (pdrs) for flow-time and due-date based measures in both static and dynamic assembly job shop scheduling Doctor et al. developed a heuristic based on construction of non-delay schedules for maximizing machine utilization in an assembly job shop subject to satisfying job deadlines. McKoy and Egbelu considered the problem of scheduling jobs in an assembly job shop and developed a heuristic method to minimize the production makespan. [...]

[...] CONCLUSION In this paper, we addressed the scheduling model of a capital goods industry in which the components of different products are processed and assembled in an assembly job shop type environment associated with multiple routings. A PSO based heuristic is proposed to solve the problem for the objective of minimization of total tardiness. The proposed algorithm is capable to rummage around the entire solution space to provide all possible instances, which an enumerative search can, and hence is capable of finding the optimal or near optimal solution under extensive searches. [...]

[...] Objective To determine the optimal assembly and job shop schedules simultaneously with the objective of minimization of total tardiness, given the processing time of all operations of all components, assembling time of all assembly operations, precedence constraints of all components and subassemblies, and product due dates. E. Mathematical Formulation The mathematical formulation for the problem under discussion with the objective of minimizing total tardiness is presented below. Objective: Minimize Assembly level 2 Assembly level 1 O101 O102 Processing operations C O111 O121 C O133 O132 O131 C O142 O141 C O152 O151 C (TR p N Subject to: TR p C p 0 J p 0 D p P Final Assembly C Component TR p 0 Fabrication/Assembly operation C pij S pij pijk :Oij∈Lk } . [...]

[...] Sculli, “Priority dispatching rules in job shops with assembly operations and random delays”, OMEGA, vol pp. 227- J. S. Goodwin and J. C. Goodwin, “Operating policies for scheduling assembled products”, Decision sciences, vol pp. 585- M. K. Reeja and C. Rajendran, “Dispatching rules for scheduling in assembly job shops - Part International Journal of Production Research, vol no pp. 2051–2066, Jun M. K. Reeja and C. Rajendran, “Dispatching rules for scheduling in assembly job shops - Part International Journal of Production Research, vol no pp. [...]

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