Novel Formulation and Resolution of Job-Shop Scheduling Problems

Yan, Bing; Bragin, Mikhail A.; Luh, Peter B.

doi:10.1109/lra.2018.2850056

Cited by 30 publications

(78 citation statements)

References 22 publications

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“…f) The Objective function Following [6], [7], the objective function to be minimized is the total weighted tardiness. The tardiness of part i is the number of time slots being late, i.e., the number of time slots that the completion time of the last operation of part i exceeds the due date di.…”

Section: E) Machine Capacity Constraintsmentioning

confidence: 99%

A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

Liu¹,

Luh²,

Yan³

et al. 2021

Preprint

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ob-shop scheduling is an important but difficult problem arising in low-volume high-variety manufacturing. It is usually solved at the beginning of each shift with strict computational time requirements. For fast resolution of the problem, a promising direction is to formulate it in an Integer Linear Programming (ILP) form so as to take advantages of widely available ILP methods such as Branch-and-Cut (B&C). Nevertheless, computational requirements on ILP methods for existing ILP formulations are high. In this paper, a novel ILP formulation is presented. In the formulation, a set of binary indicator variables indicating whether an operation begins at a time slot on a machine group or not is selected as decision variables, and all constraints are innovatively formulated based on this set of variables. For fast resolution of large problems, our recent decomposition-and-coordination method “Surrogate Absolute-Value Lagrangian Relaxation” (SAVLR) is enhanced by using a 3-segment piecewise linear penalty function, which more accurately approximates a quadratic penalty function as compared to an absolute-value function. Testing results demonstrate that our new formulation drastically reduces the computational requirements of B&C as compared to our previous formulation. For large problems where B&C has difficulties, near-optimal solutions are efficiently obtained by using the enhanced SAVLR under the new formulation.<br><a></a>

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Section: E) Machine Capacity Constraintsmentioning

confidence: 99%

A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

Liu¹,

Luh²,

Yan³

et al. 2021

Preprint

Self Cite

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“…Consider the scheduling problem with a single-operation part with p = 3 and K = 8 in used in Subsection III-C. Constraints (2), (3), (5) and (11) in Fig. 7 have been explored in Subsection III-C, and inequality (12) is redundant given the binary requirements of .…”

Section: Example 1: Single Part A) One Operationmentioning

confidence: 99%

“…(25b) -(25e). This set of constraints has been reported in our previous work [5]. The above set of tightened constraints can be generalized for all operations with different processing time as follows,…”

Section: ) Inequality Constraintsmentioning

confidence: 99%

“…In summary, the values  k must be 1 for k  [k 0 , k 0 + p-1] and 0 otherwise. Thus the values of b and c uniquely determine the values of .The above implies that when s are binary and Eqs (3)(4)(5). are all satisfied, the values of integer decision variables b and c can be uniquely determined by the values of s, and vice versa.…”

mentioning

confidence: 97%

“…Ex.1-c) Tightened constraintsBy combining equalities (2),(5) and(10) inFig. 11, the following constraint is obtained,…”

mentioning

confidence: 99%

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An Innovative Formulation Tightening Approach for Job-Shop Scheduling

Yan¹,

Bragin²,

Luh³

2020

Preprint

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Job shops are an important production environment for low-volume high-variety manufacturing.<i> </i>Its scheduling has recently been formulated as an Integer Linear Programming (ILP) problem to take advantages of popular Mixed-Integer Linear Programming (MILP) methods, e.g., branch-and-cut. When considering a large number of parts, MILP methods may experience difficulties. To address this, a critical but much overlooked issue is formulation tightening. The idea is that if problem constraints can be transformed to directly delineate the problem convex hull in the data pre-processing stage, then a solution can be obtained by using linear programming methods without much difficulty. The tightening process, however, is NP hard because of the existence of integer variables. In this paper, an innovative and systematic approach is established for the first time to tighten the formulations of individual parts, each with multiple operations, in the data pre-processing stage. It is a major extension from our previous work on problems with binary and continuous variables to integer variables. The idea is to first link integer variables to binary variables by innovatively combining constraints so that the integer variables are uniquely determined by binary variables. With binary variables and continuous only, the vertices of the convex hull can be obtained based on the vertices of the linear problem after relaxing binary requirements with proved tightness. These vertices are then converted to tight constraints for general use. This approach significantly improves and extends our previous results on tightening single-operation parts without actually achieving tightness. Numerical results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other ILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved.

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A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

Sun

Bragin

et al. 2022

J Adv Manuf & Process

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In a manufacturing system, production control-related decision-making activities occur at different levels. At the process level, one of the main control activities is to tune the parameters of individual manufacturing equipment. At the system level, the main activity is to coordinate production resources and to route parts to appropriate workstations based on their processing requirement, priority indices, and control policy. At the factory level, the goal is to plan and schedule the processing of parts at different operations for the entire system in order to optimize certain objectives. Note that the results of such activities at different levels are closely coupled and affect the overall performance of the manufacturing system as a whole. Therefore, it is important to systematically integrate these control and optimization activities into one unified platform to ensure the goal of each individual activity is aligned with the overall performance of the system. In this paper, we develop a simulation-based virtual testbed that implements dynamic optimization, automatic information exchange, and decision-making from the process-level, system-level, and factory-level of a manufacturing system into an integrated computation environment. This is demonstrated by connecting a Python-based numerical computation program, discrete-event simulation software (Simul8), and an optimization solver (CPLEX) via a third-party master program. The application of this simulation-based virtual testbed is illustrated by a case study in a machining shop.

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Novel Formulation and Resolution of Job-Shop Scheduling Problems

Cited by 30 publications

References 22 publications

A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

An Innovative Formulation Tightening Approach for Job-Shop Scheduling

A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

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