A Mixed Integer Programming Formulation for Generating Shared Press-Brake Setups

Author(s):  
Satyandra K. Gupta ◽  
Deepak Rajagopal

Abstract To enable cost-effective small batch manufacturing, we need to eliminate unnecessary setup operations, improve tool utilization, and thereby increase throughput. In sheet metal bending, the time taken for the actual process of bending is significantly less compared to the time taken for setup and tool changes. Press-brakes for sheet metal bending can be setup to produce more than one type of parts without requiring a setup change. To exploit this flexibility, we need setup planning techniques so that press-brake setups can be shared among many different parts. In this paper, we describe an approach based on mixed integer programming to generate a shared setup for a set of parts. We expect that by producing many different types of parts on the same setup, we can significantly reduce the number of setups required and enable cost-effective small-batch manufacturing.

Author(s):  
Satyandra K. Gupta

Abstract Sheet metal bending press-brakes can be setup to produce more than one type of parts without requiring a setup change. To exploit this flexibility, we need setup planning techniques to generate press-brake setups that can be shared among many different parts. In this paper, we describe an algorithm which partitions a given set of parts into setup compatible part families which can be produced on the same setup. Our algorithm is based on a two step approach. The first step is to identify setup constraints for each individual part. The second step is to form setup-compatible part families based on the compatibility of setup constraints. We expect that by producing many different types of parts on the same setup, we can significantly reduce the required number of setups and enable cost effective small batch manufacturing.


2020 ◽  
Vol 8 (3-4) ◽  
pp. 241-261 ◽  
Author(s):  
Gerald Gamrath ◽  
Timo Berthold ◽  
Domenico Salvagnin

Abstract Dual degeneracy, i.e., the presence of multiple optimal bases to a linear programming (LP) problem, heavily affects the solution process of mixed integer programming (MIP) solvers. Different optimal bases lead to different cuts being generated, different branching decisions being taken and different solutions being found by primal heuristics. Nevertheless, only a few methods have been published that either avoid or exploit dual degeneracy. The aim of the present paper is to conduct a thorough computational study on the presence of dual degeneracy for the instances of well-known public MIP instance collections. How many instances are affected by dual degeneracy? How degenerate are the affected models? How does branching affect degeneracy: Does it increase or decrease by fixing variables? Can we identify different types of degenerate MIPs? As a tool to answer these questions, we introduce a new measure for dual degeneracy: the variable–constraint ratio of the optimal face. It provides an estimate for the likelihood that a basic variable can be pivoted out of the basis. Furthermore, we study how the so-called cloud intervals—the projections of the optimal face of the LP relaxations onto the individual variables—evolve during tree search and the implications for reducing the set of branching candidates.


1999 ◽  
Vol 121 (4) ◽  
pp. 689-694 ◽  
Author(s):  
S. K. Gupta ◽  
D. A. Bourne

Contemporary process planners for sheet metal bending solve the process planning problem for individual parts. Quite often, many different parts can be produced on shared setups. However, plans generated by current process planning systems fail to exploit this commonality between setups and try to generate optimal setups for individual parts. In this paper, we present an algorithm for multi-part setup planning for sheet metal bending. This algorithm takes a set of parts and operation sequences for these parts, and tries to find a shared setup plan that can work for every part in the set. Setup changes constitute a major portion of the production time in batch production environments. Therefore, multi-part setup planning techniques can be used to significantly cut down the total number of setups and increase the overall through-put.


2009 ◽  
Vol 35 (2) ◽  
pp. 180-185
Author(s):  
Mi ZHAO ◽  
Zhi-Wu LI ◽  
Na WEI

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