A fast and effective subset sum based improvement procedure for workload balancing on identical parallel machines

Schwerdfeger, Stefan; Walter, Rico

doi:10.1016/j.cor.2016.03.008

Cited by 12 publications

(7 citation statements)

References 19 publications

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“…Polynomialtime approximation schemes were proven to exist for a large class of multiprocessor scheduling problems where the objective depends on the completion times of the machines (Alon et al 1998). Recently, Schwerdfeger and Walter (2016) studied a variant of multiprocessor scheduling that accounts for balancing issues between the machines and for which the objective incorporates the completion times of all machines (by minimizing the NSSWD [normalized sum of squares for workload deviations] criterion). This objective resembles the leveling objectives of the PLP, with the only difference being that we consider linear instead of quadratic deviations from the target demand with respect to completion time.…”

Section: Related Workmentioning

confidence: 99%

Exact and meta-heuristic approaches for the production leveling problem

Vass

Lackner

Musliu

2022

J Sched

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In this paper, we introduce a new problem in the field of production planning, called the production leveling problem. The task is to assign orders to production periods such that the load in each period and for each product type is balanced, capacity limits are not exceeded, and the orders’ priorities are taken into account. Production leveling is an important intermediate step between long-term planning and the final scheduling of orders within a production period, as it is responsible for selecting good subsets of orders to be scheduled within each period. We provide a formal model of the problem and study its computational complexity. As an exact method for solving moderately sized instances, we introduce a mixed integer programming (MIP) formulation. For solving large problem instances, metaheuristic local search is investigated. A greedy heuristic and two neighborhood structures for local search are proposed in order to apply them using simulated annealing. Furthermore, three possible extensions that arise from the application in practice are described and implemented, both within the MIP model and within simulated annealing. We make publicly available a set of realistic problem instances from the industry as well as from random instance generators. The experimental evaluation on our test sets shows that the proposed MIP model is well suited for solving instances with up to 250 orders. Simulated annealing produces solutions with less than $$3\%$$ 3 % average optimality gap on small instances, and scales well up to thousands of orders and dozens of periods and product types. The metaheuristic method presented herein is already being successfully used in the industry.

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Section: Related Workmentioning

confidence: 99%

Exact and meta-heuristic approaches for the production leveling problem

Vass

Lackner

Musliu

2022

J Sched

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“…In the particular case of identical parallel machines, P||NSSWD is equivalent to [15,17]). It makes no difference whether we minimize NSSWD or…”

Section: Performance Criteria For Workload Balancingmentioning

confidence: 99%

“…This formulation was first introduced by [17] to deal with the problem P|| NSSWD. This formulation considers binary variables x jm , which take the value 1 if job j is assigned to machine m and 0 otherwise.…”

Section: Mixed-integer Quadratic Programming (Miq1)mentioning

confidence: 99%

“…The following two formulation represent a new contribution based on the theoretical analysis developed in Section 3. First, we incorporate the new bounds, established by Proposition 4, as new cats in the mixed-integer quadratic programming (MIQ1) proposed by [17] in order to reduce the solution space. Then, based on the same development we introduce a new mixed-integer linear programming (MILP) to solve the problem.…”

Section: Mixed-integer Quadratic Programming (Miq1)mentioning

confidence: 99%

“…One of the recent works dealing with this problem is that of Schwerdfeger and Walter [17]. The authors investigated the workload balancing problem on a parallel machines environment where the objective was to minimize the normalized sum of square for workload deviations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

2021

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This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.

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Optimization in Outbound Logistics—An Overview

Schwerdfeger

2020

Operations Research Proceedings

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A fast and effective subset sum based improvement procedure for workload balancing on identical parallel machines

Cited by 12 publications

References 19 publications

Exact and meta-heuristic approaches for the production leveling problem

Exact and meta-heuristic approaches for the production leveling problem

Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

Optimization in Outbound Logistics—An Overview

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