Abstract
This paper considers a variant of the relocation problem, which is formulated from an urban renewal project. There is a set of jobs to be processed in a two-machine flow shop subject to a given initial resource level. Each job consumes some units of the resource to start its processing on machine 1 and will return some amount of the resource when it is completed on machine 2. The amount of resource released by a job is not necessarily equal to the amount of resource acquired by the job for starting the process. Subject to the resource constraint, the problem is to find a feasible schedule whose makespan is minimum. In this paper, we first prove the NP-hardness of two special cases. Two heuristic algorithms with different processing characteristics, permutation and non-permutation, are designed to construct feasible schedules. Ant colony optimization (ACO) algorithms are also proposed to produce approximate solutions. We design and conduct computational experiments to appraise the performances of the proposed algorithms.
Highlights
Mathematics 2021, 9, 1527. https://Scheduling is a decision-making process that allocates limited resources to tasks in a given time period to optimize certain objectives in manufacturing as well as service industries [1]
We discuss the results of Ant colony optimization (ACO) algorithms with permutation and non-permutation options
We considered the relocation problem in a two-machine flow shop scheduling problem with the second machine introduced for recycling the resource returned by jobs completed on the first machine
Summary
Scheduling is a decision-making process that allocates limited resources to tasks in a given time period to optimize certain objectives in manufacturing as well as service industries [1]. Current tenants of the buildings under reconstruction needed to be relocated to temporary housing units. Kaplan [8] first formulated the relocation problem of determining a feasible redevelopment sequence of the buildings with the initial budget. Lin and Huang [13] presented an integer linear program formulation for the permutation case, in which the job sequences on all machines are the same. We present heuristic algorithms and ant colony optimization (ACO) algorithms for both permutation and non-permutation sequences to find feasible schedules with resource constraints for minimum makespan.
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