A Time Window Approach to Simultaneous Scheduling of Machines and Material Handling System in an FMS

Abstract

This paper exploits the interactions between the machine scheduling and the scheduling of the material handling system in an FMS by addressing them simultaneously. The material transfer between machines is done by a number of identical automated guided vehicles (AGVs) which are not allowed to return to the load/unload station after each delivery. This operating policy introduces an additional complexity to the problem because it results in sequence-dependent travel times for the deadheading trips between successive loaded trips of the AGVs. The problem is formulated as a nonlinear mixed integer programming model. Its objective is makespan minimization. The formulation consists of constraint sets of a machine scheduling subproblem and a vehicle scheduling subproblem which interact through a set of time window constraints for the material handling trip starting times. An iterative procedure is developed where, at each iteration, a new machine schedule is generated by a heuristic procedure, the operation completion times obtained from this schedule are used to construct time windows for the trips, and a feasible solution is searched for the second subproblem, which is handled as a sliding time window problem. The procedure is numerically tested on 90 example problems.

Tabu search algorithms for job-shop problems with a single transport robot

“…, n) and each job is processed on each machine exactly once. The processing times of the operations in the instance P 1 are from the interval [1,10] and in P 2 from the interval [1,100]. Various test instances were obtained by adding transportation and empty moving times with different characteristics.…”

“…For the transportation times t jkl we distinguished the following four cases: job-and machine-dependent times t jkl randomly generated from the interval [1,10] (adjusted in such a way that the triangle inequality holds), job-independent transportation times t kl analogously to the first case, job-independent transportation times t kl = D|k − l| with different values D (proportional to the distance between the corresponding machines when they are assumed to be ordered in a single line), and constant transportation times t jkl = T . Analogously, we distinguished the following three cases for the empty moving times: randomly generated values t kl , values t kl = d|k − l| depending on the machine distances and constant times t kl = t.…”

“…Langston [15] derived some approximation algorithms for a flexible flow-shop environment with two stages and interstage transportation times. Bilge & Ulusoy [1] proposed a heuristic for simultaneously scheduling the machines and vehicles in a flexible manufacturing system with job-shop structure.…”

A review of design and control of automated guided vehicle systems

“…Bilge and Ulusoy (1995) formulate the integrated scheduling problem of machines and the AGV system as a MIP formulation. Since the problem is very difficult to solve by an exact method, they propose a heuristic for the solution.…”

Modeling of capacitated transportation systems for integral scheduling

“…they assume fixed transportation times and neglect the parking aspects within terminals and the handling of empty vehicles (see e.g. Bilge & Ulusoy [2] or Hurink & Knust [11])…”