Ameur Soukhal

Complexity of flow shop scheduling problems with transportation constraints

Abstract In most manufacturing and distribution systems, semi-finished jobs are transferred from one processing facility to another by transporters such as Automated Guided Vehicles, robots and conveyors, and finished jobs are delivered to warehouses or customers by vehicles such as trucks. This paper investigates two-machine flow shop scheduling problems taking transportation into account. The finished jobs are transferred from the processing facility and delivered to customers by truck. Both transportation capacity and transportation times are explicitly taken into account in these models. We study the class of flow shop problems by analysing their complexity. For the makespan objective function, we prove that this problem is strongly NP-hard when the capacity of a truck is limited to two or three parts with an unlimited buffer at the output of the each machine. This problem with additional constraints, such as blocking, is also proven to be strongly NP-hard.

Resolution of a scheduling problem in a flowshop robotic cell

We develop in this paper a generic and precise identification of a scheduling problem in a flexible manufacturing system. We consider a flowshop robotic cell that processes several jobs. We assume that there is no intermediate buffer between machines. So, jobs may be blocked when downstream machines are busy. We present an integer programming model to determine the sequence of jobs that minimizes the makespan criterion. In order to solve large size problems, we propose a genetic algorithm (GA). Finally, computational experiments are proposed in order to compare the makespan returned by the GA to a lower bound.

Due dates assignment and JIT scheduling with equal-size jobs

This paper deals with due date assignment and just-in-time scheduling for single machine and parallel machine problems with equal-size jobs where the objective is to minimize the total weighted earliness-tardiness and due date cost. These two problems, but with a common due date to be calculated, were shown to be polynomially solvable in O(n4) time. We first show that this complexity can be reduced to O(n3) by modeling the single machine scheduling problem as an assignment problem without necessary due date enumeration. We next prove that the general case with identical parallel machines and a given set of assignable due dates where the cardinality of this set is bounded by a constant number is still polynomially solvable.

Two-Agent scheduling on an unbounded serial batching machine

We study a scheduling problem, in which two agents compete to perform their jobs on the same serial batching machine. On this machine, jobs of the same batch start and complete simultaneously and the batch processing time is equal to the total processing time of its jobs. Each agent aims at minimizing a function which depends only on the completion times of its jobs. The problem is to find a schedule that minimizes the objective function of one agent, subject to the objective function of the other agent does not exceed a given threshold Q. Polynomial and pseudo-polynomial time algorithms are derived for settings with various combinations of the objective functions.

A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

This paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77-84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems.

Scheduling on parallel machines with preemption and transportation delays

This paper deals with an identical parallel machines scheduling problem, where independent jobs can be preempted and transported from one machine to another. The transportation of a preempted job requires a time called the transportation delay. The goal is to find a solution that minimizes the total completion time (makespan). We first study the case of equal-size jobs where new complexity results are given. Then, to solve the problem with two identical machines, we present a dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS). Experimental results show the efficiency of the FPTAS compared to a previously published heuristic.

On an extension of the Sort & Search method with application to scheduling theory

In this paper, we focus on the Sort & Search method initially proposed by Horowitz and Sahni (1974) [6] to solve the knapsack problem, which has already show its applicability to derive exponential-time algorithms for some scheduling problems. We propose an extension of this method to a general class of problems called Multiple Constraint Problems and show that the extended Sort & Search method enables one to derive new exponential-time algorithms, with O^*(m^n^2) worst-case complexity, for two scheduling problems.

Some new polynomial cases in just-in-time scheduling problems with multiple due dates

Coming from the ldquojust-in-timerdquo philosophy in management and production theory, minimizing total weighted earliness-tardiness on machine scheduling problems has wide industrial applications. In the case of a single machine with a given common due date, the problem is known NP-hard. In this paper, n jobs with identical processing times should be scheduled on m uniform machines. The objective is to minimize the total weighted earliness-tardiness penalties. In this study, we consider l given due dates (l<n). We show that the scheduling problem on m uniform machines is polynomially solvable.

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.

Parallel Machine Scheduling Problems

This chapter, presents some results on scheduling jobs on parallel machines in the Competitive and the Interfering scenarios. First, we study the case where job preemption is allowed, i.e. when the processing of a job can be interrupted and resumed later, possibly on another machine. Next, we study the case without job preemption. The chapter is composed of five sections. In Sect. 5.1, we consider parallel machine scheduling problems without job preemption. In Sects. 5.2 and 5.3, we consider preemptable parallel machine scheduling problems with arbitrary and equal job processing times, respectively. We end the chapter with Sects. 5.4 and 5.5 including, respectively, complexity tables and bibliographic remarks.