Two machine flow shop scheduling problems with sequence dependent setup times: A dynamic programming approach

Abstract

This paper considers the two different flow shop scheduling problems that arise when, in a two machine problem, one machine is characterized by sequence dependent setup times. The objective is to determine a schedule that minimizes makespan. After establishing the optimality of permutation schedules for both of these problems, an efficient dynamic programming formulation is developed for each of them. Each of these formulations is shown to be comparable, from a computational standpoint, to the corresponding formulation of the traveling salesman problem. Then, the relative merits of the dynamic programming and branch and bound approaches to these two scheduling problems are discussed.

Towards Solving Travelling Salesperson Problem using Hybrid of Genetic Algorithm and Lin-Kernighan Algorithm: A Comparative Evaluation with Neural Network Model

“…The list of the state capitals is given in Table 2 with the abbreviation. In the case study, unique identification numbers (ranging from one to seventeen) are used to represent each state capital in alphabetical order as follows: (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17), these numbers are arranged in different order randomly to generate several tours. The tours that were generated are then put together and termed the "initial population."…”

“…The authors consider path representation method which simply lists the label of nodes. For example, let "1, 2, 3, 4, 5, 6, 7" be the labels of nodes in a seven node instance, then a tour "1→ 4→ 3→ 5→ 7→ 6→ 2→1" may be represented as (1,4,3,5,7,6,2). …”

“…An NP-hard problem is the one that cannot be solved exactly in polynomial time, that is, it does not have an exact but approximate solution. TSP research finds its application in different areas such as transportation problem, logistic distribution problem, delivery order problem, minimum spanning tree (MST) for communication network, electricity network or water pipelining, and machine flow shop scheduling [1]. Another variant of TSP is the Dynamic traveling salesman problem (DTSP), which is a modified version of the travelling salesman [2,3].…”

Scheduling flexible flow lines with sequence-dependent setup times

“…Corwin and Esogbue (1974) considered the situation of a two stage flow line where one of the machines incurs a sequence-dependent setup time. Dynamic programming formulations were created and discussed with regard to computing time and space requirements in con^arison to the TSP.…”

“…First, they are optimal in the case of two or three machines. Corwin and Esogbue (1974) discuss two stage flow shops where either the first or second stage machine has sequencedependent setup times and report that there exists a permutation schedule with the optimal makespan in this situation. The essence of the proof is that the schedule of the non-sequence-dependent stage can be changed to be the same as that in the sequencedependent stage without increasing the makespan.…”