A branch and bound algorithm for minimizing makespan in a two machine flowshop with linear deteriorating jobs

In this paper, a two machine flow shop scheduling problem under linear deteriorating jobs is investigated where objective is to minimize the makespan. The problem is known to be NP-hard; therefore, a branch and bound algorithm with dominance rules and lower bounds is established to solve the problem optimally. Several easy heuristic procedures are also proposed to derive the near optimal solutions. The computational experiments extracted based on the recent literature are presented to evaluate the performance of proposed algorithms. Deteriorating jobs lead to an increase in the makespan of the problems; therefore, it is important to obtain the optimal or near optimal solution. The results demonstrate that the branch and bound algorithm is able to solve the most medium-sized problems in reasonable times and the heuristic is quite accurate with an average error percentage of less than 1.67%.