This paper addresses the hybrid flow shop scheduling problem by considering job rejection to minimize the sum of the total tardiness cost of the scheduled jobs and total cost of the rejected jobs as a single-objective problem. A mixed-integer linear programming model is proposed to solve small-sized problems within an acceptable computational time. Also, this paper exhibits two innovative heuristic algorithms, which are presented to discover fast solutions for the problem along with five meta-heuristics are adapted to solve large-sized problems in the model. Another contribution of this paper is to illustrate the different encoding and decoding methods adapted to algorithms, which are capable of obtaining a feasible schedule and furthermore, to guarantee the efficiency of the solutions based on the schedule. The results obtained from the computational study demonstrate the mathematical model and proposed algorithms effectiveness. Additionally, this paper studies the efficacy of job rejection noting the scheduling for a real-world hybrid flow shop in the tile industry production system. As well as, in this paper, the problem is viewed from a bi-objective problem perspective, so that the tardiness costs of the scheduled jobs and rejection costs of rejected jobs as two objectives are minimized simultaneously to obtain the Pareto solutions. We analyze relationship between the results of the single-objective and bi-objective approaches on small and large-sized problems.