The Flexible flow shop (FFS) is defined as a multi-stage flow shops with multiple parallel machines. FFS scheduling problem is a complex combinatorial problem which has been intensively studied in many real world industries. This review paper gives a comprehensive exploration review on the FFS scheduling problem and guides the reader by considering and understanding different environmental assumptions, system constraints and objective functions for future research works. The published papers are classified into two categories. First is the FFS system characteristics and constraints including the problem differences and limitation defined by different studies. Second, the scheduling performances evaluation are elaborated and categorized into time, job and multi related objectives. In addition, the resolution approaches that have been used to solve FFS scheduling problems are discussed. This paper gives a comprehensive guide for the reader with respect to future research work on the FFS scheduling problem.

Deteriorating inventory models are used as decision support tools for managers primarily, although not exclusively, in the retail trade. The mathematical modeling of deteriorating items allows managers to analyze their inventory management systems to identify areas that can be improved and to measure the corresponding potential benefits. This study develops an enhanced deteriorating inventory model for optimizing the inventory control strategy of companies operating in sectors with deteriorating products. In contrast with previous studies, our model holistically accounts for the overall financial effect of a company’s policies on product price discounting and on inventory shortages while considering the time value of money (TVM). We aim to find the optimal replenishment strategy and the optimal price reductions that maximize the discounted profit function of this analytical model over a fixed planning horizon. To this end, we use an economic order quantity model to study the effects of the TVM and inflation. The model accounts for pre- and post-deterioration discounts on the selling price for non-instantaneous deteriorating products with the demand rate being a function of time, price-discounts and stock-keeping units. Shortages are allowed and partially backordered, depending on the waiting time until the next replenishment. Additionally, we consider the effect of discounts on the selling price when items have either an instant deterioration or a fixed lifetime. We propose five implementable solutions for obtaining the optimal values, and examine their performance. We present some numerical examples to illustrate the applicability of the models, and carry out a sensitivity analysis. The study reveals that accounting for TVM and inventory shortages is complex and time-consuming; nevertheless, we find that accounting for TVM and shortages can be valuable in terms of increasing the yields of companies. Finally, we provide some important managerial implications to support decision-making processes.

This work is devoted to the study of the Uncertain Quay Crane Scheduling Problem (QCSP), where the loading /unloading times of containers and travel time of quay cranes are considered uncertain. The problem is solved with a Simulation Optimization approach which takes advantage of the great possibilities offered by the simulation to model the real details of the problem and the capacity of the optimization to find solutions with good quality. An Ant Colony Optimization (ACO) meta-heuristic hybridized with a Variable Neighborhood Descent (VND) local search is proposed to determine the assignments of tasks to quay cranes and the sequences of executions of tasks on each crane. Simulation is used inside the optimization algorithm to generate scenarios in agreement with the probabilities of the distributions of the uncertain parameters, thus, we carry out stochastic evaluations of the solutions found by each ant. The proposed optimization algorithm is tested first for the deterministic case on several well-known benchmark instances. Then, in the stochastic case, since no other work studied exactly the same problem with the same assumptions, the Simulation Optimization approach is compared with the deterministic version. The experimental results show that the optimization algorithm is competitive as compared to the existing methods and that the solutions found by the Simulation Optimization approach are more robust than those found by the optimization algorithm.

Designing a production process normally is involved with some important constraints such as uncertainty, trade-off between production costs and quality, customer’s expectations and production tolerances. In this paper, a novel multi-objective robust optimization model is introduced to investigate the best levels of design variables. The primary objective is to minimize the production cost while increasing robustness and performance. The response surface methodology is utilized as a common approximation model to fit the relationship between responses and design variables in the worst-case scenario of uncertainties. The target mean ratio α is applied to ensure the quality of the process by providing the robustness for all types of quality characteristics and with a trade-off between variability and deviance from the ideal point. The Lp metric method is used to integrate all objectives in one overall function. In order to estimate target value of the quality loss by considering production tolerances, the process capability ratio (Cpm) is applied. At the end, a numerical chemical mixture problem is served to show the applicability of the proposed method.