This study develops a dynamic pricing and advertising model for perishable products under an admissible price ceiling, where prices may vary over time but cannot exceed a market-accepted upper bound, while dynamic discounts are allowed. The demand function jointly depends on the selling price, advertising-induced goodwill, and the remaining time until product expiration, a combination rarely addressed in prior research. The problem is formulated as a finite-horizon optimal control model, explicitly incorporating perishability and the price ceiling constraint. By applying Pontryagin’s maximum principle, time-dependent optimal trajectories for price and advertising are derived. Numerical experiments and sensitivity analyses illustrate how changes in price sensitivity, advertising effectiveness, and the remaining shelf life effect on demand influence optimal strategies and profitability. The results reveal critical trade-offs between pricing flexibility, advertising intensity, and perishability effects, offering practical guidance for decision-makers in food, pharmaceutical, and fast-moving consumer goods markets with fixed price tags compared to more flexible pricing environments.

The issue of integrated scheduling and sequencing operation of unloading and loading equipment in container ports has been one of the most important issues concerning time efficiency. In addition, with the emergence of green harbor concepts, the inclusion of criteria for minimizing energy consumption, fuel and emission reduction are among the other issues that have been noticed by planners in the field of energy efficiency. Furthermore, due to the complexity and scope of activities of a container terminal, uncertainty in operational parameters such as transportation time, time of readiness and entry of work into the system and the velocity of the transportation fleet are inevitable in this operational environment. Therefore, this research with the aim of sharing trucks among loading and unloading equipment, proposes a robust multi-objective integer programming model for the synchronized scheduling of truck operations with other handling equipment to decrease the fuel consumption of trucks and the flow time of containers, considering the uncertainty in operational parameters as fuzzy numbers. To find the Pareto solutions for this model, the ε-Constraint technique is employed. Finally, the performance of the model in deterministic and uncertain modes is evaluated, compared and analyzed employing the inputs gathered from Shahid Rajaei port. The findings demonstrate that using this model will result in a substantial decrease in both fuel consumption and flow time of containers in comparison to the current procedure. Additionally, results will demonstrate the extent to which the terminal's fuel and time consumption will increase under conditions of uncertainty in operational parameters when the optimal plans derived from the robust model are implemented.

In this article, the application of the Multi-Skilled Resource-Constrained Flow Shop Scheduling Problem (MSRC-FSSP) in preventive maintenance as a case study has been investigated. In other words, to complete each maintenance order at each stage, in addition to the machine, a set of required human resources with different skills must be available. According to human resources skills, each of them can perform at least one order or at most N orders, and each maintenance order must be done by a set of human resources with different skills. To carry out a maintenance order, different human resources must be in communication and cooperation so that a preventive maintenance order can be completed. In this article, these resources are considered as technical supervisors, repairmen and maintenance managers who complete all maintenance orders in a flow shop environment as a job. For this problem, a new Mixed Integer Linear Programming (MILP) model has been formulated with the two-objective functions, minimizing total orders completion time and the human resources idle time. To solve the model on a small scale, CPLEX is used, and to solve it on a large scale, due to the fact that this problem is NP-Hard, a meta-heuristic algorithm named Genetic Algorithm (GA) is presented. Finally, the computational results have been done to validate the model, along with the analysis of the human resources idle time.

Inspired by the industries such as food and beverage, metal and steel, as well as petroleum and petrochemical ones, the current study addresses a joint order acceptance and scheduling, lot streaming in a flexible flow shop and batch delivery problem. For maximizing a profit objective function with trading off between the revenue of the accepted orders and the costs incurred, a novel mixed integer linear programming is proposed. This paper develops a hybrid metaheuristic algorithm based on the Genetic Algorithm. In the developed algorithm, (1) a heuristic, (2) a local search, and (3) a restart phase is proposed. To set the appropriate parameters of the algorithms, Taguchi experimental design was applied. The obtained results reveal the appropriate performance of the hybrid genetic algorithm.

This paper analyzes a supply chain, which consists of a manufacturer, a retailer and several suppliers in which the retailer orders jobs to the manufacturer and the suppliers provide the requiring parts. The manufacturer schedules and processes the orders and dispatches them to the retailer either individually or collectively in batches. The manufacturer incurs a penalty cost for each tardy job and a transportation cost for every delivered batch and therefore, searches for a schedule that yields minimum number of tardy jobs and batches. Moreover, the manufacturer tries to optimize its supplying cost through locating the suppliers that offer appropriate release times and costs for manufacturing parts. Since the release times of parts directly affect scheduling of orders, in this research, we develop an integrated mathematical model for the manufacturer that incorporates suppliers & apos; selection issue into the scheduling and batching decisions. Furthermore, we present a heuristic algorithm (greedy algorithm) and also a local search to quickly determine the optimal or near-optimal solutions. The computational analysis shows the importance of the integrated model and also the superiority and effectiveness of the heuristic algorithms.

During the past few years, despite tremendous contribution on deterministic flow shop problem, there are only limited number of works dedicated on stochastic cases. This paper examines stochastic scheduling problems in two-machine flow shop environment for expected makespan minimization where processing times of jobs are normally distributed. Since jobs have stochastic processing times, to minimize the expected makespan, the expected sum of the second machine’s free times is minimized. In other words, by minimization waiting times for the second machine, it is possible to reach the minimum of the objective function. A mathematical method is proposed which utilizes the properties of the normal distributions. Furthermore, this method can be used as a heuristic method for other distributions, as long as the means and variances are available. The performance of the proposed method is explored using some numerical examples.