augmented constraint

In today's world economy, companies must focus all their activities and capabilities on customer satisfaction because customers are the only source of return on investment. Besides, customer satisfaction in supplying and distributing short-lived commodities especially food, due to their special and perishable properties, has doubled the importance of the issue. When a vehicle carries the demand of a number of customers in one shipment, due to the long travel time and the frequent opening of the refrigerator door, the quality of the remaining products in the vehicle decreases and, as a result, the satisfaction of customers reduces. The main purpose of this article is to maximize customer satisfaction in the food supply chain network. The study integrates the decisions of the different parts of a food supply chain under uncertainty. The first part includes food suppliers. Because the studied supply chain is multi-commodity, one supplier is not able to supply all the food. Therefore, it can supply part of the customer needs according to its conditions and expertise. The second part includes the heterogeneous transport fleet, which serves as a VRP problem. Thus, a vehicle can receive food from a supplier and deliver it to customers located in different geographical locations. In addition, the preparation time of vehicles is also considered as a constraint. The transport fleet consists of several refrigerated vehicles with different carrying capacities and speeds. Since one vehicle is not able to carry all the orders, each product, according to the required temperature and storage conditions, must be transported by vehicles specific to that product. Also, due to weather and traffic conditions, the vehicle travel time is not definite. So, in this study, the uncertainty of vehicle travel time (triangular fuzzy) is taken into account too. The third part of this supply chain includes end users, whose geographical location and the amount of demand of each is definite and specific. There is a time window like (x,y) for each user. If the orders are delivered to the customer before time x, it will cause earliness. If it is delivered after time y, it will cause tardiness. The objectives of this study are minimizing the sum of tardiness and earliness of deliveries to customers and maximizing the quality of products delivered to them. A mathematical model of the problem is presented, and the augmented ε constraint method is used to solve the model. It has been shown that the exact solution method cannot solve large-scale problems within a reasonable time. Therefore, meta-heuristic algorithms should be used. This research has presented the MOTTH meta-heuristic algorithm, which is a new development of the genetic algorithm and is inspired by the long-standing human desire to travel throughout history. In this algorithm, the best solutions of the current generation replace the worst solutions of R generations, and, thus, the algorithm’s premature convergence is prevented and more solutions are searched in the solution area. As the mathematical model was solved through the augmented ε constraint method, the relationship between the two objective functions was explained. It was also shown that an increase in the quality of the products delivered to customers leads to a rise in the sum of the tardiness and earliness of deliveries to customers. Therefore, considering the importance of each of the objective functions, every company should establish a balance between the two objective functions.For validation, the results of the NSGA-II and MOTTH algorithms were compared with those of the exact solution of the augmented  constraint method. The results of the algorithms were also compared. It was shown that the MOTTH meta-heuristic algorithm performs better. For the mathematical modeling of this research and for solving the model, the resources available in the literature and the GAMS and MATLAB software programs were used respectively. According to the results of this study, a practical suggestion for frozen food supply chain managers is to use the MOTTH algorithm. This algorithm offers better solutions than the NSGA-II algorithm, the sum of tardiness and earliness of deliveries to customers is less, and the quality of the products delivered to customers remains higher. Moreover, the use of frozen food trucks partitioned with separate doors and equipped with cooling systems is another practical suggestion of this research; if the door of a partition is opened and the products are emptied, the other products in the other partitions will not receive a heat shock and their quality does not decline.

Hazardous waste management incorporates collection, separation, treatment, recycling and disposal of hazardous wastes. In this paper, a new multi-objective mixed integer model is presented for hazardous waste collection problem. The model aims to minimize transportation and construction costs, and environmental and population risks in hazardous waste management systems. This model is applied in a case study of Iran in order to help decision makers to decide on the location of separation, treatment, recycle, disposal centers, and established technology in treatment center. Moreover, this paper specifies routes between different facilities in collection network. For addressing population and environmental impacts and economical costs, three objective functions including total costs, total population exposure risk, and environmental risks are considered. An augmented ε-constraint method is used to generate Pareto optimal solution for these conflicting objectives. Finally, proposed model is utilized in our case study and numerical results and some managerial insights are provided