This paper presents a model to solve the multi-objective location-routing problem with capacitated vehicles. The main purposes of the model are to find the optimal number and location of depots, the optimal number of vehicles, and the best allocation of customers to distribution centers and to the vehicles. In addition, the model seeks to optimize vehicle routes and sequence to serve the customers. The proposed model considers vehicles’ traveled distances, service time and waiting time while guaranteeing that the sum of these parameters is lower than a predetermined value. Two objective functions are investigated. First objective function minimizes the total cost of the system and the second one minimizes the gap between the vehicles’ traveled distances. To solve the problem, a Multi-Objective Imperialist Competitive Algorithm (MOICA) is developed. The efficiency of the MOICA is demonstrated via comparing with a famous meta-heuristics, named Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Based on response surface methodology, for each algorithm, several crossover and mutation strategies are adjusted. The results, in terms of two well-known comparison metrics, indicate that the proposed MOICA outperforms NSGA-II especially in large sized problems.

In this study, we incorporate trade credit policy into a joint marketing and pricing problem in which demand rate depends on the length of the credit period provided by the retailer for her customers, marketing expenditure, and selling price. The trade credit policy adopted here is a delayed payment policy in partial form in which the customers must pay a percent of the total purchasing cost at the time of placing an order and can pay the remaining amount later. Shortages are allowed and partially backordered. The main objective of this study is to determine the optimal credit period, marketing expenditure, selling price, and variables of inventory control simultaneously in order to maximize retailer’s total profit. For solving the proposed problem, first an approximation method is applied to simplify the profit function and transform the problem into a constrained Signomial Geometric Programming (SGP) problem, then a global optimization approach is used for solving the model. Finally, a numerical example and sensitivity analysis of the important parameters are conducted to show the effectiveness of proposed approach.

Learning curves monitor the performance of workers for the given new task as well as it is a mathematical representation of the same learning process which can be analyzed after frequent repetitions. Now-a-days learning curve is a promotion effective tool for management concern with designing and controlling the process of imperfect production and redesigning unbalanced business operations in the production of goods or services related to scheduling, uncontrolled inventory management, quality management as well as inspection. Learning effect has direct impact in calculation of profit or loss. Generally, a business seller, in order to increase his sale prefers to lend his products to buyers for a definite period of time. There is no penalty before or during this definite time period however after the duration of lending time period is over, he will assign some extra charges. For this action, seller offers a trade credit financing period to his buyer. Assuming when buyer receives a lot he separates the defective and non-defective items by a screening process and defective items are then sold at a discounted price. The percentage of defective items decreases per lot according to learning curve. Seller too plans which condition is beneficial for good coordination of retailers and analysts. Different cases are explained broadly in this model to get maximum profit. In this paper, a fiscal construction feature model for imperfect quality items with trade credit policy is analyzed under the effects of learning. Total profit function per cycle has been derived with the help of involvement of different costs and related parameters for the retailers and a numerical example given ahead shows the verification of results. The impacts of key parameters of the model are studied by sensitivity analysts to deduce managerial insights.

In this era of industrialization, there is an increase rate of e-logistic services, which has raised the necessity to pay more attention on e-logistic customer satisfaction. E-logistic services spread so rapidly worldwide which overlook the significant segment of customer satisfaction. Therefore, the prime objective of the current research study is to develop a comprehensive framework for e-logistics customer satisfaction. Various studies highlighted the area of e- logistic customer satisfaction, however, in a rare case, literature formally documented the problem of e-logistic customer satisfaction. Hence, less attention has been paid to the aspect of customer satisfaction in e-logistic. To address this gap, four hypotheses are proposed concerning the relationship of low distribution charges (LDC), low transit time (LTT), effective payment method (EPM), information technology (IT) and e-logistic customer satisfaction. An e-mail survey was preferred, and questionnaires were distributed by using simple random sampling technique. The three hundred (300) questionnaires were distributed among the e-logistic users. The results of the current study found that low distribution charges, low transit time, effective payment method and information technology had a positive significant relationship with e-logistic customer satisfaction. Furthermore, information technology found main contributory element between effective payment method and e-logistic customer satisfaction. This study is contributing to the body of knowledge by developing a comprehensive framework to solve various e-logistic problems. Hence, the current study is helpful for e-logistic companies to mitigate e-logistic customer satisfaction problems.

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.

In this study, a single product is considered which starts to deteriorate with constant rate of replenishment and demand rate is time and price dependent exponential function. Shortage is allowed with partial back logging and the relationship between backorder rate and waiting time is considered to be exponential. The aim is to decide pricing strategy and maximize total average profit function. Total profit function is optimized analytically and proved to be concave function of price. Finally, numerical example is given to illustrate the implementation of the algorithm followed by the sensitivity analysis.

In this paper, a mathematical model for multi-product inventory management in a three-tier supply chain consisting of multi-supplier, a manufacturer, and several retailers is presented. The model determines different factors such as the optimum ordering of the raw materials and the optimal level of the production items with the optimal order of the products by retailers at each level of the chain, with the objective of minimizing inventory management costs in the supply chain. An algorithm is presented to determine the solution of the problem and the implementation of the proposed method is demonstrated using some numerical example.