Vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. Previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. This paper presents a bi-objective mathematical model for single manufacture multi-retailer with multi-product in order to maximize their benefits. It is assumed that demand is a decreasing and convex function of the retail price. In this paper, common replenishment cycle is considered for the manufacturer and its retailers. Then, the proposed model converts to the single-objective optimization problem using a weighted sum method. A genetic algorithm (GA) is applied to solve it and response surface methodology is employed to tune the GA parameters. Finally, several numerical examples are investigated to demonstrate the applicability of the proposed model and solution approach.

In this paper, multi-objective optimization of railway wheel web profile using bidirectional evolutionary structural optimization (BESO) algorithm is investigated. Using a finite element software, static analysis of the wheel based on a standard load case, and its modal analysis for finding the fundamental natural frequency is performed. The von Mises stress and critical frequency as the problem objectives are combined using different weight factors in order to find the sensitivity number in the method, which specifies which elements to be omitted and which to be added. The iterative process is continued until convergence to an a priori specified material volume. The resulted web profiles show that when the stress is important, material removal is from the middle part of the web, while for frequency as the important objective, the removal is from near the rim part of the web. The suggested profile, corresponding to equal weight factor for the objectives, has a better volume and stress state compared to a standard web profile, and has a more uniform stress distribution. However, higher natural frequency, compared to that of the standard profile, are obtained for larger frequency weight factors, although with a bigger volume. In the end, considering manufacturability of the wheel, the jagged profile resulted from BESO is replaced with a fitted smooth curve and performing the finite element analysis on it. It is seen that there is an improvement in the obtained objectives for the smoothened profile, with no significant change in volume.

Here, a collection of base functions and sub-functions configure the nodes of a web-based (digital) network representing functionalities. Each arc in the network is to be assigned as the link between two nodes. The aim is to find an optimal tree of functionalities in the network adding value to the product in the web environment. First, a purification process is performed in the product network to assign the links among bases and sub-functions. Then, numerical values as benefits and costs are determined for arcs and nodes, respectively. To handle the bi-objective Steiner tree, a particle swarm optimization algorithm is adapted to find the optimal tree determining the value adding sub-functions to bases in a convergent product. An example is worked out to illustrate the applicability of the proposed approach.

This paper considers a parallel system that has a random number of units. The number of units follows a power series distribution which includes several distributions such as geometric, logarithmic and zero-truncated Poisson distributions. Pareto distribution is considered for the lifetime distribution of units. The optimal parameter is obtained for the distribution of sample size so that the expected cost is minimized and the whole reliability of the system is maximized. The weighted sum method has been utilized to convert this bi-objective model into a one-objective model. Numerical calculations have been performed to evaluate the obtained results.

Here, scalarization techniques for multi-objective optimization problems are addressed. A new scalarization approach, called unified Pascoletti-Serafini approach, is utilized and a new algorithm to construct the Pareto front of a given bi-objective optimization problem is formulated. It is shown that we can restrict the parameters of the scalarized problem. The computed efficient points provide a nearly equidistant approximation of the whole Pareto front. The performance of the proposed algorithm is illustrated by various test problems and its effectiveness with respect to some existing methods is shown.

Due to the increasing amount of natural disasters such as earthquakes and floods and unnatural disasters such as war and terrorist attacks, Humanitarian Relief Chain (HRC) is taken into consideration of most countries. Besides, this paper aims to contribute humanitarian relief chains under uncertainty. In this paper, we address a humanitarian logistics network design problem including local distribution centers (LDCs) and multiple central warehouses (CWs) and develop a scenario-based stochastic programming (SBSP) approach. Also, the uncertainty associated with demand and supply information as well as the availability of the transportation network's routes level after an earthquake are considered by employing stochastic optimization. While the proposed model attempts to minimize the total costs of the relief chain, it implicitly minimize the maximum travel time between each pair of facility and the demand point of the items. Additionally, a data set derived from a real disaster case study in the Iran area, and to solve the proposed model a exact method called ɛ-constraint in low dimension along with some well-known evolutionary algorithms are applied. Also, to achieve good performance, the parameters of these algorithms are tuned by using Taguchi method. In addition, the proposed algorithms are compared via four multi-objective metrics and statistically method. Based on the results, it was shown that: NSGA-II shows better performances in terms of SNS and CPU time, meanwhile, for NPS and MID, MRGA has better performances. Finally, some comments for future researches are suggested.