In this paper we propose a simple but efficient modification of the well known Nelder Mead (NM) simplex search method for unconstrained optimization, Instead of moving all n simplex vertices at once in the direction of the best vertex, our "shrink" step moves them in the same direction but one by one until an improvenlent is obtained, In addition, for solving non convex problems, we sbnply restart the so modified NM (MNM) method by constructing an initial simplex around the solution obtained in the previous phase, We repeat restarts until there is no improvement in the objective function value, Thus, our restarted modified NM (RMNM) is a descent and deterministic method and may be seen as an extended local search for continuous optimization, In order to improve computational complexity and efficiency, we use the heap data structure for storing and updating simplex vertices, Extensive empirical analysis shows that: our modified method outperforms in average the original version as well as some other recent successful modifications; in solving global optimization problems, it is comparable with the state of-the art heuristics.

This paper considers a two-level vendor managed inventory (VMI) system comprising a distribution center (DC) and a retailer. Both the DC's and the retailer's replenishment decisions follow the order-up-to-level policy and aim at maximizing the profit of the overall system. We critically examine the potential of the DC's ability to modify delivery decisions, identify and quantify the cost factors that influence the DC's modification ability, establish a relationship between the DC's location and its modification ability, and show the trade-off between the DC's modification ability and related costs. Our analysis provides a new insight into the role of the DC and reveals the full potential of the VMI system. Our findings and their practical implications, demonstrated

This paper addresses an integrated inventory and routing problem in a three-echelon logistics system, which consists of a supplier, a central warehouse and a group of retailers. The inventory decision of each member and the routing decision among members of the system are made simultaneously, with the objective of minimizing the overall average cost of the system. A strategy named fixed partition and power-of-two (FP-POT) is proposed for the considered problem and a variable large neighborhood search (VLNS) algorithm, which is a special case of variable neighborhood search (VNS) algorithm, is developed. The efficiency of the strategy as well as the algorithm is illustrated by comparing computational results with a lower bound. The advantage of the proposed VLNS algorithm is further shown by getting better results for the problems in a two-echelon logistics system, which have been solved by a Tabu Search algorithm recently.

In this study we focus on the integration of inventory control and vehicle routing schedules for a distribution system in which the warehouse is responsible for the replenishment of a single item to the retailers with demands occurring at a specific constant (but retailer-dependent) rate, combining deliveries into efficient routes. This research proposes a fixed partition policy for this type of problem, in which the replenishment interval of each of the retailers' partition region as well as the warehouse is accorded the power of two (POT) principle. A lower bound of the long-run average cost of any feasible strategy for the considered distribution system is drawn. And a tabu search algorithm is designed to find the retailers' optimal partition regions under the fixed partition policy proposed. Computational results reveal the effectiveness of the policy as well as of the algorithm.

In this paper, we address the problem of deciding the optimal ordering quantity and frequency for a supplier–retailer logistic system in which the transportation cost as well as the multiple uses of the vehicles are considered. Based on the traditional economic order quantity (EOQ) formula, a modified EOQ model is set up and an algorithm for the model is presented. Computational results verify the proposed model as well as the efficiency of the algorithm.