Computational Methods in Engineering

---

In most stochastic inventory models, such as continuous review models and periodic review models, it has been assumed that the stockout period during a cycle is small enough to be neglected so that the average number of cycles per year can be approximated as D/Q, where D is the average annual demand and Q is the order quantity. This assumption makes the problem more tactable, but it should not be adopted when the beck order and lost sales penalty costs are relatively small. In this paper, considering a continuous review inventory model, we relax the above assumption and we explicitly take into account the stockout period when computing the expected cycle length. Further, we consider the effect of using exact number of cycles rather than using approximate of cycles in a continuous review inventory model. Keywords: Inventory control, Stochastic demand, Continuous review, Inventory cycle

---

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of duplicable arcs in this method differs from that of Dodin’s so that it must be considered a different method. In this method, best duplicable arcs are adopted using a new mechanism. It is proved that duplicating numbers is minimized by this method. The distribution function of this method is a lower bound on exact network distribution function and an upper bound on distribution function of Dodin’s and Kleindorfer’s methods. After the algorithm for the method is presented, its efficiency is discussed and illustration examples will be used to Compare numerical results from this method with those from exact network distribution and Dodin’s method.

---

A novel version of Ant Colony Optimization (ACO) algorithms for solving continuous space problems is presented in this paper. The basic structure and concepts of the originally reported ACO are preserved and adaptation of the algorithm to the case of continuous space is implemented within the general framework. The stigmergic communication is simulated through considering certain direction vectors which are memorized. These vectors are normalized gradient vectors that are calculated using the values of the evaluation function and the corresponding values of object variables. The proposed Gradient-based Continuous Ant Colony Optimization (GCACO) method is applied to several benchmark problems and the results are compared and contrasted with other population-based algorithms such as Evolutionary Strategies (ES), Evolutionary Programming (EP), and Genetic Algorithms (GA). The results obtained from GCACO compare satisfactorily with those of other algorithms and in some cases are superior in terms of accuracy and computational demand.