Trajectories of Random Quadratic Operators of the Random Mendelian Model of Heredity

It is considered random Mendelian model of heredity, when the random quadratic stochastic operators, which define this model, admit two values and Vii' where 0 :s; a :s; I, 0 :s; f3:S; 1. This paper provides a full description of the behaviour of random trajectories of random quadratic operators

Ant Colony Optimization For Split Delivery Inventory Routing Problem

A one-to-many inventory routing problem (IRP) network comprising of a warehouse and geographically dispersed customers is studied in this paper. A fleet of a homogeneous vehicle located at the warehouse transports multi products from the warehouse to meet customer's demand on time in a finite planning horizon. We allow the customers to be visited more than once in a given period (split delivery) and the demand for each product is deterministic and time varying. Backordering is not allowed. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (the best integer solution) for each problem considered. We propose a modified ant colony optimization (ACO) which takes into account not only the distance but also the inventory that is vital in the IRP. We also carried the sensitivity analysis on important parameters that influence decision policy in ACO in order to choose the appropriate parameter settings. The computational results show that ACO performs better on large instances compared to the upper bound and performs equally well for small and medium instances. The modified ACO requires relatively short computational time

Three-Phase Methodology Incorporating Scatter Search for Integrated Production, Inventory, and Distribution Routing Problem

This paper proposes the use of scatter search metaheuristic to solve an integrated production, inventory, and distribution routing problem. The problem is based on a single production plant that produces a single product that is delivered to N geographically dispersed customers by a set of homogenous fleet of vehicles. The objective is to construct a production plan and delivery schedule to minimize the total costs and ensuring each customer’s demand is met over the planning horizon. We assumed that excess production can be stored at the plant or at customer’s sites within some limits, but stockouts due to backordering or backlogging are not allowed. Further testing on a set of benchmark problems to assess the effectiveness of our method is also carried out. We compare our results to the existing metaheuristic algorithms proposed in the literature

Matheuristic approach for production-inventorydistribution routing problem

In this paper, the integrated Production, Inventory and Distribution Routing Problem (PIDRP) is modelled as a one-to-many distribution system, in which a single warehouse or production facility is responsible for restocking geographically dispersed customers whose demands are deterministic and time-varying. The demand can be satisfied either from inventory held at the customer sites or from daily production. A fleet of homogeneous capacitated vehicles for making the deliveries is also considered. Capacity constraints for the inventory are given for each customer and the demand must be fulfilled on time. We propose a two-phase approach within a MatHeuristic framework. Phase I solves a mixed integer programming model which includes all the constraints in the original model except the routing constraints. In phase 2, we propose a variable neighborhood search procedure as the metaheuristics for solving the problem. We carried out a statistical analysis and the findings showed that our results are significantly superior to those from the Greedy Randomized Adaptative Search Procedure (GRASP) in all instances. We also managed to improve 23 out of 30 instances when compared to the Memetic Algorithm with Population Management (MA|PM). The superiority of our algorithm is reemphasized when tested on larger instances with the results showing significantly improved solutions by 100% and 90% respectively when compared to GRASP and MA|PM

An efficient hybrid genetic algorithm for the multi-product multi-period inventory routing problem

The inventory routing problem (IRP) addressed in this study is a many-to-one distribution network consisting of an assembly plant and many distinct suppliers where each supplies a distinct product. We consider a finite horizon, multi-periods, multi-suppliers and multi-products where a fleet of capacitated homogeneous vehicles, housed at a depot, transport products from the suppliers to meet the demand specified by the assembly plant in each period. The demand for each product is deterministic and time varying. A mathematical formulation of the problem is given and CPLEX 9.1 is run for a finite amount of time to obtain lower and upper bounds. A hybrid genetic algorithm, which is based on the allocation first route second strategy and which considers both the inventory and the transportation costs, is proposed. In addition to a new set of crossover and mutation operators, we also introduce two new chromosome representations. Several medium and small sized problems are also constructed and added to the existing data sets to show the effectiveness of the proposed approach

Hybrid Genetic Algorithm with Multiparents Crossover for Job Shop Scheduling Problems

The job shop scheduling problem (JSSP) is one of the well-known hard combinatorial scheduling problems. This paper proposes a hybrid genetic algorithm with multiparents crossover for JSSP. The multiparents crossover operator known as extended precedence preservative crossover (EPPX) is able to recombine more than two parents to generate a single new offspring distinguished from common crossover operators that recombine only two parents. This algorithm also embeds a schedule generation procedure to generate full-active schedule that satisfies precedence constraints in order to reduce the search space. Once a schedule is obtained, a neighborhood search is applied to exploit the search space for better solutions and to enhance the GA. This hybrid genetic algorithm is simulated on a set of benchmarks from the literatures and the results are compared with other approaches to ensure the sustainability of this algorithm in solving JSSP. The results suggest that the implementation of multiparents crossover produces competitive results