Given an array with n elements, we want to rearrange them in ascending order. In this paper, we introduce Quick Sort, a divide-and-conquer algorithm to sort an N element array. We evaluate the O(NlogN) time complexity in best case and O(N) in worst case theoretically. We also introduce a way to approach the best case.

Given a sequence of N elements a1, a2, a3, ..., aN. The desired output will be a’1, a’2, a’3,..., a’N such that a’1≤, a’2≤, a’3≤...≤a’N using merge sort. In this paper, we propose a modification to the existing merge sort algorithm to sort the given elements when the input sequence (or a part of it) is in ascending or descending order in a more efficient way by reducing the number of comparison...

Given an array with n elements, we want to rearrange them in ascending order. Sorting algorithms such as the Bubble, Insertion and Selection Sort all have a quadratic time complexity that limits their use when the number of elements is very big. In this paper, we introduce Merge Sort, a divide-andconquer algorithm to sort an N element array. We evaluate the O(NlogN) time complexity of merge sor...

Focusing on production processes is the decisive factor in managing an efficient supply chain that leads to company's success. The objective constraints model include all goals company seeks achieve and level for each. In addition clarifying contribution of each decision variable achieving specified levels different goals, conclusions reached are results prove possibility solving a problem. App...

integrated production-distribution planning (pdp) is one of the most important approaches in supply chain networks. we consider a supply chain network (scn) to consist of multi suppliers, plants, distribution centers (dcs), and retailers. a bi-objective mixed integer linear programming model for integrating production-distribution designed here aim to simultaneously minimize total net costs in ...