Analytical and metaheuristic solutions for emerging scheduling problems in e-commerce and robotics

Appropriate scheduling of activities have a significant impact on revenues for both e-commerce and manufacturing. The problems investigated in this research are emerging scheduling problems in e-commerce and robotics. These particular problems are NP-hard and therefore difficult to solve optimally. We consider scheduling problems in two different domains. The first is the problem of scheduling advertisements on web pages while the second addresses the problem of scheduling robot moves in large robotic cells. In the web advertisement scheduling problem, we consider two problems, namely, MINSPACE and MAXSPACE. For these problems, a set of n ads A = {A 1,…,An} compete to be placed on a web page in a planning horizon which is divided into slots. An ad Ai is specified by its size si and frequency wi. Size si represents the amount of space the ad occupies in a slot. Ad Ai is said to be scheduled if exactly wi copies of Ai are placed in the slots subject to the restriction that a slot contains at most one copy of an ad. The MINSPACE problem minimizes the maximum fullness among all the slots, where the fullness of a slot is the sum of sizes of ads scheduled in that slot. For the MAXSPACE problem, the fullness of any slot cannot exceed a given value S. The objective is to find a feasible schedule A′ ⊆ A of ads such that the total occupied slot space Ai∈A′ wisi is maximized. We provide approximation algorithms for both of these web advertisement scheduling problems with worst case performance bounds significantly better than the existing bounds. We also develop a hybrid genetic algorithm (GA) to solve the MAXSPACE problem. Our computational results show that the hybrid GA outperforms the existing heuristic for a variety of randomly generated problems. In the robotic cell scheduling problem, the objective is throughput rate maximization, which is equivalent to minimizing the per unit cycle time (i.e., the average time required to produce a part). A robotic cell contains two or more robot-served processing stations, repetitively producing a family of similar parts, in the steady state. We develop GAs to obtain near optimal solutions for three different robotic cells being used at a Texas based company. It is shown that the GA is superior over the existing scheduling method for all three robotic cells.