Minimizing Maximum Lateness on Unbounded Single Batching Machine with Family Jobs

The scheduling problem on a single batching machine with family jobs was proposed.The single batching machine can process a group of jobs simultaneously as a batch.Jobs in the same batch complete at the same time.The batch size is assumed to be unbounded.Jobs that belong to different families can not be processed in the same batch.The objective function is minimizing maximum lateness.For the problem with fixed number of m families and n jobs,a polynomial time algorithm based on dynamic programming with time complexity of O(n(n/m+1)m)was presented.

A Cooperated Imperialist Competitive Algorithm for Unrelated Parallel Batch Machine Scheduling Problem

This study focuses on the scheduling problem of unrelated parallel batch processing machines(BPM)with release times,a scenario derived from the moulding process in a foundry.In this process,a batch is initially formed,placed in a sandbox,and then the sandbox is positioned on a BPM formoulding.The complexity of the scheduling problem increases due to the consideration of BPM capacity and sandbox volume.To minimize the makespan,a new cooperated imperialist competitive algorithm(CICA)is introduced.In CICA,the number of empires is not a parameter,and four empires aremaintained throughout the search process.Two types of assimilations are achieved:The strongest and weakest empires cooperate in their assimilation,while the remaining two empires,having a close normalization total cost,combine in their assimilation.A new form of imperialist competition is proposed to prevent insufficient competition,and the unique features of the problem are effectively utilized.Computational experiments are conducted across several instances,and a significant amount of experimental results show that the newstrategies of CICAare effective,indicating promising advantages for the considered BPMscheduling problems.

APPROXIMATION SCHEMES FOR SCHEDULING A BATCHING MACHINE WITH NONIDENTICAL JOB SIZE

In this paper we study the problem of scheduling a batching machine with nonidentical job sizes. The jobs arrive simultaneously and have unit processing time. The goal is to minimize the total completion times. Having shown that the problem is NP-hard, we put forward three approximation schemes with worst case ratio 4, 2, and 3/2, respectively.

Flow-Shop Scheduling with Transportation Capacity and Time Consideration

Planning and scheduling is one of the most important activity in supply chain operation management.Over the years,there have been multiple researches regarding planning and scheduling which are applied to improve a variety of supply chains.This includes two commonly used methods which are mathematical programming models and heuristics algorithms.Flowshop manufacturing systems are seen normally in industrial environments but few have considered certain constraints such as transportation capacity and transportation time within their supply chain.A two-stage flowshop of a single processing machine and a batch processing machine are considered with their capacity and transportation time between twomachines.The objectives of this research are to build a suitable mathematical model capable of minimizing the maximum completion time,to propose a heuristic optimization algorithm to solve the problem,and to develop an applicable program of the heuristics algorithm.AMixed Integer Programming(MIP)model and a heuristics optimization algorithmwas developed and tested using a randomly generated data set for feasibility.The overall results and performance of each approach was compared between the two methods that would assist the decision maker in choosing a suitable solution for their manufacturing line.

Competitive Project Scheduling on Two Unbounded Parallel Batch Machines

This paper considers competitive project scheduling on two unbounded parallel batch machines.There are two competing firms,and each firm has an unbounded parallel batch machine.All projects must be performed in batches by Firms 1 and 2 on their machines,respectively.The profit that each firm obtains from each project depends on whether the firm finishes the job before or after its competitor.In the first problem,given a feasible schedule for Firm 1,the objective is to find an optimal schedule to maximize the total reward for Firm 2 under the given schedule for Firm 1.The corresponding total reward for Firm 1 is called the worst-case total reward of the given schedule for Firm 1.In the second problem,the objective is to find an optimal schedule for Firm 1 to maximize the worst-case total reward.We provide optimal algorithms for the two problems,respectively.

Two-stage scheduling on batch and single machines with limited waiting time constraint

This study addresses the problem of two-stage scheduling on batch and single machines with limited waiting time constraint; thus, the makespan is minimized.A mixed-integer linear programming model is proposed for this problem. Three tight lower bounds and a heuristic algorithm are developed. The worst-case performance of the proposed algorithm is discussed. A hybrid differential evolution algorithm is also developed to improve the solution quantity. Numerical results show that the hybrid algorithm is capable of obtaining high-quality solutions and exhibits a competitive