This paper considers the integrated production and delivery scheduling on a serial batch machine,in which split is allowed in the delivery of the jobs.The objective is to minimize the makespan,i.e.,the maximum deliver...This paper considers the integrated production and delivery scheduling on a serial batch machine,in which split is allowed in the delivery of the jobs.The objective is to minimize the makespan,i.e.,the maximum delivery completion time of the jobs.Lu et al.(Theor Comput Sci 572:50–57,2015)showed that this problem is strongly NP-hard,and presented a 32-approximation algorithm.In this paper,we present an improved 43-approximation algorithm for this problem.We also present a polynomial-time algorithm for the special case when all jobs have the identical weight.展开更多
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 batche...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.展开更多
基金This research was supported by the National Natural Science Foundation of China(Nos.11271338,11771406,11571321,U1504103).
文摘This paper considers the integrated production and delivery scheduling on a serial batch machine,in which split is allowed in the delivery of the jobs.The objective is to minimize the makespan,i.e.,the maximum delivery completion time of the jobs.Lu et al.(Theor Comput Sci 572:50–57,2015)showed that this problem is strongly NP-hard,and presented a 32-approximation algorithm.In this paper,we present an improved 43-approximation algorithm for this problem.We also present a polynomial-time algorithm for the special case when all jobs have the identical weight.
基金This research was supported in part by the National Natural Science Foundation of China(Nos.11771406,11571321 and U1504103).
文摘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.
