可拆分有调整时间的平行机排序问题的一个算法

考虑有独立调整时间的同型号平行机排序问题,极小化最迟完工时间,产品允许拆分,同一产品被拆分后各部分可以在不同机器上同时加工,该问题是ＮＰ－ｈａｒｄ问题。本文首先给出该问题的一个启发式算法ＭＬ,然后证明了其最坏情况估计不超过７／４－１／ｍ（ｍ≥２）。     

The multi-item capacitated lot-sizing problem with setup times and shortage costs

We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of Miller et al. [A.J. Miller, G.L. Nemhauser, M.W.P. Savelsbergh, On the polyhedral structure of a multi-item production planning model with setup times, Mathematical Programming 94 (2003) 375–405] and Marchand and Wolsey [H. Marchand, L.A. Wolsey, The 0–1 knapsack problem with a single continuous variable, Mathematical Programming 85 (1999) 15–33] results. We also describe fast combinatorial separation algorithms for these new inequalities. We use them in a branch-and-cut framework to solve the problem. Some experimental results showing the effectiveness of the approach are reported.     

Learning and forgetting effects on a group scheduling problem

This paper proposes to investigate learning and forgetting effects on the problem of scheduling families of jobs on a single machine to minimize total completion time of jobs. A setup time is incurred whenever the single machine transfers job processing from a family to another family. To analyze the impact of learning and forgetting on this group scheduling problem, we structure three basic models and make some comparisons through computational experiments. The three models, including no forgetting, total forgetting and partial forgetting, assume that the processing time of a job is dependent on its position in a schedule. Some scheduling rules and a lower bound are derived in order to constitute our branch-and-bound algorithm for searching an optimal sequence. In addition, an efficient and simply-structured heuristic is also built to find a near-optimal schedule.     

Single-machine scheduling against due dates with past-sequence-dependent setup times

Recently Koulamas and Kyparisis [Koulamas, C., Kyparisis, G.J., in press. Single-machine scheduling with past-sequence-dependent setup times. European Journal of Operational Research] introduced past-sequence-dependent setup times to scheduling problems. This means that the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. Koulamas and Kyparisis [Koulamas, C., Kyparisis, G.J., in press. Single-machine scheduling with past-sequence-dependent setup times. European Journal of Operational Research] were able to show for a number of single-machine scheduling problems with completion time goals that they remain polynomially solvable. In this paper we extend the analysis to problems with due dates. We demonstrated that some problems remain polynomially solvable. However, for some other problems well-known polynomially solution approaches do not guarantee optimality any longer. Consequently we concentrated on finding polynomially solvable special cases.     

A hybrid two-stage transportation and batch scheduling problem

We study the coordinated scheduling problem of hybrid batch production on a single batching machine and two-stage transportation connecting the production, where there is a crane available in the first-stage transportation that transports jobs from the warehouse to the machine and there is a vehicle available in the second-stage transportation to deliver jobs from the machine to the customer. As the job to be carried out is big and heavy in the steel industry, it is reasonable assumed that both the crane and the vehicle have unit capacity. The batching machine processes a batch of jobs simultaneously. Each batch occur a setup cost. The objective is to minimize the sum of the makespan and the total setup cost. We prove that this problem is strongly NP-hard. A polynomial time algorithm is proposed for a case where the job transportation times are identical on the crane or the vehicle. An efficient heuristic algorithm for the general problem is constructed and its tight worst-case bound is analyzed. In order to further verify the performance of the proposed heuristics, we develop a lower bound on the optimal objective function. Computational experiments show that the heuristic algorithm performs well on randomly generated problem instances.     

The significance of reducing setup times/setup costs

Scheduling with setup times or setup costs plays a crucial role in todays modern manufacturing and service environments where reliable products/services are to be delivered on time. Scheduling activities profoundly depend on the times/costs required to prepare the facility for performing the activities. However, the vast majority of existing scheduling literature ignores this fact. We define and emphasize the importance, applications, and benefits of explicitly considering setup times/costs in scheduling research. Moreover, a review of the latest research on scheduling problems with setup times/costs is provided.     

Flow-shop scheduling with setup and assembly operations

A scheduling model for a production system including machining, setup and assembly operations is considered. Production of a number of single-item products is ordered. Each product is made by assembling a set of several different parts. First, the parts are manufactured in a flow-shop consisting of multiple machines. Then, they are assembled into products on a single assembly stage. Setup operation and setup time are needed when a machine starts processing the parts or it changes items. The operations are partitioned into several blocks. Each block consists of the machining operations, the setup operations, and the assembly operation(s) for one or several products. The parts of the same item in a block are processed successively. The objective function is the mean completion time for all products. We consider a problem to partition the operations into blocks and sequence the parts in each block so as to minimize the objective function. Solution procedures using pseudo-dynamic programming and a branch-and-bound method are proposed. Computational experiments are carried out to evaluate the performance of the solution procedures. It has been found that a good near-optimal schedule is obtained efficiently by the proposed solution procedures.     

Comments on “A bicriteria flowshop scheduling problem with setup times”

The aim of this paper is to point out that the integer programming model proposed by Eren and Güner [T. Eren, E. Güner, A bicriteria flowshop scheduling problem with setup times, Appl. Math. Comput. 183 (2006) 1292-1300] is incorrect. We propose a new integer programming model for the same scheduling problem based on their model.     

Controlling adverse effect on work in process inventory while reducing machine setup time

Earlier research has found that the presence of setup time variance can cause an adverse effect on waiting time and inventory as one reduces setup time for a product on a single machine that processes a number of products in a cyclic production system [Sarkar, D., Zangwill, W.I., 1991. Variance effects in cyclic production systems. Management Science 37 (4) 444–453; Zangwill, W.I., 1987. From EOQ towards ZI. Management Science 33 (10) 1209–1223]. This finding validates what other researchers had believed from a rather anecdotal perspective: “variability reduction” is extremely important for improving overall effectiveness of a pull or JIT system [Schonberger, Richard J., 1982. Japanese Manufacturing Techniques: Nine Hidden Lessons in Simplicity. The Free Press, New York]. In this paper, we offer explicit mathematical equations that characterize the variance levels in order to offer exact conditions under which WIP improves or worsens when one reduces setup time.     

A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times

We consider the problem of scheduling n independent jobs on m unrelated parallel machines with sequence-dependent setup times and availability dates for the machines and release dates for the jobs to minimize a regular additive cost function. In this work, we develop a new branch-and-price optimization algorithm for the solution of this general class of parallel machines scheduling problems. A new column generation accelerating method, termed “primal box”, and a specific branching variable selection rule that significantly reduces the number of explored nodes are proposed. The computational results show that the approach solves problems of large size to optimality within reasonable computational time.