Jinwen Ou

Order acceptance and scheduling with machine availability constraints

We consider an order acceptance and scheduling model with machine availability constraints. The manufacturer (machine) is assumed to be available to process orders only within a number of discontinuous time intervals. To capture the real-life behavior of a typical manufacturer who has restrictions of time availability to process orders, our model allows the manufacturer to reject or outsource some of the orders. When an order is rejected or outsourced, an order-dependent cost of penalty will occur. The objective is to minimize the makespan of all accepted orders plus the total penalty of all rejected/outsourced orders. We study the approximability of the model and some of its important special cases.

Parallel machine scheduling with multiple unloading servers

We study a parallel machine scheduling problem with multiple unloading servers. After a machine completes processing one job, an unloading server is needed to remove the job from the machine. Only after unloading, the machine is available for processing the next job. The model is motivated by the milk run operations of a logistics company that faces limited unloading docks at the warehouse. Our interest is to minimize the total completion time of the jobs. We show that the shortest-processing-time-first (SPT) algorithm has a worst-case bound of 2. We also develop other improved heuristic algorithms as well as a branch-and-bound algorithm to solve the problem. Computational experiments show that our algorithms are efficient and effective.

An improved heuristic for parallel machine scheduling with rejection

In this paper we study a classical parallel machine scheduling model with m machines and n jobs, where each job is either accepted and then processed by one of the machines, or rejected and then a rejection penalty is paid. The objective is to minimize the completion time of the last accepted job plus the total penalty of all rejected jobs. The scheduling problem is known to be NP-hard in the strong sense. We find some new optimal properties and develop an O(nlog n + n/e) heuristic to solve the problem with a worst-case bound of 1.5 + e, where e > 0 can be any small given constant. This improves upon the worst-case bound 2−1m of the heuristic presented by Bartal et al. (Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., & Stougie, L. (2000). Multiprocessor scheduling with rejection. SIAM Journal on Discrete Mathematics, 13, 64–78) in the scheduling literature.

Faster algorithms for single machine scheduling with release dates and rejection

We consider the single machine scheduling problem with release dates and job rejection with an objective of minimizing the makespan of the job schedule plus the total rejection penalty of the rejected jobs. Zhang et al. 6 have presented a 2-approximation algorithm with an O ( n 2 ) complexity for this problem and an exact algorithm with an O ( n 3 ) complexity for the special case with identical job processing times. In this note, we show that the 2-approximation algorithm developed by Zhang et al. 6 can be implemented in O ( n log ? n ) time. We also develop a new exact algorithm with an improved complexity of O ( n 2 log ? n ) for the special case with identical job processing times. The second algorithm can be easily extended to solve the parallel-machine case with the same running time complexity, which answers an open question recently raised by Zhang and Lu 5. We study a single machine scheduling problem with release dates and job rejection.An improved implementation of a 2-approximation algorithm is developed.An improved algorithm is provided for the case with identical job processing times.

Improved exact algorithms to economic lot-sizing with piecewise linear production costs

In this article we study a classical single-item economic lot-sizing problem, where production cost functions are assumed to be piecewise linear. The lot-sizing problem is fundamental in lot-sizing research, and it is applicable to a wide range of production planning models. The intractability of the problem is related to the value of m, the number of different breakpoints of the production cost functions. When m is arbitrary, the problem is known to be NP-hard (Florian, Lenstra & Rinnooy Kan, 1980). However, if m is fixed, then it can be solved in polynomial time (Koca, Yaman & Akturk, 2014). So far, the most efficient algorithm to solve the problem has a complexity of O(T2m+3), where T is the number of periods in the planning horizon (Koca et al., 2014). In this article we present an improved exact algorithm for solving the problem, where the complexity is reduced to O(Tm+2·logT). As such it also improves upon the computational efficiency of solving some existing lot-sizing problems which are important special cases of our model. In order to achieve a more efficient implementation, our algorithm makes use of a specific data structure, named range minimum query (RMQ).

Bicriteria order acceptance and scheduling with consideration of fill rate

In this paper, we study bicriteria order acceptance and scheduling with consideration of fill rate in a parallel-machine environment. In our scheduling model, either the number of orders being rejected, or the total processing time of the orders being rejected, is not allowed to be greater than a given value, so that a specific constraint of order fill rate is satisfied. We present efficient approximation algorithms with a performance ratio arbitrarily approaching 4/3.

Production lot-sizing with dynamic capacity adjustment

Abstract In this paper we study a single-item lot-sizing model in which production capacity can be adjusted from time to time. There are a number of different production capacity levels available to be acquired in each period, where each capacity level is assumed to be a multiple of a base capacity unit. To reduce the waste of excess of capacity but guarantee meeting the demand, it is important to decide which level of capacity should be acquired and how many units of the item should be produced for every period in the planning horizon. Capacity adjustment cost incurs when capacity acquired in the current period differs from the one acquired in the previous period. Capacity acquisition costs, capacity adjustment costs, and production costs in each period are all time-varying and depend on the capacity level acquired in that period. Backlogging is allowed. Both production costs and inventory costs are assumed to be general concave. We provide optimal properties and develop an efficient exact algorithm for the general model. For the special cases with zero capacity adjustment costs or fixed-plus-linear production costs, we present a faster exact algorithm. Computational experiments show that our algorithm is able to solve medium-size instances for the general model in a few seconds, and that cost can be reduced significantly through flexible capacity adjustment.