Chung-Lun Li

Machine scheduling with deliveries to multiple customer locations

One important issue in production and logistics management is the coordination of activities between production and delivery. In this paper, we develop a single-machine scheduling model that incorporates routing decisions of a delivery vehicle which serves customers at different locations. The objective is to minimize the sum of job arrival times. The problem is NP-hard in the strong sense in general. We develop a polynomial time algorithm for the case when the number of customers is fixed. More efficient algorithms are developed for several special cases of the problem. In particular, an algorithm is developed for the single-customer case with a complexity lower than the existing ones.

Scheduling with multiple-job-on-one-processor pattern

Most scheduling literature considers a “one-job-on-one-processor” pattern, which assumes that a processor processes exactly one job at a time. In this paper we consider a new scheduling problem with a “multiple-job-on-one-processor” pattern, where several jobs can be processed by a single processor simultaneously, provided that the total size of the jobs being processed does not exceed the capacity of the processor at any point in time. This problem is motivated by the operation of berth allocation, which is to allocate vessels (jobs) to a berth (processor), where the vessels, if small in dimension, may share the berth with some other vessels for loading/unloading the goods. We consider the problem to minimize the makespan of the schedule. The well-known First-Fit Decreasing heuristic is generalized and applied to several variations of the problem, and the worst-case behavior of the generalized heuristics is studied. Worst-case error bounds are obtained for those models. Computational experiments are cond...

Scheduling with agreeable release times and due dates on a batch processing machine

Abstract We consider the problem of scheduling semiconductor burn-in operations, where burn-in ovens are modeled as batch processing machines. The job release times and due dates are assumed to be agreeable. Two different objective functions are considered: minimize the maximum tardiness and minimize the number of tardy jobs. We study the complexity of the problems. Efficient algorithms are also provided for the case when the job release times, due dates, and processing times are agreeable, which generalize those provided by Lee, Uzsoy and Martin-Vega (1992).

On the Distance Constrained Vehicle Routing Problem

We analyze the vehicle routing problem with constraints on the total distance traveled by each vehicle. Two objective functions are considered: minimize the total distance traveled by vehicles and minimize the number of vehicles used. We demonstrate a close relationship between the optimal solutions for the two objective functions and perform a worst case analysis for a class of heuristics. We present a heuristic that provides a good worst case result when the number of vehicles used is relatively small.

Finding disjoint paths with different path-costs: Complexity and algorithms

Consider a network G = (V,E) with distinguished vertices s and t, and with k different costs on every edge. We consider the problem of finding k disjoint paths from s to t such that the total cost of the paths is minimized, where the j th edge-cost is associated with the j th path. The problem has several variants: The paths may be vertex-disjoint or arcdisjoint and the network may be directed or undirected. We show that all four versions of the problem are strongly NP-complete even for k = 2. We describe polynomial time heuristics for the problem and a polynomial time algorithm for the acyclic directed case.

Two-echelon spare parts inventory system subject to a service constraint

In this paper, we consider a spare parts inventory problem faced by a manufacturer of electronic machines with expensive parts that are located at various customer locations. The parts fail infrequently according to a Poisson process. To serve customers when a failure occurs, the manufacturer operates a central warehouse and many field depots that stock spare parts. The central warehouse acts as a repair facility and replenishes stock at the field depots. There is a centralized decision-maker who manages the inventory in both the central warehouse and the field depots. We develop a continuous review, base stock policy for this two-echelon, multi-item spare parts inventory system. We formulate a model to minimize the system-wide inventory cost subject to a response time constraint at each field depot. We present an efficient heuristic algorithm and study its computational effectiveness.

Berth allocation with time-dependent physical limitations on vessels

We consider a berth allocation problem in container terminals in which the assignment of vessels to berths is limited by water depth and tidal condition. We model the problem as a parallel-machine scheduling problem with inclusive processing set restrictions, where the time horizon is divided into two periods and the processing sets in these two periods are different. We consider both the static and dynamic cases of the problem. In the static case all of the vessels are ready for service at time zero, while in the dynamic case the vessels may have nonzero arrival times. We analyze the computational complexity and develop efficient heuristics for these two cases. Computational experiments are performed to test the effectiveness of the heuristics and to evaluate the benefits of taking tidal condition into consideration when making berth allocation decisions.

Scheduling with subcontracting options

Motivated by a problem commonly faced by time-sensitive product manufacturers, an analytical model to study the joint decisions of subcontracting and detailed job scheduling is proposed. In the proposed model, a manufacturer operates in a make-to-order fashion and receives a set of orders from its customers at the beginning of the planning horizon. The orders can be either processed by the manufacturer in-house or subcontracted to one of several available subcontractors, possibly at a higher cost. The manufacturer needs to determine which orders should be produced in-house and which orders should be subcontracted. Furthermore, it needs to determine a production schedule for the orders to be produced in-house. The objective is to minimize the total production and subcontracting cost, subject to a constraint on the maximum completion time of the orders. We analyze the computational complexity of the model, develop a heuristic for solving it and analyze worst-case and asymptotic performances of the heuristic. We also study the value of subcontracting by comparing our model and a model where no subcontracting option is available to the manufacturer. Computational results demonstrate that the subcontracting option gives the manufacturer a significant performance improvement. Related managerial insights are also provided.

Dynamic Lot Sizing with Batch Ordering and Truckload Discounts

This paper studies two important variants of the dynamic economic lot-sizing problem that are applicable to a wide range of real-world situations. In the first model, production in each time period is restricted to a multiple of a constant batch size, where backlogging is allowed and all cost parameters are time varying. Several properties of the optimal solution are discussed. Based on these properties, an efficient dynamic programming algorithm is developed. The efficiency of the dynamic program is further improved through the use of Monge matrices. Using the results developed for the first model, an O(n3log n) algorithm is developed to solve the second model, which has a general form of product acquisition cost structure, including a fixed charge for each acquisition, a variable unit production cost, and a freight cost with a truckload discount. This algorithm can also be used to solve a more general problem with concave cost functions.

The parallel machine min-max weighted absolute lateness scheduling problem

Given a set of jobs, a processing time and a weight for each job, several parallel and identical machines, and a common due date that is not too early to constrain the scheduling decision, we want to find an optimal job schedule so as to minimize the maximum weighted absolute lateness. We show that this problem is NP-complete even for the single-machine case, and is strongly NP-complete for the general case. We present a polynomial time heuristic for this problem and analyze its worst-case performance. Empirical testing of the heuristic is reported, and the results suggest that the performance is asymptotically optimal as the number of jobs tends to infinity.