Ming-Zheng Wang

Single-machine scheduling with nonlinear deterioration

In this paper, we consider the single-machine scheduling problems with nonlinear deterioration. By the nonlinear deterioration effect, we mean that the processing times of jobs are nonlinear functions of their starting times. We show that even with the introduction of nonlinear deterioration to job processing times, single machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm utilizing the V-shaped property is proposed, and computational experiments show that it performs effectively and efficiently in obtaining near-optimal solutions.

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of −1 < a < 0, where a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.

Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects

A real industrial production phenomenon, referred to as learning effects, has drawn increasing attention. However, most research on this issue considers only single machine problems. Motivated by this limitation, this paper considers flow shop scheduling problems with a general position-dependent learning effects. By the general position-dependent learning effects, we mean that the actual processing time of a job is defined by a general non-increasing function of its scheduled position. The objective is to minimize one of the five regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems. We also analyze the worst-case bound of our heuristic algorithms.

Minimizing makespan in three-machine flow shops with deteriorating jobs

In this paper, a three-machine permutation flow shop scheduling problem with time-dependent processing times is considered. By the time-dependent processing times we mean that the jobs processing time is an increasing function of its starting time. The objective is to find a sequence that minimizes the makespan. This problem is well known to be NP-hard. Several dominance properties and a lower bound are derived to speed up the elimination process of a branch-and-bound algorithm. Moreover, two heuristic algorithms are proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational experiments on randomly generated problems are conducted to evaluate the branch-and-bound algorithm and heuristic algorithm. Computational results show that the proposed heuristic algorithm M-NEH perform effectively and efficiently.

The Effect of Lead Time and Demand Uncertainties in (r, q) Inventory Systems

We study a single-item (r, q) inventory system, where r is the reorder point and q is the order quantity. The demand is a compound-Poisson process. We investigate the behavior of the optimal policy parameters and the long-run average cost of the system in response to stochastically shorter or less-variable lead times. We show that although some of the properties of the base-stock system can be extended to this more general model, some cannot. The same findings also apply when the comparison is conducted on the lead-time demand distributions.

Single-machine scheduling to minimize total convex resource consumption with a constraint on total weighted flow time

In this paper, we consider single-machine scheduling problem in which processing time of a job is described by a convex decreasing resource consumption function. The objective is to minimize the total amount of resource consumed subject to a constraint on total weighted flow time. The optimal resource allocation is obtained for any arbitrary job sequence. The computational complexity of the general problem remains an open question, but we present and analyze some special cases that are solvable by using polynomial time algorithms. For the general problem, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm proposed to solve the problem. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions. The results show that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%. Highlights? Problem with convex resource dependent processing times is modeled and studied. ? A branch-and-bound algorithm and a heuristic algorithm were proposed. ? Experimental results show that the proposed algorithms run very efficiently.

Parallel machines scheduling with deteriorating and learning effects

In this paper parallel identical machines scheduling problems with deteriorating jobs and learning effects are considered. In this model, job processing times are defined by functions of their starting times and positions in the sequence. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. We show that the problems remain polynomially solvable under the proposed model.

SCHEDULING JOBS WITH PROCESSING TIMES DEPENDENT ON POSITION, STARTING TIME, AND ALLOTTED RESOURCE

We consider single-machine scheduling problem in which the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total resource cost. The problem is modeled as an assignment problem, and thus can be solved in polynomial time. Some extensions of the problem are also shown.

Effects of Carbon Emission Taxes on Transportation Mode Selections and Social Welfare

In this paper, we analyze how carbon emissions affect the selection of transportation modes and social welfare by using a two-stage Stackelberg gaming model. Based on this model, the governments optimal carbon-emission tax scheme and the companys optimal transportation mode and production decisions are explored. We find that: 1) whether or not the transport carbon-emission tax can increase social welfare depends on the relationships among the social cost of carbon (SCC), the transportation mode shifting threshold (TMST), and the biggest carbon-emission tax that a company can afford (BCRA); 2) a greater SCC implies a higher probability of improving social welfare via imposing transportation carbon-emission tax; and 3) a smaller TMST or BCRA yields a higher probability of improving social welfare when a carbon-emission tax is imposed. Further study shows that imposing a carbon-emission tax on the product with a higher production cost, a bigger product volume, or a bigger product density can increase the probability of improving social welfare.

On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L♮-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.