Asia-Pacific Journal of Operational Research

This paper discusses casualty and medical group scheduling for disaster response in order to reduce casualities. First, triage levels and their stochastic transition, Markov Chain, are introduced to establish a function from treated time to probability of death. Then, job shop scheduling model and a genetic algorithm are designed. Finally, we performed a simulation experiment, partially using real data of 5.12 Wenchuan earthquakes for reference. The results show that the algorithm reduces number of mortalities stably and efficiently while considering disturbance events.

In this paper, we study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queuing system can be modeled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions. We present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modeled into a QBD process where the block elements of the generator matrix have finite dimensions. The sojourn time distributions of both high and low priority customers are obtained. Some managerial insights are given after comparing the discretionary priority rule with the preemptive and nonpreemptive disciplines numerically.

In this paper, zero-sum two-person finite undiscounted (limiting average) semi-Markov games (SMGs) are considered. We prove that the solutions of the game when both players are restricted to semi-Markov strategies are solutions for the original game. In addition, we show that if one player fixes a stationary strategy, then the other player can restrict himself in solving an undiscounted semi-Markov decision process associated with that stationary strategy. The undiscounted SMGs are also studied when the transition probabilities and the transition times are controlled by a fixed player in all states. If such games are unichain, we prove that the value and optimal stationary strategies of the players can be obtained from an optimal solution of a linear programming algorithm. We propose a realistic and generalized traveling inspection model that suitably fits into the class of one player control undiscounted unichain semi-Markov games.

In this paper, we consider a two-agent batch scheduling problem on a single machine such that the processing times of agent 1 and the due date of agent 2 in the same batch are identical. The objective is to minimize the total completion time of agent 1 with a constraint on the maximum tardiness of agent 2. First, we propose the optimality conditions. Then, we show that the problem is strongly NP-hard. Finally, we prove the problem remains NP-hard even for the case with one batch of agent 2, and develop a pseudo-polynomial algorithm and an approximation algorithm for this case.

This paper investigates a single-machine scheduling problem involving both the due-window assignment and position-dependent processing times under a group technology environment. By position-dependent processing times, we mean that the processing time of a job is dependent of its processing position in the job sequence within the group it belongs to. A setup time is incurred whenever the single machine transfers job processing from a group to another group. Each group is assigned an assignable common due-window. A job completed earlier (respectively, later) than the common due-window of the group it belongs to will incur an earliness (respectively, tardiness) penalty. The objective is to determine the optimal group sequence, the optimal job sequence, and the optimal due-window assignment so as to minimize the total cost including the earliness and tardiness (or weighted number of tardy jobs) penalties, black and the due-window starting time and due-window size costs. We show that both the problems can be solved in polynomial times.

We consider the problem of estimation and confidence interval construction of a Markovian controllable queueing system with unreliable server and constant retrial policy. For the fully observable system the standard parametric estimation technique is used. The arrived customer finding a free server either gets service immediately or joins a retrial queue. The customer at the head of the retrial queue is allowed to retry for service. When the server is busy, it is subject to breakdowns. In a failed state the server can be repaired with respect to the threshold policy: the repair starts when the number of customers in the system reaches a fixed threshold level. To obtain the estimates for the system parameters, performance measures and optimal threshold level we analyze the system in a stationary regime. The performance measures including average cost function for the given cost structure are presented in a closed matrix form.

This paper studies the online preemptive scheduling of equal-length intervals on a single machine with lookahead. Let $p$ be the length (processing time) of all intervals. In the problem, at every time point $t$, online algorithms can foresee all the intervals that will arrive in the time segment $(t,t+L)$ for a certain $L$. When $L=p$, Zheng et al. [Comput- ers & Operations Research, 2013] established a lower bound of $\sqrt{2}$ and provided an online algorithm with a competitive ratio of 3. In this paper, we provide for this problem an improved online algorithm with a competitive ratio of 2.

Scheduling multi-project is a complex decision making process. It involves the effective and timely allocation of resources to different projects. In the case of multi-project, resources are often transferred between the projects. It consumes both time and cost, when projects are situated in different geographic locations. As a result, the net present value (NPV) of multi-projects is significantly impacted by the resource transfer time. In this paper, a new genetic algorithm (GA) approach to the multi-project scheduling problem with resource transfer times is presented, where the NPV of all projects is maximized subject to renewable resource constraints. The paper also presents a heuristic approach using two phase priority rules for the same problem. We conduct a comprehensive analysis of 60 two-phase priority rules. The proposed GA approach is compared to the heuristic approach using the well-known priority rules. An extensive computational experiment is reported.

In this paper, We deal with the scheduling problems with simple linear deterioration function on unrelated parallel-machine and identical parallel-machine. We assume that all the jobs (tasks) are available at time zero, but all machines (processors) may not be available simultaneously at time zero. The objective functions are to minimize the total logarithm of completion time, the total logarithm of machine load, the total absolute differences in logarithm completion times and the total absolute differences in logarithm waiting times respectively. We provide the polynomial-time algorithms to solve the problems under the proposed model respectively.

The $n$-job and $m$-machine permutation flow shop scheduling problem with a proportional deterioration is considered in which all machines process the jobs in the same order, i.e., a permutation schedule. A proportional deterioration means that the job deterioration as an increasing function that is proportional to a linear function of time. The objective is to minimize the makespan, i.e., the maximum completion time. When some dominant relationships between $m-1$ machines can be satisfied, we show that some special cases of the problem can be polynomial solvable. For the general case, we also propose a heuristic algorithm and give the computational experiments.