Asia-Pacific Journal of Operational Research

The Lanchester Model has been widely used to explain the main features of the battle. However, its application to actual cases seems to be limited. The purpose of this study is to attempt to extend the Lanchester Model with the System Dynamics approach in order to better suit the real modern AirLand Battle case. To demonstrate how the AirLand Battle System Dynamics model works and how it provides easier ways to account for variables, normally present in real combat situations, three common tactical scenarios are employed for simulation. The results indicate that the developed model can fully describe AirLand Battle and reflect the synergy that results from the interaction of strategies and force redeployment. The proposed model, in addition, allows users to easily adjust settings when simulating different scenarios.

We focus on rating of non-life insurance contracts. We employ multiplicative models with basic premium levels and specific surcharge coefficients for various levels of selected risk/rating factors. We use generalized linear models (GLM) to describe the probability distribution of total losses for a contract during one year. We show that the traditional frequency–severity approaches based only on GLM with logarithmic link function can lead to estimates which do not fulfill business requirements. For example, a maximal surcharge and monotonicity of coefficient can be desirable. Moreover, our approach can handle total losses, which are based on arbitrary loss distributions, possibly decomposed into several classes, e.g., small and large or property and bodily injury. Various costs and loadings can be also incorporated into the tariff rates. We propose optimization problems for rate estimation which enable hedging against expected losses and taking into account a prescribed loss ratio and other business requirements. Moreover, we introduce stochastic programming problems with reliability type constraints which take into account individual risk of each rate cell or collective risk. In the numerical study, we apply the approaches to Motor Third Party Liability (MTPL) policies.

In this paper, a modified non-monotone BFGS (MNBFGS) method for non-convex unconstrained optimization is proposed. Under some mild conditions, the global convergence of the given method is established, when the objective function is non-convex. Preliminary numerical comparisons, which show the proposed method is competitive, are also reported.

Many authors have used continuous optimization models for class-based storage allocation for unit load warehouses employing AS/RS system assuming the same setup to holding cost ratio for all products in their EOQ inventory policy. Accordingly, an ABC curve based on demand ordering of products is used to determine pallet turnovers in their travel distance models which is not applicable in many practical situations and can be inaccurate. This paper develops a new model to determine two/three class optimal partitions while relaxing assumption of constant setup to holding cost ratio in the EOQ formula and as a consequence uses an ABC curve based on decreasing ranking of product turnovers rather than that based on demand. Computational experience shows that this new continuous model approximates pick travel distances which are very close to as compared to that of a semi-discrete model (SDM) proposed in this paper. Further computational experiments are also provided comparing traditional models with our formulations.

We consider a supply chain consisting of a retailer and a supplier, which is influenced by e-business market. To control the uncertainty in demand, the retailer can purchase futures or options from the supplier. Futures or options can be exercised by the retailer to replenish inventory in the season. Moreover, redundant futures or options might be traded in the e-business market. The retailer's equilibrium ordering decision and the supplier's equilibrium pricing decision are analyzed under each kind of contracts. In addition, a comparison of futures and options is also presented and the conditions under which futures (or options) are superior are also identified. Our research shows that both the supplier and the retailer can be better off comparing with the newsvendor cases by using the two contracts. Furthermore, due to superior flexibility of the options, channel coordination can be achieved by using options. However, more cost needs to be paid to replenish by options, which may hurt the retailer. Hence, if the cost of replenishing by options is not overly high, the options are recommended to use; otherwise, the futures are recommended to choose.

We consider a single-machine common due-window assignment scheduling problem, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, window size, earliness, and tardiness. For two different processing time functions, we provide a polynomial time algorithm to find the optimal job sequence and resource allocation, respectively.

This paper considers single machine scheduling with an availability constraint and rejection. It is assumed that the machine is not available for processing during a given time interval. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the weighted total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. For this NP-hard problem, we present a pseudo-polynomial dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS).

Batch processing machine scheduling in uncertain environment attracts more and more attention in the last decade. This paper deals with semi-online scheduling on two parallel batch processing machines with non-decreasing processing time of job. Jobs arrive over time in the online paradigm, and the processing time of any batch is equal to the length of the last arrival job in the batch. We study the unbounded model where each processing batch may contain an unlimited number of jobs, and the objective is to minimize the makespan. Given any job J_j together with its following job J_j+1, it is assumed that their processing times satisfy p_j+1 ≥ αp_j where α ≥ 1 is a constant. That is, jobs arrive in a non-decreasing order of processing times. We mainly propose an optimal ϕ-competitive online algorithm where ϕ ≥ 1 is a solution of equation ϕ³ + (α-1)ϕ² + (α² - α - 1)ϕ - α² = 0.

We study a preemptive scheduling problem on two identical parallel machines that share a common server. Each job has to be loaded by the server before being processed on one of the machines and unloaded by the server after its processing. The loading and unloading times are both equal to one time unit. The goal is to minimize the makespan. We propose a O(n log n) solution algorithm for the preemptive variant of the problem.

This paper considers a new scheduling model in which both two-agents and a time-dependent deterioration exist simultaneously. By the time-dependent deterioration, it means that the actual processing time of a job belonging to the two-agents is defined as a non-decreasing linear function of its starting time. Two-agents compete to perform their respective jobs on a common single-machine and each agent has his own criterion to be optimized. The aim is to focus on minimizing total (weighted) earliness cost of one agent, subject to an upper bound on the maximum earliness cost of the other agent. The main contribution of this paper is to propose the optimal properties and present the complexity results for the problems addressed here.