Asia-Pacific Journal of Operational Research

In this article, we generalize Lev and Weiss's (1990) finite horizon economic order quantity (EOQ) model with cost change to the inventory system with deterioration. Supplier announces some or all of cost parameters may change after a decided time. Depending on whether the inventory is depleted at the time of the last opportunity to purchase before some or all of the cost parameters may change, there are two types of inventory models to be discussed. The main objective of this paper is to identify the optimal ordering policy of the inventory system by comparing the minimum cost of the two types of models. We suggest a finite horizon EOQ model to combine the above two types and propose a theorem that can quickly identify the optimal policy of the suggested model. In considering temporary price discount problem and discrete-time EOQ problem, in general, there are integer operators in mathematical models, but our approach offers a closed-form solution to these kinds of problems. Numerical examples are presented to demonstrate the results of the proposed properties and theorem.

The aim of this note is to point out and correct some vital mistakes in the paper by P K Nayak and M Pal, "Linear programming technique to solve two person matrix (games with interval pay-offs). Asia-Pacific Journal of Operational Research, 26(2), 285–305". Lots of serious mistakes on the definitions, conclusions, models, methods, proofs and computing results have been corrected and modified in this note. We also indicate inappropriate formulations regarding their proposed linear programming models for solving generic matrix games with interval pay-offs and suggest a pair of linear programming models with any minimal acceptance degree of the interval inequality constraints which may be allowed to violate. The lexicographic method is suggested so that a rational and credible solution of the generic matrix game with interval pay-offs can be achieved.

Given a finite set of spheres of different sizes, we study the three-dimensional Strip Packing Problem (3D-SPP) as well as the three-dimensional Knapsack Problem (3D-KP). The 3D-SPP asks for a placement of all spheres within a cuboidal strip of fixed width and height so that the variable length of the cuboidal strip is minimized. The 3D-KP requires packing of a subset of the spheres in a given cuboid so that the wasted space is minimized. To solve these problems two greedy algorithms were developed which adapt the algorithms proposed by Huang et al. (2005) to the 3D case with some important enhancements. The resulting methods were tested using the instances provided by Stoyan et al. (2003). Additionally, two series of 12 instances each for the 3D-SPP and for the 3D-KP are introduced and results for these new instances are also reported.

Regularization method proposed by Scholtes (2011) has been a recognized approach for deterministic mathematical programs with complementarity constraints (MPCC). Meng and Xu (2006) applied the approach coupled with Monte Carlo techniques to solve a class of one stage stochastic MPCC and presented some promising numerical results. However, Meng and Xu have not presented any convergence analysis of the regularized sample approximation method. In this paper, we fill out this gap. Specifically, we consider a general class of one stage stochastic mathematical programs with complementarity constraint where the objective and constraint functions are expected values of random functions. We carry out extensive convergence analysis of the regularized sample average approximation problems including the convergence of statistical estimators of optimal solutions, C-stationary points, M-stationary points and B-stationary points as sample size increases and the regularization parameter tends to zero.

We consider two-agent scheduling on a single machine, where there are job families and setup requirements exist between these families. Each agent's objective function is to minimize his own makespan. One of our goals is to find the optimal solution for one agent with a constraint on the other agent's makespan (constrained optimization). This problem is equivalent to the caudate Knapsack problem that we define in the paper. The other goal is to find single nondominated schedules (i.e., such that a better schedule for one of the two agents necessarily result in a worse schedule of the other agent), and to enumerate all nondominated schedules. Finally, two special cases, one with equal job processing times and the other with equal family setups are studied. We prove that the constrained optimization problems in both cases can be solved in polynomial time and that the cases have a polynomial number of nondominated schedules.

Manufacturers of the TFT-LCD (Thin-Film Transistor Liquid-Crystal Display) panels in Taiwan face challenges from increasing competition and falling prices. Additionally, these manufacturers are heavily reliant on the reliability of their supply chains, making the choice of upstream suppliers a mission-critical issue in the industry. This study employs Operating Costs, Research and Development (R&D) Expenses, Net Fixed Assets, and Total Assets as input parameters to output Operating Revenue and Quality System Audit (QSA) Scores for the TFT-LCD industry in Taiwan. Traditional DEA models are used in the confirmation analyses, whereas the Grey System entropy weight method is applied to calculate the relative weights of the various parameters. The weighting results are included in the DEA as constraint weights to be substituted into the CCR-AR, SBM-AR, and Additive-AR models. The results are then compared to evaluate efficiency in terms of satisfying practical application needs. Finally, a case study based on a large TFT-LCD company in Taiwan is analyzed to provide insight into variations in Decision Making Units (DMUs) caused by the use of various models. The results are valuable in terms of optimizing the selection of an appropriate model to carry out future studies.

This paper examines the allocation of yard cranes and blocks for yard activities in container terminals. In this paper, the yard cranes are confined to rail mounted gantry cranes (RMGC), which are characterized by the restricted traveling range on a pair of rails. Since RMGCs and yard blocks are tightly bound to each other, when allocating them, we should make sure that the RMGCs allocated for a yard activity are able to together cover the blocks allocated for the corresponding yard activity. In addition, considering that there are four basic activities occurring in the yard which compete with each other for the scarce resources and have different requirements and priorities in the allocation of blocks and yard cranes, we treat them in a single model rather than in multiple independent models as were generally done in literature. A mixed integer programming model is constructed, and an iterative decomposition solution procedure is proposed for the problem. Based on the solution procedure, a decision support system is developed and implemented for a terminal in Tianjin seaport. Using the actual data, the numerical experiments show the effectiveness and efficiency of the decision support system.