Edward Yu-Hsien Lin

A Bibliographical Survey On Some Well-Known Non-Standard Knapsack Problems

AbstractKnapsack problem and its generalizations have been intensively studied during the last three decades with a rich literature of research reports. Over the years, surveys and reviews have been conducted mostly on the standard knapsack problems, namely, the single-constraint linear model. This paper reports the solution approaches developed for some non-standard knapsack problems with wide range of applications through a bibliographical review. The non-standard knapsack problems reviewed in this paper include the multidimensional knapsack problem, the multiple-choice knapsack problem, the 0–1 multiple knapsack problem, the quadratic knapsack problem, the maximin knapsack problem and the collapsing knapsack problem. Features of the solution approaches for each type of these non-standard knapsack problems and the computational experience as reported in the literature are summarized into several concise tables to provide a quick and broad reference for future researches.

On the calculation of true and pseudo penalties in multiple choice integer programming

Abstract The general solution approach leading to the global optimum for multiple choice integer programming uses the branch-and-bound procedure designed for special ordered sets. Incorporated in such a solution procedure, the partitioning strategy based on a weighted mean method is most often adopted to calculate the pseudo penalties on the partitioned subconstraints for branching and backtracking. Based on a reformulation and transformation technique, we show that the calculation of true penalties of these partitioned subconstraints can be performed efficiently.

Multiple choice programming: A state-of-the-art review

Abstract Multiple choice programming, originated from Healy Jr, belongs to the non-convex mathematical programming with special ordered sets of variables type 1 as identified by Beale and Tomlin. The high applicability of multiple choice programming in many decision-making problems has made it a focus of many OR researchers and practitioners in the fields of integer programming, and combinatorics. We report a survey on the structures of multiple choice programming problems and their solution approaches. Applications of multiple choice programming and some prospective future researches are also discussed.

Computational comparison on the partitioning strategies in multiple choice integer programming

Abstract In this paper we review the theoretical background of two partitioning strategies, the Weighted-Mean-Method (WMM) and the Reformulation-and-Transformation-Technique (RTT), incorporated in the special ordered set branch-and-bound procedures leading to the global optimum in Multiple Choice Integer Programming (MCIP). Procedure flow is developed with a numerical example presented to illustrate the effect of these two partitioning strategies in the algorithm. This procedure flow is then coded using IBM APL2. A total of 24 test problems are solved by this APL2 code for MCIP to analyze the performance of WMM and RTT in MCIP. The preliminary computational results indicate that, on the average, RTT produces smaller branching trees than does WMM. Its performance tends to be better for those MCIP problems having more multiple choice sets and a fewer average number of variables in each set. However, the average CPU time consumed by using RTT does not differ much from that consumed by using WMM.

The role of the activity adjacency matrix in the critical path method

This paper introduces the use of an activity adjacency matrix in the critical path method to avoid the confusion created by converting the project into its network representation, particularly in performing the cost time trade-offs. A set of APL code was developed to illustrate this point.

Implementing the recursive APL code for dynamic programming

Despite the importance and wide applicability of dynamic programming technique in optimization, the complexity and uniqueness of various dynamic programming models often make the comprehension of their solution procedures difficult, particularly for a novice. Although it can be argued that, unlike the Simplex method in linear programming, no general dynamic programming algorithm exists, with the recursive capability of APL, it is feasible to develop a “systematic” solution approach for deterministic dynamic programming. In this paper, we introduce a set of such APL code developed be solve various types of dynamic programming problems with minor modifications on some of its key functions to accommodate the nature of each type of dynamic programming problems.

Measuring Conditional Partial Expected Loss Under Uniformly Distributed Uncertain Timing

ABSTRACT This note extends the Initial partial-mean concept for present worth analysis of risk by Buck and Askin (1986) to a two random variable case where the magnitude of a single cash flow Is a random variable, and the time duration is a random variable with uniform distribution. This extension leads to the calculation of the expected magnitude of a project loss given that the loss occurs. Computational formulas and numerical Illustrations are presented.

An ARIMA model for Canadian Union membership growth, 1911–1985

An ARIMA (1, 1, 0) model for the Canadian union membership growth from 1911 to 1985 is introduced. Predictions for the period 1986–91 are made, and the actual figures for 1986–88 are compared to assess the predictability of the model. Diagnostic checks of the validity of this ARIMA model are also performed.

ON THE GLOBAL OPTIMUM OF THE NUMERICAL CONTROLLED PUNCH PRESS TOOL LOCATION AND HIT SEQUENCING PROBLEM

Abstract Walas and Askin developed a heuristic algorithm for the NC (Numerical Controlled) punch press tool location and hit sequencing problem. However, no exact algorithm to this problem has been discussed. This technical note pesents a different formulation of such problems which leads to an exact algorithm for a global optimum. Such an exact algorithm can be established based on the concept of minimum spanning 1-tree in network theory and Lagrangian relaxation

Multiple choice programming: an APL approach

In this paper, we introduce a set of APL code for the optimization in multiple choice programming using the special-ordered-set branch-and-bound procedure incorporating the partitioning strategy of weighted-mean method.