Asia-Pacific Journal of Operational Research

This paper describes an algorithm for producing visually attractive and operationally robust solutions to a real-life vehicle routing problem with time windows. Visually attractive and operationally robust solutions are usually synonymous with compact, nonoverlapping routes with little or no intra-route cross over. The visual attractiveness of routes, for practical routing applications, is often of paramount importance.

We present a two phase solution approach. The first phase is inspired by the sequential insertion algorithm of Solomon (1987) and includes a range of novel enhancements to ensure visually attractive solutions are produced in the face of a range of nonstandard real-life constraints: A constrained and heterogeneous vehicle fleet; tight time windows and banned delivery windows; multiple route capacity measures; driver breaks; minimum route volumes; vehicle-location compatibility rules; nonreturn to base routes; peak hour traveling times; vehicle type dependent service times; and replenishment back at the depot. The second phase is based on the guided local search algorithm of Kilby et al. (1999). It uses an augmented objective function designed to seek solutions which strike a balance between minimizing traditional cost measures, whilst maximizing the visual attractiveness of the solution.

Our two phase solution approach is particularly adept at producing solutions that both aggressively minimize the total number of routes, a feature that we believe has been missing in algorithms presented in equivalent literature, as well as minimizing traditional cost measures whilst delivering a very high degree of visual attractiveness.

The algorithm presented has been successfully implemented and deployed for the real-life, daily beverage distribution problem of Schweppes Australia Pty. Ltd. for a range of capital cities throughout Australia.

This paper considers the empty container repositioning problem in an on-line scheduling setting. This optimization problem arising from container transportation management aims to balance empty containers distribution among transportation sites so as to minimize the total operating cost of loaded container shipping, empty container allocation and leasing. In this highly uncertain on-line environment we introduce a heuristic that does not attempt to balance the empty container distribution, and evaluate its competitive performance mathematically and empirically.

We address the nonresumable version of the scheduling problem with proportionally deteriorating jobs on a single machine subject to availability constraints. The objective is to minimize the total weighted completion time. We show that there exists no polynomial-time algorithm with a constant worst-case ratio for the problem with two nonavailability intervals unless . Furthermore, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for the problem with a single nonavailability interval.

In this paper, we consider a semi-on-line scheduling problem of two identical machines with common maintenance time interval and nonresumable availability. We prove a lower bound of 2.79129 on the competitive ratio and give an on-line algorithm with competitive ratio 2.79633 for this problem.

This paper presents a trust region subspace method for minimizing large-scale unconstrained problems. We choose a subspace that consists of some old directions which are invariable and some newest directions which are changed at each iteration. A restart technique is used when the old directions have little contribution. Numerical results are reported which indicate that the method is promising.

Recently Leleu [A linear programming framework for free disposal hull (FDH) technologies and cost functions: Primal and dual models] presented a linear model for assessing the FDH-cost function with various returns to scale assumptions. He stated that economic inefficiency can be computed as the ratio of the observed cost to the minimum cost and, as usual, the allocative inefficiency is computed as the ratio between the economic and the technical inefficiencies. In this paper, we propose a modified model with various returns to scale assumptions that has fewer constraints and variables than Leleu's model and obtains the FDH-cost efficiency directly. Reducing nm constraints and nm variables, where n is the number of DMUs and m is the number of inputs, leads to the computational advantage of our model over that of Leleu.

Offering warranty for a second-hand item stimulates the sales of the item, but at the same time, it accumulates additional warranty servicing cost. This additional cost can be reduced through actions that improve the reliability of the item, such as overhaul and upgrade. An upgrade action brings the second-hand item to an improved functional state and it effectively reduces the age of the item. In this paper, we propose a model aiming to determine the optimal upgrade action strategies that achieve a sensible trade-off between the cost of an upgrade action and the reduction of the expected warranty cost due to this action. A practical application case on electric drills is used to illustrate our findings.

Lifetime warranties are becoming more popular as these types of warranties provide assurance for a longer reliable service life, protection of customers against poor quality and the potential high cost of failure occurring during the long uncertain life of products. Chattopadhyay and Rahman (2008) proposed taxonomy for Lifetime warranty policies and developed cost models for Free rectification lifetime warranty (FRLTW) policies. In line with Chattopadhyay and Rahman, in this paper, stochastic models for two most potential and currently practiced Cost sharing lifetime warranty (CSLTW) policies, Specific parts excluded lifetime warranty and Limit on individual cost lifetime warranty have been developed to estimate the customers' and manufacturers' costs. The developed models capture the uncertainties of lifetime warranty coverage period and implication in offering such warranties on both manufacturer and customers. The developed models are analyzed using illustrative examples considering products with time-dependent failures.