Asia-Pacific Journal of Operational Research

Symmetrizing the Dai–Liao (DL) search direction matrix by a rank-one modification, we propose a one-parameter class of nonlinear conjugate gradient (CG) methods which includes the memoryless Broyden–Fletcher–Goldfarb–Shanno (MLBFGS) quasi-Newton updating formula. Then, conducting an eigenvalue analysis, we suggest two choices for the parameter of the proposed class of CG methods which simultaneously guarantee the descent property and well-conditioning of the search direction matrix. A global convergence analysis is made for uniformly convex objective functions. Computational experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. Results of numerical comparisons made by the Dolan–Moré performance profile show that proper choices for the mentioned parameter may lead to promising computational performances.

In this paper, we consider the problem of selecting the top $m$ systems when the number of alternative systems is very large. We propose a sequential procedure that consists of two stages to solve this problem. The procedure is a combination of the ordinal optimization (OO) technique and optimal computing budget allocation (OCBA) method. In the first stage, the OO is used to select a subset that overlaps with the set of actual best $k\%$ systems with high probability. Then in the second stage the optimal computing budget is used to select the top $m$ systems from the selected subset. The proposed procedure is tested on two numerical examples. The numerical tests show that the proposed procedure is able to select a subset of best systems with high probability and short simulation time.

The first-order and the second-order directional derivatives of singular values are used to characterize the tangent cone, the normal cone and the second-order tangent set of the epigraph of the nuclear norm of matrices. Based on the variational geometry of the epigraph, the no gap second-order optimality conditions for the optimization problem, whose constraint is defined by the matrix cone induced by the nuclear norm, are established.

An original online problem with decreasing profit growth rate is proposed to optimize the work hours of employees, named the online work-break problem (WBP). In this problem, the manager has to answer for an abstract worker when he should have a break for his work efficiency declines with the durative time of work period. The efficiency of the worker is presented by a work efficiency function $P(t)$ in the description of our problem. We present the online algorithms to solve the WBP based on linear estimation of $P(t)$ under two levels. Both the problems with single-period and dynamic multi-periods have 2-competitive online algorithms.

Digital revolution has resulted in a paradigm shift in the field of marketing with online advertising becoming increasingly popular as it offers the reach, range, scale and interactivity to organizations to influence their target customers. Moreover, web advertisement is the primary revenue stream for several websites that provide free services to internet users. The website management team needs to do a lot of planning and optimally schedule various advertisements (ads) to maximize revenue, taking care of advertisers’ needs under system constraints. In this paper, we have considered the case of news websites that provide news to its viewers for free with ads as the primary source of their revenue. The considered news website consists of many webpages with different banners for advertisement. Each banner consists of different number of partitions and cost per partition varies for different rectangular banners. Many ads compete with each other for their placement on a webpage on a specific banner, based on partition requirement, at specific time interval(s). Here, we have formulated a mixed integer 0–1 linear programming advertisement scheduling problem to maximize the revenue over planning horizon divided into time intervals under various system and technical constraints. A case is presented to show the applicability of the model. Branch and bound integer programming and goal programming techniques have been used to solve the formulated problem.

The set of anchor points is an important subset of the set of extreme efficient points of the production possibility set (PPS) in data envelopment analysis (DEA). In this paper, some new results, under variable returns to scale (VRS) assumption, are given which characterize these points from different points of view. First, we prove two necessary and sufficient conditions leading to geometrical characterizations. Afterwards, four sufficient conditions are given with respect to the level values of the supporting hyperplanes, infeasibility of the super efficiency models, maximum/minimum data, and zero data. Some of the given conditions can be checked without solving any mathematical programming problems. Also, some of them can be tested by solving standard DEA models. The investigated conditions are useful in designing pre-processors and heuristics.

In this paper, we investigate the retailer’s behavior under the supplier-driven semi-Stackelberg newsvendor situation in which (i) the supplier plays as a semi-Stackelberg leader with or without his discounts schedule being offered to the retailer, (ii) the retailer plays as a Stackelberg follower with or without her discounts schedule being offered to the end customer, and (iii) neither party has perfect information on the endogenous price-dependent demand function or exogenous probability distribution of demand. In this situation, the retailer’s concern is identifying the dominant strategy by which she can safely implement her own scheme for customer discounts regardless of the order quantity rather than finding the best strategy yielding the optimal order quantity that maximizes her expected profit. We show that a consistent dominance relationship exists among the retailer’s strategies when the newsvendor chooses to offer progressive multiple discounts to customers regardless of the supplier’s strategy of offering the retailer either all-units discounts or no-discounts.