Asia-Pacific Journal of Operational Research

This work investigates an unrelated parallel machine scheduling problem in the shared manufacturing environment. Based on practical production complexity, five job and machine-related factors, including job splitting, setup time, learning effect, processing cost and machine eligibility constraint, are integrated into the considered problem. Parallel machines with uniform speed but non-identical processing capabilities are shared on a sharing service platform, and jobs with different types can only be processed by the machines with matching eligibilities. The platform pays an amount of processing cost for using any machine to process the jobs. To balance the processing cost paid and the satisfaction of customers, we aim to minimize the weighted sum of total processing cost and total completion time of jobs in the considered problem. We establish a mixed integer linear programming model, and provide a lower bound by relaxing the machine eligibility constraint. The CPLEX solver is employed to generate optimal solutions for small-scale instances. For large-scale instances, we propose an efficient heuristic algorithm. Experimental results demonstrate that for various instance settings, the proposed algorithm can always produce near optimal solutions. We further present several managerial insights for the shared manufacturing platform.

Multi-attribute decision-making (MADM) methods are widely used by decision makers as decision support tools. Most MADM methods have shortcomings in the solution process that combined with other decision making methods can eliminate these shortcomings or improve the performance of the method. One of the methods that can be used to improve MADM methods is preferential voting, which is actually a linear programming (LP) model with weight restrictions. The Kemeny Median Indicator Ranks Accordance (KEMIRA) is one of the most modern MADM methods; in this paper, we provide an improved version in this relative, by utilizing the concept of preferential voting. The new model, in being implemented on a real-world problem, will be compared to the previous method and ultimately some of its advantages will be rendered.

In this paper, we study a single machine scheduling problem with group-dependent due window assignment and further incorporate autonomous and induced learning effects. Here, autonomous learning refers to learning by doing, while induced learning denotes that proactive investments can promote the learning effect, i.e., the learning effect is controllable. The proactive spending could include any management efforts like professional training programs, among others. The objective is to find optimal strategies of due window assignments, sequence of groups and jobs, and level of induced learning that optimize the total cost comprising the due window-related penalty costs and the investment cost. We present a polynomial-time algorithm capable of solving this problem and an improved idea to further reduce the time complexity. In addition, a detailed numerical example is conducted. Our study shows that the learning effect can be tuned to fit the demand of the manufacturing system better and lead to a more flexible operating system.

This paper studies a novel form of last-mile delivery that combines delivery optimization of E-commerce and Online-to-Offline (O2O) parcels. While O2O parcels must first be picked up from O2O shops before being delivered to the appropriate customers, E-commerce parcels are delivered to customers from a predetermined number of depots. The goal is to use the same fleet of vehicles to provide integrated delivery services for various merchant types. We propose a branch-and-price algorithm based on the set partitioning formulation, where the pricing problem is solved by a label-setting algorithm. Several acceleration techniques including elementary path relaxation, ng-path relaxation and decremental space search are designed to speed up the price problem. Both the conventional dataset used in the literature and a real-world database with up to 75 clients are utilized to test the performance of the suggested method, demonstrating its efficacy.

In this note, we establish sufficient optimality conditions in terms of upper convexificators for a robust multiobjective optimization problem (UCP) involving nonsmooth/nonconvex real-valued functions. For this purpose, two kinds of generalized convex functions are defined in terms of upper convexificators.

In this paper, we seek to provide real-time replenishment policy for a capacitated company that faces an exogenous demand and has to procure and store sufficient quantities of certain items with uncertain procurement prices. The objective is to minimize the total cost of the procuring cost and inventory holding cost without stock out. Motivated by the fact that a large variability in the price process often makes forecasting difficult, in contrast to the traditional approaches of the stochastic inventory theory, we study this problem from the perspective of competitive analysis who is free of any price distribution assumption. We propose an online replenishment model, which generalizes several previous online models. We give a real-time replenishment policy whose decisions are made based entirely on the past and present prices and the current inventory level. We prove that our policy achieves superior performance, and outperforms all of the previous theoretical results. Furthermore, we present the numerical studies to show that our replenishment policy achieves an even better empirical performance.

In this paper, we construct an implementable augmented Lagrangian method to solve second-order cone constrained variational inequalities (SOCCVI) problem. By considering a special optimization problem that has the same solution as the SOCCVI problem, we obtain different equivalent transformation forms of the SOCCVI problem. Using the equivalent transformation forms and the properties of the projection operators, the augmented Lagrangian method can be established and its global convergence is proved. The inexact Newton method is used to solve the inner problems which arise from the augmented Lagrangian method for solving the numerical examples. Numerical results for three examples are reported to verify the effectiveness of the augmented Lagrangian method for obtaining approximate solutions.

In this paper, we study optimal procurement policies with advance contracting option over a finite multi-period horizon for a seasonal product. In this setting, each period is defined by the time between two consecutive inventory replenishment stages where demand is not stationary across periods. Demand for the product in each period is stochastic whose probabilistic distribution is a function of the market signal received right before the beginning of the selling season. The firm receives price discounts by making quantity contracts in advance of the selling season and thus, before the realization of the market signal. Replenishment costs vary across periods during the selling season. We investigate optimal combination of advance contracting and expedited replenishment policies using stochastic dynamic programming. Our research is primarily motivated by applications in the cruise line industry where contracts are made before the final number of bookings is realized and additional purchases can be made at ports of call with varying local prices. Our results show that optimal replenishment policies follow order-up-to policies and there is a unique advance contract amount that minimizes the expected costs over the planning horizon. We provide a numerical sensitivity analysis to investigate the effects of replenishment prices, demand volatility, and disparity between periods in terms of demand on the advance contract amount, replenishments from the spot markets, service levels, and the overall expected cost.

In this paper, we seek analytically checkable necessary and sufficient condition for copositivity of a three-dimensional symmetric tensor. We first show that for a general third-order three-dimensional symmetric tensor, checking copositivity is equivalent to solving a quartic equation and some quadratic equations. All of them can be solved analytically. Thus, we present an analytical way to check copositivity of a third-order three-dimensional symmetric tensor. Then, we consider a model of vacuum stability for ${\mathbb{Z}}_3$ scalar dark matter. This is a special fourth-order three-dimensional symmetric tensor. We show that an analytically expressed necessary and sufficient condition for this model bounded from below can be given, by using a result given by Ulrich and Watson in 1994.

The classical reverse 1-median problem on trees is to adjust the edge lengths within a budget so as to reduce the 1-median function at a predetermined vertex as much as possible. This paper concerns the corresponding problem with uncertain vertex weights presented by linear functions. Moreover, we use the minmax regret criterion to measure the maximum loss of a feasible solution with respect to the worst-case scenario. The regarding problem is called the minmax regret reverse 1-median problem on trees. We first partition the set of scenarios into parts such that the optimal solution of the corresponding reverse 1-median problem does not change in each part. Then the problem can be reformulated as the minimization of a quadratic number of affine linear functions. We finally develop a greedy algorithm that solves the problem in $O(n^3)$ time where n is the number of vertices in the underlying tree.

In this paper, we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting, these distances may be cut off at a given value $C>0$, and we allow for the option of an empty solution at a fixed cost $C^{\prime }$. We analyze under which circumstances these problems can be reduced to the simpler Weber problem, and also when we definitely have to solve the more complex problem with cutoff.

We furthermore present adaptions of the algorithm of Drezner, Mehrez and Wesolowsky (1991 [The facility location problem with limited distances. Transportation Science, 25(3), 183–187, INFORMS]) to our setting, which in certain situations are able to substantially reduce computation times as demonstrated in a simulation study. The sensitivity with respect to the cutoff value is also studied, which allows us to provide an algorithm that efficiently solves the problem simultaneously for all $C>0$.

In an effort to make modification on the classical Polak–Ribière–Polyak method, Wei et al. suggested an efficient nonlinear conjugate gradient method which possesses the sufficient descent property when the line search fulfills the strong Wolfe conditions (by restricting the line search parameters). Here, we develop a three-term extension of the method which satisfies the sufficient descent condition independent of the line search. Also, under a backtracking Armijo-type line search, we establish global convergence of the method without convexity assumption. Using a scalar approximation of the Hessian of the objective function, we suggest an acceleration scheme that can be used in the iterative line search methods of unconstrained optimization. At last, practical merits of the proposed method are investigated by numerical experiments on a set of CUTEr test functions as well as the well-known image restoration problem. The results show numerical efficiency of the method.