Asia-Pacific Journal of Operational Research

The cumulative capacitated vehicle routing problem (CCVRP) is a variant of the classical capacitated vehicle routing problem in which the objective is the minimization of customers’ total waiting time prior to service. Inspired by the first-mile pick-up service within 3rd-Party Logistics operations, we study a dynamic and stochastic variant of the CCVRP. In this variant, a capacitated vehicle undertakes a single tour to collect customers’ parcels, taking into account stochastic service requests, stochastic service cancellations, and stochastic demand (i.e., changes in parcel size) simultaneously. Conditional on maximizing the usage of the vehicle’s capacity, we minimize the total waiting time of both customers who are served and those who request services but are not served due to cancellation or capacity violation. We formulate this problem as a Markov decision process and solve it using a hybrid approach that combines approximate dynamic programming and rollout algorithm. Our main contributions include ($\mathrm{\text{i}}$) the construction of the $stage$ $cost$ that leverages a property of the Poisson process, and ($\mathrm{\text{ii}}$) consideration of service fairness-based acceptance/rejection rule in response to excessive stochastic service requests. In the numerical study, our approach is examined to outperform an 2-Opt-based re-optimization policy in terms of both customers’ waiting time and service-request satisfying rate. More importantly, computational results heuristically show that there is no cost to adopting the service fairness-based rule, which is obviously a valuable managerial insight.

This paper addresses single-machine scheduling problems with past-sequence-dependent (denoted by $\widetilde{psd}$) delivery times, due-window assignments and deteriorating jobs simultaneously. The $\widetilde{psd}$ delivery time of a job is proportional to the job’s waiting time, and the deteriorating jobs mean that the processing time of a job is a proportional increasing function of its starting time. For common, slack and different due-window assignments, the goal is to minimize the weighted sum of earliness, tardiness, due-window starting time and size. Some optimal propositions of the problems are given, and by these propositions, polynomial time algorithms are proposed to optimally solve the above problems.

This paper studies the inefficiency of Nash equilibria (NE) for scheduling games on hierarchical machines with quadratic social cost. There is a set of hierarchical machines and a set of jobs. Each job can choose one machine from the set of machines that are permitted to process it, and the cost associated with the job is equal to the load of the selected machine. A schedule is an NE if no job can reduce its cost by ultimately moving to a different eligible machine. The social cost is the sum of squares of the loads of all the machines. We show that the Price of Anarchy for two, three and four machines is $\frac{3+\sqrt{5}}{4}$, $\frac{2+\sqrt{2}}{2}$ and $\frac{2+\sqrt{2}}{2}$, respectively.

In this paper, we deal with the different due windows assignment proportionate flow shop problem with position-dependent weights, where the sequence is a permutation. The objective is to determine an optimal job sequence and due windows of all jobs such that the weighted sum of earliness–tardiness, the starting time and size of all due windows is to be minimized, where the weight is not related to the job but to the position in which some job is scheduled, i.e., position-dependent weights. According to a series of optimal properties, we prove that the problem can be solved in polynomial time $O(n^2)$, where $n$ is the number of jobs.

Cleaning up a polluted river requires coordinated actions among different firms along the river. The key to promoting and enriching the firms’ cooperation is to share the pollution cleanup cost among these firms fairly and reasonably. In this paper, we propose a new cost-sharing scheme, called the entire upstream agents compensation method (the EUAC method for short), for a line-structure river cleanup cost-sharing problem by considering the waste transfer rate for each river segment. On the one hand, we offer a re-allocation scenario in order to implement the EUAC method. On the other hand, to reveal the rationality and stability of this proposed method, we formulate a cooperative cost game for the line-structure river cleanup cost-sharing problem, and show that the EUAC method coincides with the Shapley value of this game and belongs to the core of this game.

The aim of this paper is to investigate the manufacturer’s product introduction decision when entering a foreign market by considering parallel importation. This paper considers a situation where a manufacturer already sells an original product directly in the domestic market and decides to introduce an original product, a new product, or both through a retailer in a foreign market, and a parallel importer may divert the original product across markets due to price gap (we call it parallel importation). This paper shows that when consumers perceive gray products as perfect substitutes for authorized products, the manufacturer switches from introducing two products to introducing a new product and still maintains the quality of the new product in the presence of parallel importation. Furthermore, in response to parallel importation, the manufacturer not only narrows the price gap for original products between two markets but also reduces the wholesale price of new products in the foreign market. In addition, parallel importation always hurts the retailer but may benefit the manufacturer. Counterintuitively, parallel importation always improves social welfare in the domestic market but may damage social welfare in the foreign market.

The geometric process (GP) has been widely utilized as a stochastic monotone model in the fields of probability and statistics. However, its practical application is often limited by certain assumptions. To address this, [Wu (2018). Doubly geometric process and applications. Journal of the Operational Research Society, 69(1), 66–67] introduced the doubly geometric process (DGP) as an extension of the GP model, relaxing some of its assumptions. Due to its ability to overcome the limitations of the GP model, the DGP has gained significant popularity in recent times. This study focuses on the parameter estimation problem for the DGP when the distribution of the first interarrival time follows a lognormal distribution with parameters $\delta$ and $\tau$. We employ the maximum likelihood method to obtain estimates for both the model parameters and the distribution parameters. Additionally, we investigate the asymptotic joint distribution and statistical properties such as asymptotic unbiasedness and consistency of the estimators. Furthermore, we propose a novel test procedure to distinguish between the GP and DGP models. To assess the performance of the estimators and the proposed test procedure, we conduct a simulation study involving various sample sizes and parameter values. Finally, we present an application of the developed methods in fitting data from bladder cancer patients.

In this paper, we develop a dynamic analysis model to investigate a monopolist’s perceived quality with product innovation and reference price effects, in which price and reference price are used both as a signal of quality, while product quality and advertising effort are used only as a signaling device. We show that (i) the stability of steady-state equilibrium depends on the admissible parameters; (ii) there is always a fixed proportional relationship between the efforts for product innovation and improving perceived quality; (iii) there is always a positive relationship between the price and product quality (or price and perceived quality; price and reference price).