Asia-Pacific Journal of Operational Research

A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The $l_1$ exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorithm with the second-order correction step and prove that the fast local superlinear convergence can be obtained under the strict complementarity and the second-order sufficient condition with the sigma term. Finally, some numerical experiments are given to show the effectiveness of the algorithm.

Operational collaboration in a supply chain is important due to the fierce competition among supply chains. However, the collaboration in a supply chain is often hindered by its distribution channel’s lack of funds. It is of significance to alleviate the capital constraint problem of the distribution channel and explore new joint operational and financial collaboration solutions. In this paper, we focus on exploring the optimal solution of operational collaboration in the presence of manufacturer collateral. We consider a supply chain consisting of a well-capitalized manufacturer and a capital-constrained retailer that faces difficulties obtaining credit from the bank. To help the retailer access financing for a purchase order, the manufacturer promises to pay the lender a proportion of the retailer’s loan if the retailer goes bankrupt. We find that when the bank credit with manufacturer collateral is considered as a mix of trade credit and bank credit, the retailer’s financing equilibrium depending on the maximum wholesale price what the manufacturer can set, can be neither trade credit nor bank credit alone, but a combination of them. Moreover, the retailer’s order quantity and the chain’s operational collaboration level will benefit from the manufacturer collateral.

This paper examines the simultaneous allocation of berths and quay cranes under discrete berth situation in container terminals. The berths of discrete type have been broadly applied in realistic production especially for the terminals whose berths are not aligned in a straight line. The typical features of such berths including wharf length constraints, water depth constraints, and berth-bound quay cranes have been considered in this paper. In contrast to the previous work which only deployed the number of quay cranes besides the assignment of berths, this paper assigns berths and quay cranes simultaneously. In addition, to better fit the realistic production, some practical features related to quay cranes including the interference between quay cranes, the berth-dependent productivity of quay cranes, and limited adjustments of the assigned quay cranes during operations have also been considered in this paper. An integer programming model is formulated for this problem, and a sub-gradient-based Lagrangian relaxation algorithm is proposed. A simple but efficient greedy insertion heuristics is developed to solve the decomposed primal problems to optimality. Based on actual data, numerical experiments are conducted to test the performance of the proposed algorithm.

In this paper, we consider the stability analysis of a convex quadratic programming (QP) problem and its restricted Wolfe dual when all parameters in the problem are perturbed. Based on the continuity of the feasible set mapping, we establish the upper semi-continuity of the optimal solution mappings of the convex QP problem and the restricted Wolfe dual problem. Furthermore, by characterizing the optimal value function as a min–max optimization problem over two compact convex sets, we demonstrate the Lipschitz continuity and the Hadamard directional differentiability of the optimal value function.

In this paper, we study an online scheduling on two parallel machines in MapReduce-like system where each job contains two kinds of tasks: map tasks and reduce tasks. A job’s reduce tasks can only be processed after all its map tasks are finished. We assume that the map tasks are fractional and the reduce tasks are preemptive. Our objective is to minimize makespan. We show that the lower bound for this MapReduce scheduling problem is $\sqrt{2}$. We then present an online algorithm with competitive ratio of $\sqrt{2}$ and thus it is optimal.

Previous literature suggests that without regulations firms have incentives to collude by fixing price or reducing quantity. This paper sets up an infinitely repeated game to examine the interplay between the manufacturer’s channel strategy and the downstream retailers’ collusive behavior. The results show that the manufacturer can deter retailer collusion by strategically changing its channel strategy. This effect occurs when the discount rate (used to calculate the present value of future profits) is relatively large and the manufacturer’s direct selling efficiency is relatively high (i.e., the variable cost of direct selling is relatively low). With the deterrence of direct selling, retailers abandon collusion and “no collusion” is a win-win strategy for both levels in the supply chain. However, when the manufacturer is not efficient in direct selling or the discount rate is small, direct selling is not effective in deterring retailer collusion and the manufacturer is worse off. These findings provide insights into channel strategies and supply chain management.

Stability of queues is of fundamental importance in the application of queueing models. To establish the stability of a queue, one has to utilize a mathematical model to describe the evolution of the queue and then defines stability on the model. However, the types of stability are various according to their underlying processes. In this study, we survey the different underlying processes of a $GI/G/1$ queue, classify the various types of stability and study the relations among them. Furthermore, from the viewpoint of sample-path, we propose a new result regarding the growth rate of the queue time when the traffic intensity equals 1.

The aim of this paper is to present a novel method for solving the minimum cost flow problem on networks with uncertain-random capacities and costs. The objective function of this problem is an uncertain random variable and the constraints of the problem do not make a deterministic feasible set. Under the framework of uncertain random programming, a corresponding $\alpha$-minimum cost flow model with a prespecified confidence level $\alpha$, is formulated and its main properties are analyzed. It is proven that there exists an equivalence relationship between this model and the classical deterministic minimum cost flow model. Then an algorithm is proposed to find the maximum amount of $\alpha$ such that for it, the feasible set of $\alpha$-minimum cost flow model is nonempty. Finally, a numerical example is presented to illustrate the efficiency of our proposed method.

We examine an option contract from a supplier’s perspective and apply mean-variance method to analyze the supplier’s risk. Compared with the newsvendor model without an option contract, we theoretically prove that the option contract can also benefit the supplier. We find for a given option exercise price, there exists an option price such that the contract with the option price dominates those with smaller option price in terms of mean variance of the supplier’s profit. Computational studies have also been conducted in the paper.

We investigate the optimal strategy of service supply chain (SSC) including one integrator and two suppliers under a two-layer game structure. Service integrator decides social responsibility and service price, while the two service suppliers with quality preference determine their quality efforts, respectively. By analyzing the two-layer game structure and eight different scenarios of decision models (i.e., CD, DD, ICD, IDD, ISD, SCD, SDD, and SSD), we establish members’ utility functions under different decision models. Meanwhile, based on game theory, the optimal strategies of SSC are obtained. Mathematical reasoning and numerical simulations show that, firstly, quality preference has impact on optimal strategy and members’ utilities under different constraints. Secondly, utility of supply chain with integrator as a leader is greater than the case with suppliers as the leader.