Asia-Pacific Journal of Operational Research

This paper presents a detailed analysis of inventory systems in which the demand for inventory is deterministic, varies by time in each order cycle, and follows a power pattern. Shortages are allowed. The decision variables are the initial stock level and the scheduling period. Holding cost, shortage cost, and replenishment cost are considered. Several scenarios are studied. First, the inventory system without shortages is analyzed, followed by systems with shortages. The full backordering and the completely lost sales systems are discussed and the optimal policy for each is explicitly determined. Several numerical examples are provided to illustrate the efficient inventory policy and the minimum cost for each inventory system.

Closed-loop supply chain (CLSC), especially the reverse logistics system with the third-party reverse logistics providers (3PRLP) is very important for materials return, remanufacturing, repair, recovery, recycling, and reusing. In this paper, based on a one-leader and multi-follower Stackelberg game with the manufacturer being the leader, we model a multi-echelon CLSC with 3PRLP under the consideration of impacts of environmental legislation on scrap recycling. Furthermore, in order to encourage the 3PRLP to exert him to return activities we design a target rebate-punish contract between the manufacturer and the 3PRLP under both stochastic price-dependent demands and stochastic effort-dependent returns. We analyze the closed-form analytic expressions for both united optimization strategies in centralized closed-loop system and the Stackelberg strategies in decentralized system, and conclude that the wholesale price contract may not coordinate the forward supply chain and the target rebate-punish may coordinate the reverse chain under certain conditions. Finally, according to the practice of Chinese steel enterprises we carry out some simulation experiments to validate our theoretical analyses and gain some insights into the impacts of reverse logistics activities on the practitioners operations and decisions.

This paper addresses a scheduling problem with random processing time when the operating system is subject to stochastic failure. First, scheduling of a single job is reviewed and the expected cost rate is obtained. Single scheduling time and multiple scheduling times for one job are discussed and the expected cost functions are obtained to setup the optimal due date. Numerical example is given to demonstrate the scheme of multiple scheduling times. Next, the scheduling problems of N tandem jobs and N parallel jobs are formulated and the expected cost functions are also derived. The optimal scheduling times which minimize the expected cost functions are discussed analytically.

This study addresses the problem of locating sugar cane loading stations and allocating cane fields to those stations. The problem is different from the general location–allocation problem in so far as this framework takes into account the different maturity periods of each cane field. If the loading station is improperly located, it can result in high transportation costs from cane fields to the station and significant fluctuations in the station utilization rate. A modification of the well-known "fuzzy c-means" (FCM) method, which takes into account both the cane supply and the different cane maturity periods, is proposed to solve this problem. The objective of the model is to minimize the sum of the transportation and station utilization costs. The performance of this method is compared to that of the traditional FCM method. The results show that the proposed approach is practical for solving the problem and that it provides a better solution than the FCM method.

We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time O(n log n) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed in (Ou et al., 2008). We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time O(n) for the case where the number of machines is fixed.

We consider single-machine scheduling problem in which the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total resource cost. The problem is modeled as an assignment problem, and thus can be solved in polynomial time. Some extensions of the problem are also shown.

In this paper, we consider a class of convex nonlinear knapsack problems in which all decision variables are integer and the objective and knapsack functions are nonlinear. This generalized problem is characterized by positive marginal cost (PMC) and increasing marginal loss-cost ratio (IMLCR). By analyzing the structural properties of the problem, we develop an efficient heuristic and propose search and branching rules to improve the branch and bound method for solving exact solution. Numerical study is done for showing the effectiveness of the proposed heuristic and the modified branch and bound method.

We are concerned with a variation of the assignment problem, where the assignment costs differ under different scenarios. We give a surrogate relaxation approach to derive a lower bound and an upper bound quickly, and show that the pegging test known for zero–one programming problems is also applicable to this problem. Next, we discuss how the computation time for pegging can be shortened by taking the special structure of the assignment problem into account. Finally, through numerical experiments we show that the developed method finds exact solutions for instances with small number of scenarios in relatively small CPU time, and good approximate solutions in case of many scenarios.