Asia-Pacific Journal of Operational Research

In this paper, some new results on the l₁ exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l₁ exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l₁ exact penalty function is also established.

It is well-known that a single machine scheduling problem of minimizing the total tardiness is NP-hard. Recently, Liu, Ng and Cheng solved some special hierarchical minimization problems with total tardiness as the primary criterion by the Algorithm TAP (Two Assignment Problems) in O(n³) time. And in this paper we present some algorithms for these problems with running time O(n log n).

An important issue in deregulated power systems is a provision of ancillary services. This paper presents a Mixed Integer Non-Linear Programming (MINLP) formulation for the provision of ancillary services (Automatic Generation Control or AGC, Spinning, Non-spinning and operational reserves) as well as the energy in simultaneous auctions by pool-based aggregated market scheme. The uncertainty of the market clearing procedure is represented by a stochastic model. Thus, the market clearing process is expressed as a stochastic optimization problem in which the expected objective function is minimized, while meeting AC power flow constraints, system reserve requirements and Lost Opportunity Cost (LOC). The model is applied to the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS), and simulation studies carried out to examine the effectiveness of the proposed method.

This note identifies and corrects an error in Keshvari, A and N Dehghan Hardoroudi (2008). Asia-Pacific Journal of Operational Research, 25, 689–696.

The purpose of this article is to construct a stochastic-demand inventory model which assumes that the whole period is stockout and the goods supply is at the end of the period. Furthermore, it also assumes that the waiting willingness of the customer depends on the length of waiting time. Based on these assumptions, the optimal supply cycle is then found so that the profit per unit time is maximized.

This paper considers minimizing total completion time in a two-stage flowshop scheduling problem with m identical parallel machines at Stage 1 and a batch processor at Stage 2. We prove that the problem when all jobs have same processing time at Stage 2 is NP – hard and gave a two-approximation algorithm in O(n³) time. In the case that all jobs have arbitrary processing time at Stage 1 and at Stage 2, we give an approximation algorithm after pointing out that in this case the problem is strongly NP – hard. Hundreds of instances of a numerical experiment show that the worst-case ratio of this approximation algorithm is nearing 2.

Environmental legislation and customer expectations increasingly force manufacturers to take recovery of used products into account in their production and inventory management. One of the areas concerned is production planning with returned products remanufacturing. In this paper, we discuss the optimal decision for a joint manufacturing and remanufacturing system in a multi-period horizon, including manufacturing decision, remanufacturing and disposal decisions of the returned product. Setup costs are considered for the manufacturing and disposal activities. For an n-period model, we derive an optimal solution structure for the three activities, where the solution parameters can be computed by dynamic programming approach.