This paper characterizes the routing problems arising in distribution of rice-for-the-poor in a district and presents a generic mathematical formulation of vehicle routing problems (VRP) for solving the problems. The proposed generic model, framed as a mixed integer linear programming, is formulated in such a way to encompass three distinct features; namely multiple depots (MD) establishment, multiple trips (MT) transportation, and split delivery (SD) mechanism. This model is implemented for a real-world problem of rice-for-the-poor distribution in the Ponorogo district of Indonesia, involved for deliveries among 3 depots—8, 17, and 23 villages depended on the distribution period—using a fleet of 5 vehicles of homogeneous capacity. Three types of distribution model are identified as MD-MT-VRP, MD-VRP-SD and MD-MT-VRP-SD.

Data envelopment analysis models play an important role in decision making. In this paper, one-stage and two-stage nonlinear programming problems are investigated in order to evaluate the efficiency of two types of network data envelopment analysis model. The first type of network data envelopment analysis model has a series structure with three stages and a feedback between the last step and the middle step, the second model has a three-stage series structure with two feedback between the final step and the first step and the middle step. By examining the overall efficiency of the models based on the one-stage programming problem, a two-stage programming problem is also applied in order to evaluate the efficiency of each step. In order to solve one-stage nonlinear programming problems and two-stage linear and nonlinear programming problems derived from modeling, a linearization method based on coordinate transformation, and constant assumption and gradual growth of some variables is presented. In the last section, the proposed methods have been discussed using some numerical examples.

This paper presents a new penalty function called logarithmic penalty function (LPF) and examines the convergence of the proposed LPF method. Furthermore, the LaGrange multiplier for equality constrained optimization is derived based on the first-order necessary condition. The proposed LPF belongs to both categories: a classical penalty function and an exact penalty function, depending on the choice of penalty parameter. Moreover, the proposed LPF is capable of dealing with some of the problems with irregular features from Hock-Schittkowski collections of test problems.

This paper proposes a framework for selecting energy storage technology (EST) for small-scale renewable energy systems. The present study was able to achieve this using the results that were generated from a Preference Ranking Organisation Method for Enrichment Evaluation (PROMETHEE) and a fuzzy quality function deployment (FQFD) model. Using the FQFD model, experts' opinions were incorporated into the framework during the evaluation of the techno-economic requirements importance for the selection process. The FQFD model considered system safety, availability, flexibility, reliability and effectiveness as customers’ requirements, while nominal voltage, nominal discharge current, peak measured voltage, operating cost and cost of energy were among the techno-economic requirements. During the framework application, a questionnaire was used to collect information from experts on the techno-economic requirements importance, while information on the techno-economic (eleven) requirements for four ESTs were obtained from literature. The FQFD model results were incorporated into a PROMETHEE and TOPSIS models. The PROMETHEE and the TOPSIS models identified Lithium-Ion EST as the best EST for small-scale renewable energy systems.