A fast algorithm for triangular plate bending element

This communication presents a simple algorithm to compute the stiffness matrix for a triangular plate bending element, without numerical integration. This brings about a substantial saving in computer time.     

Large amplitude supersonic flutter of panels with ends elastically restrained against rotation

Nonlinear supersonic flutter of panels is studied for end conditions of simply supported, clamped and partial restrained against rotation by a unified approach. The effects of large deflection and inplane forces on flutter boundary is included. Based on convergence study an eight element solution is given for all the results presented.     

Combining an alternative multi-delivery policy into economic production lot size problem with partial rework

This paper combines an alternative multi-delivery policy into an imperfect economic production quantity (EPQ) model with partial rework, with the purpose of reducing supplier’s stock holding cost. We extend the problem examined by Chiu et al. [Chiu, Y.-S. P, Chiu, S. W., Li, C.-Y., & Ting, C.-K. (2009). Incorporating multi-delivery policy and quality assurance into economic production lot size problem. Journal of Scientific and Industrial Research, 68(6), 505-512] by considering an n + 1 delivery policy in lieu of n multi-delivery plan for the specific EPQ model with partial rework. Under such a policy, an initial delivery of perfect (finished) items is distributed to customer for satisfying product demand during manufacturer’s regular production time and rework time. At the end of rework, fixed quantity n installments of the finished products are delivered to customer at a fixed interval of time. As a result, a closed-form optimal replenishment batch size solution to the problem is obtained. A numerical example with analysis and comparison is provided to show practical usage of the proposed model and demonstrate its significant savings in stock holding cost.     

Robust planning in optimization for production system subject to random machine breakdown and failure in rework

This study is concerned with robust planning in optimization, specifically in determining the optimal run time for production system that is subject to random breakdowns under abort/resume (AR) control policy and failure in rework. In most real-life production processes, generation of defective items and breakdowns of manufacturing equipment are inevitable. In this study, random defective rate is assumed and all manufactured items are screened. The perfect quality, reworkable and scrap items are identified and separated; failure-in-rework is assumed. The system is also subject to random machine breakdown; and when it occurs, the AR policy is adopted. Under such policy, the production of the interrupted lot will be immediately resumed when the machine is restored. Mathematical modeling and derivation of the production-inventory cost functions for both systems with/without breakdowns are presented. The renewal reward theorem is used to cope with the variable cycle length when integrating cost functions. The long-run average cost per unit time is obtained. Theorems on convexity and on bounds of production run time are proposed and proved. A recursive searching algorithm is developed for locating the optimal run time that minimizes the expected production-inventory costs. A numerical example with sensitivity analysis is provided to give insight into the optimal operational control of such an unreliable system.     

Intra-supply chain system with multiple sales locations and quality assurance

The emergence of the global economy has transformed the interdepartmental nature of a transnational enterprise into a highly collaborative oriented team. This transformation enables the enterprise to lower its transaction and coordination costs and increase its competitive advantage in the global market. This study investigates such a so-called intra-supply chain system that exists in present-day transnational firms, wherein a single production unit manufactures products to meet the demands of multiple regional sales offices and incorporates quality assurance in its production. The objective of the present study is to determine an optimal production quantity and shipment policy that minimizes the integrated production–inventory–delivery costs for the intra-supply chain system. In this study, considerations related to a product’s quality assurance include inspection for quality, rework of defective items and failure in rework. Delivery of the finished products starts when quality of the entire production lot is assured. Multi-shipment policy is used to synchronously transport finished items to multiple locations for satisfying customer demands in each cycle. Mathematical modeling along with Hessian matrix equations is employed to solve the proposed intra-supply chain system. A numerical example with a discussion and cost-benefit analysis of outsourcing work to an external distributor is presented to demonstrate the practical applicability of the obtained results.     

A note on “intra-supply chain system with multiple sales locations and quality assurance”

In a recent paper, Chiu et al. [Intra-supply chain system with multiple sales locations and quality assurance, Expert Systems with Applications, http://dx.doi.org/10.1016/j.eswa.2012.11.008] used the mathematical modeling and differential calculus to derive the optimal replenishment lot-size and shipment policy that minimizes overall costs for a specific intra-supply chain system. This paper proposes a two-phase straightforward algebraic approach to replace the use of calculus on the cost function for determining the optimal production-shipment policy for such a specific system. This alternative approach enables practitioners who may not have sufficient knowledge of calculus to manage the real-world intra-supply chain systems more effectively.     

Incorporating expedited time and cost of the end product into the product structure diagram

This paper presents an algorithm for determining expedited time and cost of the end product in the product structure diagram (PSD) using critical path method (CPM) and time-costing method. The classical PSD provides essential information for the consequent material requirement planning (MRP). Such information includes the parent–child relationship between the end item and its components at each level, the number of components required at the child level in order to produce one unit at the parent level, and the number of periods required for production of each component. Selecting an appropriate acquisition method (either manufacturing process or speed of assembly or specific supplier) for each component is one of the early tasks faced by a product/process design team and it is critical because that the resulting decisions are then translated into the PSD and its subsequent material requirement planning. In this study, we propose a step-by-step decision procedure using the CPM and time-costing method for determining the optimal component procuring alternatives when expediting end product's completion time is desired. A numerical example demonstrates its practical usage.     

Determining the materials procurement policy based on the economic order/production models with backlogging permitted

This paper considers the materials procurement decision-making based on the economic order quantity and economic production quantity models with backlogging permitted. Make-or-buy is one of the fundamental decisions routinely made by most manufacturing firms. Cost is always considered as the biggest determinant in the decision to make or buy. Four terms composing the total inventory cost per unit time are analyzed in this study; they are annual setup cost, purchase/manufacturing cost, holding cost, and backordering cost. The impact of different values of the unit backorder cost b _i , setup cost K _i, and unit cost c _i to the make-or-buy decision is studied specifically in our mathematical analysis. As a result, the guidelines in terms of simplified formulas for the make-or-buy decision makings are derived. Numerical examples are provided to demonstrate their practical usages.     

Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework

Conventional approach for solving the replenishment lot size problem is by using differential calculus on the long-run average production cost function with the need to prove optimality first. Recent studies proposed an algebraic approach to the solution of classic economic order quantity (EOQ) and the economic production quantity (EPQ) models without reference to the use of derivatives. This paper extends it to the solution of a specific EPQ model as was examined by Chiu et al. [Chiu, S. W, Chen, K. -K, Lin, H. -D. Numerical method for determination of the optimal lot size for amanufacturing system with discontinuous issuing policy and rework. International Journal forNumerical Methods in Biomedical Engineering. doi: 10.1002/cnm.1369. (in Press; Published online March-10-2010).]. As a result, optimal replenishment lot size and a simplified optimal production-inventory cost formula for such a particular EPQ model can be derived without derivatives. This alternative approach may enable practitioners who with little knowledge of calculus to understand the realistic production systems with ease.