A single-producer multi-retailer integrated inventory model with a rework process

This study considers a single-producer multi-retailer integrated inventory model with the reworking of random defective items produced. The objective is to find the optimal production lot size and optimal number of shipments that minimizes total expected costs for such a specific supply chains system. It is assumed that a product is manufactured by a producer. All items are screened for quality purpose and random nonconforming items will be picked up and reworked at the end of regular production in each cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in each production cycle. Each retailer has its own annual product demand, unit stock holding cost, and fixed and variable delivery costs. Mathematical modeling and analysis is used to deal with the proposed model and to derive the expected system cost. Hessian matrix equations are employed to prove the convexity of the cost function. As a result, a closed-form optimal replenishment-delivery policy for such a specific single-producer multi-retailer integrated inventory model is obtained. A numerical example is provided to show the practical usage of the proposed model

A delayed differentiation multi-product FPR model with scrap and a multi-delivery policy – I: Using single-machine production scheme

This study examines a delayed differentiation multi-product single-machine finite production rate (FPR) model with scrap and a multi-delivery policy. The classic FPR model considers a single product, single stage production with all items manufactured being of perfect quality and product demand satisfied by a continuous inventory issuing policy. However, in real-life production-shipment integrated systems, multi-product production is usually adopted by vendors to maximize machine utilization, and generation of scrap items appear to be inevitable with uncontrollable factors in production. Further, distribution of finished products is often done through a periodic or multi-delivery policy rather than a continuous issuing policy. It is also assumed that these multiple products share a common intermediate part. In this situation, the producer would often be interested in evaluating a two-stage production scheme with the first stage producing common parts for all products and the second stage separately fabricating the end products to lower overall production-inventory costs and shorten the replenishment cycle time. Redesigning a multi-product FPR system to delay product differentiation to the final stage of production has proved to be an effective supply chain strategy from an inventory-reduction standpoint. Using mathematical modelling, we derive the optimal replenishment cycle time and delivery policy. A numerical example is provided to demonstrate its practical usage and compare our result to that obtained from the traditional single-stage multi-product FPR model

Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model

Traditionally, supply chain planning problems consider variables with uncertainty associated with uncontrolled factors. These factors have been normally modelled by complex methodologies where the seeking solution process often presents high scale of difficulty. This work presents the fuzzy set theory as a tool to model uncertainty in supply chain planning problems and proposes the particle swarm optimisation (PSO) metaheuristics technique combined with a backward calculation as a solution method. The aim of this combination is to present a simple effective method to model uncertainty, while good quality solutions are obtained with metaheuristics due to its capacity to find them with satisfactory computational performance in complex problems, in a relatively short time period.This research is partly supported by the Spanish Ministry of Economy and Competitiveness projects 'Methods and models for operations planning and order management in supply chains characterised by uncertainty in production due to the lack of product uniformity' (PLANGES-FHP) (Ref. DPI2011-23597) and 'Operations design and Management of Global Supply Chains' (GLOBOP) (Ref. DPI2012-38061-C02-01); by the project funded by the Polytechnic University of Valencia entitled 'Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics' (PAID-06-12); and by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the incentive program of the National Council for Scientific and Technological Research (CONICIT) (contract No FI-132-2011).Grillo Espinoza, H.; Peidro Payá, D.; Alemany Díaz, MDM.; Mula, J. (2015). Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model. International Journal of Bio-Inspired Computation. 7(3):157-169. https://doi.org/10.1504/IJBIC.2015.069557S1571697

Supply chain outsourcing risk using an integrated stochastic-fuzzy optimization approach.

a b s t r a c t A stochastic fuzzy multi-objective programming model is developed for supply chain outsourcing risk management in presence of both random uncertainty and fuzzy uncertainty. Utility theory is proposed to treat stochastic data and fuzzy set theory is used to handle fuzzy data. An algorithm is designed to solve the proposed integrated model. The new model is solved using the proposed algorithm for a three stage supply chain example. Computation suggests an analysis of risk averse and procurement behavior, which indicates that a more risk-averse customer prefers to order less under uncertainty and risk. Tradeoff game analysis yields supported points on the trade-off curve, which can help decision makers to identify proper weighting scheme where Pareto optimum is achieved to select preferred suppliers

Effective Multi-echelon Inventory Systems for Supplier Selection and Order Allocation

Successful supply chain management requires an effective sourcing strategy to counteract uncertainties in both the suppliers and demands. Therefore, determining a better sourcing policy is critical in most of industries. Supplier selection is an essential task within the sourcing strategy. A well-selected set of suppliers makes a strategic difference to an organization\u27s ability to reduce costs and improve the quality of its end products. To discover the cost structure of selecting a supplier, it is more interesting to further determine appropriate levels of inventory in each echelon for different suppliers. This dissertation focuses on the study of the integrated supplier selection, order allocation and inventory control problems in a multi-echelon supply chain. First, we investigate a non-order-splitting inventory system in supply chain management. In particular, a buyer firm that consists of one warehouse and N identical retailers procures a type of product from a group of potential suppliers, which may have different prices, ordering costs, lead times and have restriction on minimum and maximum total order size, to satisfy stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the proposed model. The model is solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained with sensitivity analysis. In the next place, we extend the study to consider the multi-echelon system with the order-splitting policy. In particular, the warehouse acquisition takes place when the inventory level depletes to a reorder point R, and the order Q is simultaneously split among m selected suppliers. This consideration is important since it could pool lead time risks by splitting replenishment orders among multiple suppliers simultaneously. We develop an exact analysis for the order-splitting model in the multi-echelon system, and formulate the problem in a Mixed Integer Nonlinear Programming (MINLP) model. To demonstrate the solvability and the effectiveness of the model, we conduct several numerical analyses, and further conduct simulation models to verify the correctness of the proposed mathematical model