A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model (original) (raw)
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Expert Systems with Applications, 2011
In this research, an economic order quantity (EOQ) model is first developed for a two-level supply chain system consisting of several products, one supplier and one retailer, in which shortages are backordered, the supplier's warehouse has limited capacity and there is an upper bound on the number of orders. In this system, the supplier utilizes the retailer's information in decision making on the replenishments and supplies orders to the retailer according to the well known (R,Q) policy. Since the model of the problem is of a nonlinear integer-programming type, a genetic algorithm is then proposed to find the order quantities and the maximum backorder levels such that the total inventory cost of the supply chain is minimized. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology and to evaluate and compare its performances to the ones of a penalty policy approach that is taken to evaluate the fitness function of the genetic algorithm.
The International Journal of Advanced Manufacturing Technology, 2014
The aim of this paper is to investigate the vendor managed inventory (VMI) problem of a single-vendor single-buyer supply chain system, in which the vendor is responsible to manage the buyer's inventory. To include an extended applicability in realworld environments, the multi-product economic production quantity (EPQ) model with backordering under three constraints of storage capacity, number of orders, and available budget is considered. The nonlinear programming model of the problem is first developed to determine the near optimal order quantities along with the maximum backorder levels of the products in a cycle such that the total VMI inventory cost of the system is minimized. Then, A genetic algorithm (GA) based heuristic is proposed to solve the model. Numerical examples are given to both demonstrate the applicability of the proposed methodology and to fine-tune the GA parameters. At the end, the performance of the proposed GA is compared to the one of the LINGO software using different problem sizes. The results of the comparison study show that while the solutions do not differ significantly, the proposed GA reaches near optimum solutions in significantly less amount of CPU time.
Vendor managed inventory control system for deteriorating items using metaheuristic algorithms
Decision Science Letters, 2018
Inventory control of deteriorating items constitutes a large part of the world's economy and covers various goods including any commodity, which loses its worth over time because of deterioration and/or obsolescence. Vendor managed inventory (VMI), which is a win-win strategy for both suppliers and buyers gains better results than traditional supply chain. In this research, we study an economic order quantity (EOQ) with shortage in form of partial backorder under VMI policy. The model is concerned with multi-item subject to multiconstraint including storage space, time period and budget constraints. Two metaheuristic algorithms, namely Simulated Annealing and Tabu Search, are used to find a near optimal solution for the proposed fuzzy nonlinear integer-programming problem with the objective of minimizing the total cost of the supply chain. Furthermore, the sensitivity analysis of the metaheuristic parameters is performed and five numerical examples containing different numbers of items are conducted in order to evaluate the performance of the algorithms.
Knowledge-Based Systems, 2013
The vendor-managed inventory (VMI) is a common policy in supply chain management (SCM) to reduce bullwhip effects. Although different applications of VMI have been proposed in the literature, the multi-vendor multi-retailer single-warehouse (MV-MR-SW) case has not been investigated yet. This paper develops a constrained MV-MR-SW supply chain, in which both the space and the annual number of orders of the central warehouse are limited. The goal is to find the order quantities along with the number of shipments received by retailers and vendors such that the total inventory cost of the chain is minimized. Since the problem is formulated into an integer nonlinear programming model, the meta-heuristic algorithm of particle swarm optimization (PSO) is presented to find an approximate optimum solution of the problem. In the proposed PSO algorithm, a genetic algorithm (GA) with an improved operator, namely the boundary operator, is employed as a local searcher to turn it to a hybrid PSO. In addition, since no benchmark is available in the literature, the GA with the boundary operator is proposed as well to solve the problem and to verify the solution. After employing the Taguchi method to calibrate the parameters of both algorithms, their performances in solving some test problems are compared in terms of the solution quality.
Vendor Managed Inventory of a Supply Chain under Stochastic Demands
In this research, an integrated inventory problem is formulated for a single-vendor multiple-retailer supply chain that works according to the vendor managed inventory policy. The model is derived based on the economic order quantity in which shortages with penalty costs at the retailers` level is permitted. As predicting customer demand is the most important problem in inventory systems and there are difficulties to estimate it, a probabilistic demand is considered to model the problem. In addition, all retailers are assumed to share a unique number of replenishments where their demands during lead-time follow a uniform distribution. Moreover, there is a vendor-related budget constraint dedicated to each retailer. The aim is to determine the near optimal or optimal order quantity of the retailers, the order points, and the number of replenishments so that the total inventory cost of the system is minimized. The proposed model is an integer nonlinear programming problem (NILP); hence, a meta-heuristic namely genetic algorithm (GA) is employed to solve it. As there is no benchmark available in the literature to validate the results obtained, another meta-heuristic called firefly algorithm (FA) is used for validation and verification. To achieve better solutions, the parameters of both meta-heuristics are calibrated using the Taguchi method. Several numerical examples are solved at the end to demonstrate the applicability of the proposed methodology and to compare the performance of the solution approaches.
Modelling and optimisation of multiproduct, multi-echelon inventory problem
International Journal of Supply Chain and Inventory Management, 2017
The purpose of this paper is to determine the optimum lot-sizes and reorder intervals of a 3-echelon supply chain system. The mathematical model is built based on Roundy's PO2 policy and integer policy of ordering as a constrained non-linear programming problem. For illustration purpose, we took two problems of single and fifty products distribution systems under deterministic condition. Problems are solved with exhaustive search method on spreadsheet and through Matlab programming. Though PO2 policy is very simple and is able to provide a few solutions, and faster, many times it fails to find an optimal solution and sometimes, any feasible solution at all. On the contrary, integer policy gives many including optimum and all PO2 solutions. Result shows that our proposed model and the simple algorithm applied for the solution have superiority and is effective on reducing the total cost of the multi-product, multi-echelon inventory system. Further, the products are grouped based on reorder interval using joint replenishment strategy.
International Journal of the Physical Sciences, 2012
In order to make the economic production quantity (EPQ) model more applicable to real-world production and inventory control problems, in this paper, we expand this model by assuming that some imperfect items of different product types are being produced such that reworks are allowed. In addition, we may have more than one product and supplier along with warehouse space and budget limitation. We show that the model of the problem is a constrained non-linear integer program and propose a genetic algorithm (GA) to solve it. Moreover, design of experiments is employed to calibrate the parameters of the algorithm for different problem sizes. At the end, a numerical example is presented to demonstrate the application of the proposed methodology.
This paper considers a two-echelon supply chain model with a single vendor and two buyers in which the vendor supplies the same item to both buyers at a finite production rate. The purpose of this study is twofold. First, mathematical models are developed for the integrated vendor-managed inventory (VMI) policy as well as the traditional retailer-managed inventory (RMI) system and solution algorithms are presented to determine the optimal lot size and total inventory cost of the supply chain. Then, the effect of key parameters including buyer's demand, buyer's transportation cost, vendor's ordering cost, and vendor's holding cost on lot size variation is studied in each policy. A weighting factor is also determined for the vendor's ordering cost which is used to compare the two policies. Detailed numerical experiments are provided to illustrate efficacy of the proposed approach. Results indicate that greater reduction in total cost of supply chain can be achieved by using VMI and provide a comprehensive insight into selection of inventory policies to improve commercial business and supply chain performance.
International Journal of Production Economics, 2013
In this study, a multi-item economic order quantity model with shortage under vendor managed inventory policy in a single vendor single buyer supply chain is developed. This model explicitly includes warehouse capacity and delivery constraints, bounds order quantity, and limits the number of pallets. Not only the demands are considered imprecise, but also resources such as available storage and total order quantity of all items can be vaguely defined in different ways. An ant colony optimization is employed to find a near-optimum solution of the fuzzy nonlinear integerprogramming problem with the objective of minimizing the total cost of the supply chain. Since no benchmark is available in the literature, a genetic algorithm is developed as well to validate the result obtained. Furthermore, the applicability of the proposed methodology along with a sensitivity analysis on its parameter is shown by four numerical examples containing different numbers of items.
In this paper, the joint replenishment problem is modelled for a two-level supply chain consisting of a single supplier and multiple retailers that employ the vendor-managed inventory (VMI) policy for several products. The aim is to find the optimal number of products to order in both VMI and traditional policies, the optimal times at which each retailer orders the products in the traditional policy, and the optimal times at which the supplier orders the product in the VMI policy. Design/methodology/approach – The problem is first formulated into the framework of a constrained integer nonlinear programming model. Then, it is solved by a teacher-learner-based optimization algorithm. As there are no benchmarks available in the literature, a genetic algorithm is utilized as well to validate the results obtained. Findings – The solutions of several numerical examples obtained using both algorithms are compared to the ones of a random search procedure for further validation. A real case is solved at the end to demonstrate the applicability of the proposed methodology and to compare both policies.