Ata Allah Taleizadeh

A hybrid method of fuzzy simulation and genetic algorithm to optimize constrained inventory control systems with stochastic replenishments and fuzzy demand

Multi-periodic inventory control problems are mainly studied by employing one of two assumptions. First, the continuous review, where depending on the inventory level, orders can happen at any time, and next the periodic review, where orders can only be placed at the beginning of each period. In this paper, we relax these assumptions and assume the times between two replenishments are independent random variables. For the problem at hand, the decision variables (the maximum inventory of several products) are of integer-type and there is a single space-constraint. While demands are treated as fuzzy numbers, a combination of back-order and lost-sales is considered for the shortages. We demonstrate the model of this problem is of an integer-nonlinear-programming type. A hybrid method of fuzzy simulation (FS) and genetic algorithm (GA) is proposed to solve this problem. The performance of the proposed method is then compared with the performance of an existing hybrid FS and simulated annealing (SA) algorithm through three numerical examples containing different numbers of products. Furthermore, the applicability of the proposed methodology along with a sensitivity analysis on its parameters is shown by numerical examples. The comparison results show that, at least for the numerical examples under consideration, the hybrid method of FS and GA shows better performance than the hybrid method of FS and SA.

Multi-product production quantity model with repair failure and partial backordering

In this paper, a production quantity model with random defective items, service level constraints and repair failure is studied. The existence of only one machine results in limited production capacity and partial backordering. The aim of this research is to determine the optimal cycle length, optimal production quantity and optimal backordered quantity of each product such that the expected total cost (holding, shortage, production, setup, defective items and repair costs) is minimized. Two numerical examples and sensitivity analysis are provided to illustrate the practical usage of the proposed method.

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.

An economic order quantity model with multiple partial prepayments and partial backordering

Abstract The classic Economic Order Quantity model assumes that an order is paid for at the time of its receipt. In practice, suppliers may require purchasers to pay a fraction of the order’s cost in advance and sometimes allow them to divide the prepayment into multiple equal-sized parts to be paid during a fixed lead time. In this paper, an EOQ model with multiple prepayments under three different conditions: (a) no shortage, (b) full backordering and (c) partial backordering, are developed. Numerical examples illustrate the proposed models and solution method.

Meta-heuristic algorithms for solving a fuzzy single-period problem

Single-period problem (SPP) is a classical stochastic inventory model that has become very popular recently. In this research, we developed a SPP with fuzzy environment. The demand of each product is considered as LR-fuzzy variables (ranking fuzzy numbers based on the left and right deviation degrees), and multiple constraints (including service level, batch order, budget, space and upper limit for each order). The aim of this paper is to maximize the total expected profit under incremental discount strategy. Five hybrid intelligent algorithms based on fuzzy simulation (FS) and meta-heuristic methods are presented; they are bees colony optimization (BCO), harmony search (HS), particle swarm optimization (PSO), genetic algorithm (GA) and simulated annealing (SA). Three numerical examples are presented to illustrate the performance of the algorithms. Our study shows that the BCO-FS hybrid method performs better than the HS-FS, GA-FS, PSO-FS, and SA-FS hybrid methods.

A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments

Multi-periodic inventory control problems are mainly studied employing one of two assumptions. The first is the continuous review, where depending on the inventory level, orders can be placed at any time, and the other is the periodic review, where orders can be placed only at the beginning of each period. In this paper, we relax these assumptions and assume that the time-periods between two replenishments are random fuzzy variables. While in the model of the problem at hand the decision variables are of integer type and there are space and service level constraints, for the shortages we consider a combination of back-order and lost-sales. We show the model of this problem to be an integer-nonlinear-programming type and in order to solve it, a hybrid method of Pareto, TOPSIS and Genetic Algorithm approach is used. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology.

Short Communication: An improved solution to replenishment lot size problem with discontinuous issuing policy and rework, and the multi-delivery policy into economic production lot size problem with partial rework

Recently, in Expert Systems with Applications journal, Chen, Wu, Chiu, and Lee (2012) present an alternative optimization solution process to determine the optimal replenishment lot size with discontinuous issuing policy considering imperfect rework process and multiple shipments. Simultaneously, Chiu, Chiu, and Yang (2012) solve a multi-delivery policy into economic production quantity with partial rework. Both papers consider the number of shipments as a fixed and a given value. In this paper both the optimal replenishment lot size and the optimal number of shipments are derived jointly for the inventory models of Chen et al. (2012) and Chiu, Chiu, et al. (2012). Two easy to apply solution procedures are proposed. The solutions reported in this paper are better than the solutions of Chen et al. (2012) and Chiu, Chiu, et al. (2012).

Optimising multi-product multi-chance-constraint inventory control system with stochastic period lengths and total discount under fuzzy purchasing price and holding costs

While the usual assumptions in multi-periodic inventory control problems are that the orders are placed at the beginning of each period (periodic review) or depending on the inventory level they can happen at any time (continuous review), in this article, we relax these assumptions and assume that the periods between two replenishments of the products are independent and identically distributed random variables. Furthermore, assuming that the purchasing price are triangular fuzzy variables, the quantities of the orders are of integer-type and that there are space and service level constraints, total discount are considered to purchase products and a combination of back-order and lost-sales are taken into account for the shortages. We show that the model of this problem is a fuzzy mixed-integer nonlinear programming type and in order to solve it, a hybrid meta-heuristic intelligent algorithm is proposed. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology and to compare its performance with one of the existing algorithms in real world inventory control problems.

An economic order quantity model with partial backordering and a special sale price

A constant unit purchase cost is one of the main assumptions in the classic economic order quantity model. In practice, suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items. In this paper we develop an EOQ model with a special sale price and partial backordering. We prove the convexity of the cost-reduction function if a special order is placed at the special sale price. A solution method is proposed and numerical examples are presented.

Multiproduct EPQ model with single machine, backordering and immediate rework process

Production systems with scrapped and rework items have recently become an interesting subject of research. While most attempts have been focused on finding the optimal production quantity in a simple production system, little work appears on a joint production environment. In this research, two joint production systems in a form of multiproduct single machine with and without rework are studied where shortage is allowed and backordered. For each system, the optimal cycle length, the backordered and production quantities of each product are determined such that the cost function is minimised. Proof of the convexity of the involved objective functions of each model is provided and numerical illustrations are given to demonstrate the applicability of the proposed models. Furthermore, the results obtained by solving the models with and without rework of defective items are compared. Sensitivity analysis and some managerial insights based on the numerical illustration are provided at the end. [Received 27 January 2010; Revised 22 May 2010; Accepted 31 May 2010]