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In this paper, a seasonal multi-product multi-period inventory control problem is modeled in which the inventory costs are obtained under inflation and all-unit discount policy. Furthermore, the products are delivered in boxes of known number of items, and in case of shortage, a fraction of demand is considered backorder and a fraction lost sale. Besides, the total storage space and total available budget are limited. The objective is to find the optimal number of boxes of the products in different periods to minimize the total inventory cost (including ordering, holding, shortage, and purchasing costs). Since the integer nonlinear model of the problem is hard to solve using exact methods, a... 

The aim of this article is presenting a new constrained multi-product pricing and inventory model in which perishable products are put into three categories: substitute, complementary and independent. The general demand is found by considering the relations of different products and the impact of their prices. The goal of the model is deciding on the prices as well as the inventory and production decisions in order to maximize the total profit. The derived model is a non-linear programming model and a genetic algorithm is developed for its solution. To enhance the performance of our genetic algorithm, we apply the Taguchi experimental design method to tune the parameters of the algorithm.... 

While the usual assumptions in multiperiodic inventory control problems are that the orders are placed either at the beginning of each period (periodic review) or depending on the inventory level they can happen at any time (continuous review), in this paper we assume the periods between two replenishments of several products are identical and independent random variables. For the problem at hand, the order quantities (decision variables) are of integertype and there are two kinds of space and service level constraints for each product. A model of the problem is first developed in which a combination of backorder and emergency orders is considered for the shortages, and the costs are... 

In this research, a single-period two-echelon inventory control problem with market targeting strategies is considered. In this problem, there are several final products and raw materials with varying usage rates. The objective is to determine the order sizes of final products and raw materials before the selling period such that customers' satisfaction is reached and expected profit is maximized within an available budget. The problem is first mathematically formulated and then a modified particle swarm optimization algorithm is employed to solve the nonlinear programming problem. To validate the results obtained, a simulated annealing algorithm is provided as a benchmark. The parameters of... 

While in multi-periodic inventory control problems the usual assumption 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 research, we relax these assumptions and assume that the periods between two replenishments of the products are independent and identically distributed random variables. Furthermore, assuming the purchasing price are triangular fuzzy variables, the quantities of the orders are of integer-type and that there are space, budget and service level constraints, incremental discount is considered to purchase products and a combination of back-order and... 

This paper points out an application of the "two-echelon single-period product (newsboy) problem," in which within a limited budget the final product and the raw materials are purchased before the start of the selling period and depending on the demand, the raw materials may be transformed into the finished product during the period. The objective of this problem is to find the order quantities of both the raw materials and the final product at the beginning of the period such that the expected profit is maximized. A new model is first developed for this problem and then a Lagrangian method is proposed to solve it. Finally, a numerical example is given to illustrate the application of the... 

Although inventory control under discrete demand in dynamic quantities and time intervals are very common in reality, existing literature has largely ignored them. In this paper, we investigate the inventory control decisions in a two echelon supply chain consisting of one vendor and several retailers. The vendor supplies a product to several retailers, who buy discrete quantities in pre-determined time intervals. The order quantity and order cycles for each retailer can be different from others. Vendor orders the required quantity from supplier and it will be immediately received at the vendor's warehouse. In this system, shortage is not allowed for the vendor. The transportation time from... 

This article studies a multi-product and multi-period location-routing-inventory problem in which location-allocation, inventory and routing decisions are to be taken in a three-level supply chain including suppliers, depots and customers. Products are distributed from depots to customers by a homogeneous fleet of vehicles. Backlogging is allowable on condition that the backlog quantity of each customer does not exceed a predefined fraction of his demand. A mixed-integer programming formulation is presented to describe the problem then a new hybrid heuristic algorithm based on the simulated annealing and imperialist competitive algorithm is designed to solve the model. Comprehensive... 

This study presents a seasonal multi-product multi-period inventory control model with inventory costs obtained under inflation and all-unit discount policy. The products are delivered in boxes of known quantities and both backorder and lost-sale quantities are considered in case of shortage. The goal is to find a representative set of Pareto optimal solutions (including the ordering quantities) in different periods and to minimize both the total inventory cost (i.e. ordering, holding, shortage, and purchasing costs) and the total storage space, simultaneously. Three multi-objective optimization algorithms of non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic... 

Multi-periodic inventory control problems are mainly studied employing two assumptions. The first is the continuous review, where depending on the inventory level orders can happen at any time and the other is the periodic review, where orders can only happen at the beginning of each period. In this study, we relax these assumptions and assum that the periodic replenishments are stochastic in nature. Furthermore, we assume that the periods between two replenishments are independent and identically random variables. For the problem at hand, the decision variables are of integer-type and there are two kinds of space and service level constraints for each product. We develop a model of the... 

In this paper, a multi-item multiperiod inventory control problem with all-unit and/or incremental quantity discount policies under limited storage capacity is presented. The independent random demand rates of the items in the periods are known and the items are supplied in distinct batch sizes. The cost consists of ordering, holding, and purchasing. The objective is to find the optimal order quantities of all items in different periods such that the total inventory cost is minimized and the constraint is satisfied. A mixed binary integer programming model is first developed to model the problem. Then, a parameter-tuned genetic algorithm (GA) is employed to solve it. Since there is no... 

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... 

In this paper, a multi-product economic production quantity problem with limited warehouse-space is considered in which the orders are delivered discretely in the form of multiple pallets and the shortages are completely backlogged. We show that the model of the problem is a constrained non-linear integer program and propose a genetic algorithm 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  

The economic production quantity (EPQ) is one of the most applicable model in production and inventory control environments. Like other classical production and inventory control models, it is derived based upon assumptions that cause limited real-world applications. Continuous and constant-rate delivery of orders, infinite availability of warehouse spaces, and applicability on a single product are some of these assumptions. In order to make the EPQ model more applicable to real-world production and inventory control problems, in this paper, we expand this model by assuming that the orders may be delivered discretely in the form multiple pallets. In addition, we may have more than one... 

In this paper we consider a two-level inventory system with one warehouse and one retailer with information exchange. The retailer applies fixed order size continuous review policy. The supplier starts with m initial batches of the same order size of the retailer, and places an order to an outside source immediately after the retailer's inventory position reaches an amount equal to the retailer's order point plus a fixed value s. Transportation times are constant and the retailer faces independent Poisson demand. In a recent paper it was pointed out that the optimal supplier policy in this inventory system is an open question. To obtain the optimal policy for this system, first we find the... 

In this paper we consider a newsvendor problem in which the suppliers offer quantity discounts. We assume that the initial inventory at the beginning of the period is a random variable. This assumption, among other applications, may apply to the case where the decision about the order quantity must be made at a time long before the start of the period and the available inventory may decrease due to several factors, such as deterioration, consumption, etc. up to the start of the period. In this paper, we obtain the optimal order quantity that maximizes the total profit for this model