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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 multiproduct inventory control problem is considered in which the periods between two replenishments of the products are assumed independent random variables, and increasing and decreasing functions are assumed to model the dynamic demands of each product. Furthermore, the quantities of the orders are assumed integer-type, space and budget are constraints, the service-level is a chance-constraint, and that the partial back-ordering policy is taken into account for the shortages. The costs of the problem are holding, purchasing, and shortage. We show the model of this problem is an integer nonlinear programming type and to solve it, a harmony search approach is used. At the... 

In this paper, we develop the multi-product, multi-constraint, Single Period Problem (SPP) with uncertain demands, considering an incremental discount situation. Three new models are presented for multi-product, multi-constraint SPP in fuzzy, stochastic and rough environments. We consider constraints, such as service rate, restriction on order quantity and restrictions on warehouse space and budget. We also consider that the order quantity is a multiplier of predefined batch size. Furthermore, three kinds of solution algorithm, (1) harmony search, (2) hybrid intelligent based on harmony search and fuzzy simulation and (3) hybrid intelligent based on harmony search and rough simulation, are... 

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 non-linear integer-programming type, a genetic algorithm is then proposed to find the order quantities and the maximum backorder levels such that the total inventory... 

There are two main assumptions in multiperiodic inventory control problems. 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 paper, these assumptions are relaxed, and the periods between two replenishments are assumed independent and identically distributed random variables. Furthermore, the decision variables are assumed integer-type and that there are two kinds of space and budget constraints. The incremental discounts to purchase products are considered, and a combination of backorder and lost sales are taken into account... 

In this paper, we develop the multi-products multi-constraints newsboyproblem with fuzzy demands considering the total discount situation. Since thedemands of products are often fuzzy in the real world, the profit of the newsboyis fuzzy too. A new model is presented for multi-products multi-constraintsnewsboy problem in fuzzy Environment (FM-PM-CNP). The objective function ofproposed model is to maximize the expected profit of newsboy. We consider theconstraints such as service rate, restriction on quantity order, and restrictionon warehouse space and budget. We also consider batch size for products order.Furthermore, a hybrid intelligent algorithm based on simulated annealing andfuzzy... 

This article points out the real-world prevalence of the multiple-product, multiple-constraint newsboy problem with two objectivesthe 'newsstand problem'in which there are total and incremental discounts on purchasing prices. The constraints are the warehouse capacity and the batch forms of the order placements. The first objective of this problem is to find the order quantities that maximize expected profit, and the second objective is maximizing the service rate. It is assumed that the holding and shortage costs, modelled by a quadratic function, occur at the end of the period. Moreover, the decision variables are integer. A formulation of the problem is presented and shown to be an... 

In this paper, a multi-product multi-chance constraint joint single-vendor multi-buyers inventory problem is considered in which the demand follows a uniform distribution, the lead-time is assumed to vary linearly with respect to the lot size, and the shortage in combination of backorder and lost-sale is assumed. Furthermore, the orders are placed in multiple of packets, there is a limited space available for the vendor, there are chance constraints on the vendor service rate to supply the products, and there is a limited budget for each buyer to purchase the products. While the elements of the buyers' cost function are holding, shortage, order and transportation costs, the set up and... 

An uncertain economic order quantity (UEOQ) model with payment in advance is developed to purchase high-price raw materials. A joint policy of replenishments and pre-payments is employed to supply the materials. The rate of demand is considered LR-fuzzy variables, lead-time is taken to be constant, and it is assumed that shortage does not occur in the cycles. The cycle is divided into three parts; the first part is the time between the previous replenishment-time to the next order-time (t0), the second part is the period between t0 to a payment-time (tk), and the third part is the period between tk to the next replenishment-time. At the start of the second part (t0), α% of the purchasing...