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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 consists of one vendor and several retailers. The vendor supplies a product to several retailers, buying 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'll be immediately received at the vendor's warehouse. In this system, shortage is not allowed for the vendor. The transportation time from the... 

Nowadays, inventory management plays a crucial role in manufacturing supply chains. Vendor-managed inventory (VMI) program is a collaborative initiative that shows considerable performances in managing inventories through the supply system. In this study, we discuss the VMI initiative in a serial manufacturing supply chain when there is an uncertainty in demand and provide an approximate closed-form formula for the economic lot size. In this paper, we consider a two-echelon supply chain system consisting of a manufacturer and a retailer. Under vendor-managed inventory program with centralized decision making, the manufacturer is authorized to manage inventories of all agreed upon stock... 

We consider an M/M/1 queueing system with inventory under the (r,Q) policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random variables and can take various distributions. The derived stationary distributions are used to formulate long-run average performance measures and cost functions in some numerical examples  

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... 

We consider M/M/1/∞ systems with inventory in which completing each service in the queueing system requires an on-hand inventory. Continuous review (r, Q) policy is considered for the inventory system, and lead times are assumed to be mixed exponentially distributed. During stockout, arriving demands get rejected from the queue and become lost (lost sale situation). We derive stationary distribution of product form of joint queue length and on-hand inventory. The resulting distribution is employed to compute performance measures which can be used to derive the optimal policy. Optimal order size for predetermined reorder policy is initially determined and finally, optimal reorder point and... 

Recently, for zero ordering cost a new ordering policy named (1, T), in which the time interval between two consecutive orders and the value of the order size are both constant, have been developed for nonperishable products. In this paper, the (1, T) policy is developed for perishable products. Using an analogy among this inventory model, a queueing model with impatient customers, and a finite dam model, the long-run average total cost function of the inventory system is derived. It is observed that the total cost rate is independent from the lead time as is for nonperishable products. Since analyzing the convexity of the model is extremely complicated, a proposition is proved to define a... 

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 deals with a single perishable item, continuous-review, two-echelon serial inventory system consisting of a warehouse and a retailer. Customer demands at the retailer are assumed to be Poisson. All items have a fixed shelf life and start aging on their arrival at the retailer. The demand that cannot be met immediately at the retailer is lost. All transportation times are fixed. If there is any stock in the warehouse, the lead time for the retailer would be the transportation time from the warehouse. Otherwise, the retailer orders are met with a delay. In this article, using an approximate technique, we first present a heuristic for finding cost-effective base stock policy and... 

This paper attempts to develop the optimal solution for an inventoryproblem consisting of a single machine which produces items some of which may bedefective. We assume that no shortages are allowed and all defective items areto be reworked. Setup cost for rework and waiting time of defectives areconsidered. We consider two different policies where in the first policy in eachcycle after the regular production the machine is setup for the rework ofdefectives of the same cycle. In the second policy several cycles constitute aperiod. All the defectives produced in the period are reworked in the last cycleof that period. At the end of the rework cycle the whole process starts allover again. One... 

In this paper a two-echelon supply chain consisting of a supplier and aretailer is considered, Customers refer to retailer according to a Poissonprocess and retailer uses one for one inventory policy. Supplier followscontinuous review (r,Q) policy. Satisfying each demand which arrives to thesupplier needs an on hand-inventory and a process/service. Process/service andreplenishment lead times are random variables which are exponentiallydistributed. During a period that supplier has non zero on-hand inventory,arriving demands from retailer join the queue. But when supplier has no on-handinventory retailer buys product from the other source with zero lead time andadditional cost. In this paper... 

In this article, we design a revenue-sharing contract to coordinate inventory control decisions in a serial supply chain consisting of one supplier, one vendor, and one retailer. We assume that the retailer faces Poisson demand and his unsatisfied demands will be lost. The retailer applies one-for-one period policy in which he constantly places an order for one unit of product to the vendor in a predetermined time interval which results in a deterministic demand for the vendor. Vendor orders the required quantity from supplier which will be immediately received at the vendor’s warehouse. Solution procedures are developed to find the equilibrium in the vendor managed inventory program with a... 

In this paper, we design a revenue sharing contract to coordinate pricing and inventory control decisions in a serial supply chain consisting of one supplier, one manufacturer and one retailer. We assume that the retailer faces Poisson demand and his unsatisfied demands will be lost. The retailer applies one-for-one period policy in which he constantly places an order for one unit of product to the manufacturer in a predetermined time interval which results in a deterministic demand for the manufacturer. Solution procedures are developed to find the equilibrium in the Vendor Managed Inventory (VMI) program with a revenue sharing contract, in which no party is willing to deviate from for the... 

In this paper, we develop an inventory model with price dependant demand rate, under time value of money and inflation, finite time horizon, exponential backlogging rate and exponential deterioration rate with the objective of maximizing the present worth of the total system profit. Using a dynamic programming based solution algorithm, we are able to find the optimal sequence of the cycles and also to obtain different optimal selling prices and optimal order quantities for the cycles with unequal lengths, which have never been done before for our model. We also use a proper numerical example to show accuracy of the solution procedure. © 2008 IEEE  

This study considers a two-level supply chain system consisting of one warehouse and a number of identical retailers. In this system, we incorporate transportation costs into inventory replenishment decisions. The transportation cost contains a fixed cost and a variable cost. We assume that the demand rate at each retailer is known and the demand is confined to a single item. First, we derive the total cost which is the sum of the holding mid ordering cost at the warehouse and retailers as well as the transportation cost from the warehouse to retailers. Then, we propose a search algorithm to find the economic order quantities for the warehouse and retailers which minimize the total cost. ©... 

In this paper we consider a two-level supply chain system consisting of one warehouse and one retailer. The retailer faces Poisson demand. We introduce a new approach to inventory control in the supply chain management which is different from the classical policies used in the literature of inventory and production control systems. In this system, the retailer constantly orders a fixed amount of product to the warehouse in a predetermined time interval; i.e., the ordering size and the time interval between any two consecutive orders from the retailer to the warehouse are fixed numbers. The advantage of this policy is that the warehouse is facing a uniform and deterministic demand which... 

In this paper we consider a dyadic supply chain consisting of one warehouse and one retailer with an unequal order batch size and information exchange. Transportation times are constant and retailer faces independent Poisson demand. The retailer applies continuous review (R,Q)-policy. The supplier starts with m initial batches (of size Q), and places an order in a batch of size nQ to an outside source immediately after the retailer's inventory position reaches R+s. In this paper using the idea of the onefor- one ordering policy we obtain the exact value of the expected system costs  

In this paper we develop two models; the without shortages and the completely backlogging shortages with the price dependant demand rate under time value of money and inflation, finite time horizon and exponentially deterioration rate with the objective of maximizing the present worth of the total system profit. Using the dynamic programming method for each model, we are able to obtain different selling price, order quantity and cycle length for each cycle. We also use a proper numerical example to show accuracy of the solution procedures and to compare the results. This research and its results are unique and have never been concluded before  

This paper considers a two-level supply chain consisting of one warehouse and a number of identical retailers. Unlike the common practice which determines the optimal ordering policy according to inventory costs only, in this model we consider the transportation cost as well. We suppose that the delivery of each order from the warehouse to any retailer is made by a single vehicle without splitting. We also assume that there are three types of vehicles which are defined as small, medium and large. Each type has its own fixed cost, variable cost, and the capacity size. We assume that the demand rate at each retailer is known and the demand is confined to a single item. Shortages are allowed... 

This paper considers economic batch quantity (EBQ) in a single machine system in which defective items are produced and are all reworked in the same cycle. In the literature of inventory control, when the rework is done in the same cycle, the setup times are not considered; the rework process starts immediately after each production run, and the waiting of defectives for rework is ignored. Considering these points we assume non-zero setup times for rework, delayed rework in the same cycle, and the cost of waiting, to obtain the EBQ for two different cases  

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...