A Production-Delivery Inventory System under Continuous Price Decrease and Finite Planning Horizon (original) (raw)
Computers & Industrial Engineering, 2011
This paper deals with an integrated multi-stage supply chain inventory model with the objective of cost minimization by synchronizing the replenishment decisions for procurement, production and delivery activities. The supply chain structure examined here consists of a single manufacturer with multi-buyer where manufacturer orders a fixed quantity of raw material from outside suppliers, processes the materials and delivers the finished products in unequal shipments to each customer. In this paper, we consider an imperfect production system, which produces defective items randomly and assumes that all defective items could be reworked. A simple algorithm is developed to obtain an optimal production policy, which minimizes the expected average total cost of the integrated production-inventory system.
Computers & Operations Research, 2006
Raw material ordering policy and the manufacturing batch size for frequent deliveries of finished goods for a finite horizon plays a significant role in managing the supply chain logistics economically. This research develops an ordering policy for raw materials and determines an economic batch size for a product in a manufacturing system that supplies finished products to customers for a finite planning horizon. Fixed quantities of finished products are delivered to customers frequently at a fixed interval of time. In this model, an optimal multi-ordering policy for procurement of raw materials and production cycle time for a two-stage production and supply system is developed to minimize the total cost incurred due to raw materials and finished goods inventories. The problem is then extended to compensate for the lost sales of finished products. A closed-form solution to the problem is obtained for the minimal total cost. A lower bound on the optimal solution is also developed for problem with lost sale. It is shown that the solution and the lower bound are consistently tight.
A Production Inventory Model Consisting Time Dependent Linear Demand and Constant Production Rate
2017
In this proposed model the products are considered to have finite life with a small amount of decay. The market demand is assumed to be linear and time dependent. It is also assumed that the production starts with zero inventories without any backlogs and the production rate is constant, stopping after inventories reach a desired highest level of inventories. Inventory depletes to zero level from where the production cycle starts. A numerical illustration for the proof of the proposed model has been shown. The objective of this model is to obtain the total optimum inventory cost. Mathematics Subject Classification: 90B05
In the present paper a volume flexible manufacturing system is considered for a decaying item with an inventory-level-dependent demand rate. In reality, the demand rate remains stock-dependent for some time and then becomes a constant after the stock falls down to a certain level. Many factors like limited number of potential customers and their goodwill, price and quality of the goods, locality of shop, etc. can be accounted for the change in the demand pattern. INTRODUCTION Inventory is a part of every fact of business life. Without inventory any business can not be performed, whether it being service organization. Under increased competition, inventory based business are forced to better coordinate their procurement and marketing decisions to avoid carrying excessive stock when sales are low or shortages when demand are high. An effective means of such coordination is to conduct the inventory control and manufacturing decision jointly. The main task is to determine the optimal rate of production and inventory policy for a given time varying demand. In the Classical Economic Production Lot Size(EPLS) model, the production rate of a machine is regarded to be pre-determinded and inflexible1.Alder and Nanda (1974), Sule (1981), Axsater and Elmaghraby (1981), Muth and Spearmann (1983) extended the EPLS model to situations where learning effects would induce an increase in the production rate. Proteus (1986), Rosenblat and Lee (1986) and Cheng (1991) considered the EPLS model in an imperfect production process in which the demand would exceed the supply. Schweitzer and Seidmann (1991) adopted, for the first time, the concept of flexibility in the machine production rate and discussed optimization of processing rates for a FMS (flexible manufacturing system). Obviously, the machine production rate is a decision variable in the case of a FMS and then the unit production cost becomes a function of the production rate. Khouja and Mehrez (1994) and Khouja (1995) extended the EPLS model to an imperfect production process with a flexible production rate. Silver (1990), Moon, Gallego and Simchi-Levi (1991) discussed the effects of slowing down production in the context of a manufacturing equipment of a family of items, assuming a common cycle for all the items. Gallego (1993) extended this model by removing the stipulation of a common cycle for all the items. But the above studies did not consider the demand rate to be variable. It is a common belief that large piles of goods displayed in a supermarket lead the customers to buy more. Silver and Peterson (1985) and Silver (1979) have also noted that sales at the retail level tend to be proportional to the inventory displayed. Baker and Urban (1988) and Urban (1992) considered an inventory system in which the demand rate of the product is a function of the on-hand inventory. Goh (1994) discussed the model of Baker and Urban18 relaxing the assumption of a constant holding cost. Mandal and Phaujder (1989) then extended this model to the case of deteriorating items with a constant production rate. Datta and Pal (1990) presented an inventory model in which the demand rate of an item is dependent on the on-hand inventory level until a given inventory level is achieved, after which the demand rate becomes constant. Giri , Pal , Goswami and Chaudhuri (1995) extended the model of Urban (1992) to the case of items deteriorating overtime. Ray and Chaudhuri (1997) discussed an EOQ (economic order quantity) model with stock-dependent demand, shortage, inflation and time discounting of different costs and prices associated with the system. Ray, Goswami and Chaudhuri (26 studied the inventory problem with a stock-dependent demand rate and two levels of storage, rented warehouse (RW) and own warehouse (OW). Giri and Chaudhuri (1998) extended the model of Goh (1994)
An inventory model with variable demand, component cost and selling price for deteriorating items
Economic Modelling, 2013
In this paper, we develop an economic order quantity (EOQ) model for finite production rate and deteriorating items with time dependent increasing demand. The component cost and the selling price are considered at a continuous rate of time. The objective of this model is to maximize the total profit over the finite planning horizon. We also want to find the integral number of orders in the finite planning horizon. A numerical example, graphical representations and sensitivity analysis are given to illustrate the model.
International Journal of Industrial and Systems Engineering, 2011
Most of the existing research has focused on a two stage single-vendor single-buyer supply chain. However, in reality, supply chain networks are more complex and involve more than just a vendor and a buyer. This paper deals with the joint economic lot sizing problem (JELP) in the context of a three stage supply chain consisting of a single supplier, single manufacturer and multi retailers. The objective is to specify the timings and quantities of inbound and outbound logistics for all parties involved such that the chain-wide total ordering, setup, raw material and finished product inventory holding costs are minimized. In developing the model, the cycle time at each stage is set to be an integer multiple of that for the adjacent downstream stage. To bear a better resemblance to practice, shipments from a particular lot are allowed to take place during production and not after producing the whole lot. We employ derivative-free methods to derive a near closed form solution for the developed model. A numerical example is presented for illustrative purposes and a comparison to models established in the literature is also provided.
A production inventory model with exponential demand rate and reverse logistics
International Journal of Industrial Engineering Computations, 2014
The objective of this paper is to develop an integrated production inventory model for reworkable items with exponential demand rate. This is a three-layer supply chain model with perspectives of supplier, producer and retailer. Supplier delivers raw material to the producer and finished goods to the retailer. We consider perfect and imperfect quality products, product reliability and reworking of imperfect items. After screening, defective items reworked at a cost just after the regular manufacturing schedule. At the beginning, the manufacturing system starts produce perfect items, after some time the manufacturing system can undergo into "out-of-control" situation from "in-control" situation, which is controlled by reverse logistic technique. This paper deliberates the effects of business strategies like optimum order size of raw material, exponential demand rate, production rate is demand dependent, idle times and reverse logistics for an integrated marketing system. Mathematica is used to develop the optimal solution of production rate and raw material order for maximum expected average profit. A numerical example and sensitivity analysis is illustrated to validate the model.
An inventory model for deteriorating items with varying demand pattern and unknown time horizon
2011
The primary assumptions with many multi-period inventory lot-sizing models are fixed time horizon and uniform demand variation within each period. In some real inventory situations, however, the time horizon may be unknown, uncertain or imprecise in nature and the demand pattern may vary within a given replenishment period. This paper presents an economic order quantity model for deteriorating items where demand has different pattern with unknown time horizon. The model generates optimal replenishment schedules, order quantity and costs using a general ramp-type demand pattern that allows three-phase variation in demand. Shortages are allowed with full backlogging of demand and all possible replenishment scenarios that can be encountered when shortages and demand pattern variation occur in multi-period inventory modeling are also considered. With the aid of numerical illustrations, the advantages of allowing for variation in demand pattern within replenishment periods, whenever they occur, are explored. The numerical examples show that the length of the replenishment period generated by the model varies with the changes in demand patterns.
Inventory control has one of the most important tasks faced by modern manager. The investment in inventories for most form their assets committed to inventories. Further inventories one often the least stable and difficult to manage type of assist. Rapid change in level of business activities effect on inventories. In recent year, change in interest rate effect the inventories. Employ and customer theft has also led to increased cost of maintaining inventories. But carrying inventory is a costly thing as the storage cost, stock out cost, capacity related cost, item cost, ordering cost, deterioration and expiration of the product etc. must be taken in to account. Some policies, procedures and techniques employed in maintaining the optimum number of amount of each inventory item is the inventory management. While inventory is an asset, it is a non productive asset since it earns no interest but costs an organization in handling insurance, taxes, shrinkage and space. Careful inventory management can make a huge difference in the profitability of a firm. K EYWORDS: Modern manager, customer INTRODUCTION Classical deterministic inventory models consider the demand rate to be either constant or time-dependent but independent of the stock status. However, for certain types of consumer goods (e.g., fruits, vegetables, donuts and other) of inventory, the demand rate may be influenced by the stock level. It has been noted by marketing researchers and practitioners that an increase in a product's shelf space usually has a positive impact on the sales of that product and it is usually observed that a large pile of goods on shelf in a supermarket will lead the customer to buy more, this occurs because of its visibility, popularity or variety and then generate higher demand. In such a case, the demand rate is no longer a constant, but it depends on the stock level. This phenomenon is termed as 'stock dependent consumption rate'. In general, 'stock dependent consumption rate' consists of two kinds. One is that the consumption rate is a function of order quantity (initial stock level) and the other is that the consumption rate is a function of inventory level at any instant of time. The consumption rate may go up or down with the on-hand stock level. These phenomena attract many marketing researchers to investigate inventory models related to stock-level. Conversely, low stocks of certain baked goods (e.g., donuts) might raise the perception that they are not fresh. Therefore, demand is often time and inventory-level dependent. This paper strives; an inventory model for deteriorating items with multi variate demand rate under inflationary environment. We have taken a more realistic demand rate that depends on two factors, one is time, and the second is the stock level available. The stock level in itself obviously gets depleted due to the customer's demand. As a result, what we witness here is a circle in which the customer's demand is being influenced by the level of stocks available, while the stock levels are getting depleted due to the customer's demands. This assumption takes the customer's interests as well as the market forces into account. The demand rate is such that as the inventory level increases, it helps to increase the demand for the inventory under consideration. While as the time passes, demand is depends upon the various factors. The competitive
Inventory models with variable lead time and present value q
The figures for inventory make up a huge proportion of a companyÕs working capital. Because of this, we formulated the optimal replenishment policy considering the time value of money to represent opportunity cost. In this article, we provide a mixed inventory model, in which the distribution of lead time demand is normal, to consider the time value. First, the study tries to find the optimal reorder point and order quantity at all lengths of lead time with components crashed to their minimum duration. Secondly, we develop a method to insure the uniqueness of the reorder point to locate the optimal solution. Finally, some numerical examples are given to illustrate our findings.