This study deals with the review and analysis of the literature and studies relevant to inventory management techniques that the researchers will be using in the optimization. It consists of information culled from studies and literature, both local and foreign, from which this study is subject to. This chapter will certainly help in giving the reader a better understanding of what is Economic Order Quantity model and Dynamic Programming to optimization of the inventory system.
Inventory refers to any kind of resources having economic value and is maintained to fulfil the present and future needs of theconsumers.
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It is a physical stock of items that business or production enterprise keeps in hand for efficient running of affairs or its production. Inventory is the quantity of goods, raw materials or other resources that are idle at any given point of time. Inventory control is the means by which materials of the correct quantity and quality is made available as a when required with due regard to economy in storage and ordering costs and working capital.
It is also defined as the systematic location, storage and recording of goods in such a way that desired degree of service can be made to the operating shops at a minimum ultimate cost” (S.C sharma (1999). P. 509, 512).
Inventory model: Economic Order Quantityand Dynamic Programming
For over a century, the literature encompassing hundreds of books and journals has included frequent writings of management scientists applying quantitative methods to help inventory managers make two critical decisions: how much inventory to order, and when to order it.
Inventory management started as early as the beginning of the 20th century when F. W. Harris originally developed the lot size formula or the EOQ model in 1915. R. H. Wilson independently developed the same formula in 1918. Apparently, Wilson popularized the model so the EOQ model is also referred to as the Wilson EOQ model.
The EOQ formula has been independently discovered many times in the last eighty years. It is simplistic and uses several unrealistic assumptions. In Cargal discussed the basic EOQ model; he said that they cannot determine what quantity of an item to order when ordering supplies. Despite the many more sophisticated formulas and algorithm available, some large corporations still use the EOQ formula. In general, large corporations that use the EOQ formula do not want the public or competitors to know they use something so unsophisticated.
The variables, graph, and the formula was also discussed in this paper. The classic EOQ model has been directly used in practice but which, more importantly, represents the key foundation of decision rules dealing with more complicated circumstances.Different variations and applications of the EOQ model in production and inventory operations were expanded over the years such as dealing with the quantity discounts, shelf-life considerations, replenishment lead time and constraints on the replenishment. Further advancements in inventory management took place when dynamic programming was used, with R. Bellman as its founding father. However, earlier works in DP were produced by Arrow, Karlin and Scarf.
Bellman, who popularized DP, used the stochastic models for the inventory management problems. But in 1958, Wagner and Within started with a deterministic model, referred to as the Wagner-Within method, with known demands in each period, and fluctuating costs from one period to the next. A few years later, results for the stochastic model were established by Iglehart and Wagner with Veinott, which involves a demand with a continuous distribution.
Inventory models have been applied and adapted by organizations. Silver enumerated the extensive research and application done over the years. In retail inventory management, retail outlets are increasingly adopting equipment that permits capture of demand data and updating of inventory records at the point of sale. In integrated logistics, a very complex system, it utilizes operations inventory management where maintenance, transportation and/or production are involved. In interactions with marketing, inventory management is applied on how to routinely take account of the effects of promotional activities on the control of inventories, how to predict and account for the effects of the system on the demand pattern, and the allocation of the shelf space in outlets such as supermarkets.
Stock on Inventory
The American Institute of Accountants defined the term inventory as “the aggregate of those items of tangible property which (1) are held for sale in the ordinary course of business, (2) are in process of production for such sale or (3) are to be available for ‘sale’. In Nigeria, inventory is usually referred to as stock-in-trade or work-in-progress. Stock may consist of (i) Raw materials and supplies to be consumed in production (ii) work-in-progress, or partly manufactured goods, (ii) Finished stock or goods ready for sale. Stocks are valued in a fundamentally different way from fixed assets; the latter are usually valued at cost less accumulated depreciation. No method of stock valuation is suitable for all types of business in all circumstances. Stock is valued at cost less any part of cost, which needs to be written off when net realizable value or the replacement price is lower than cost.
The Functions of Inventory
Inventories perform a number of vital functions in the operations of a system, which in turn makes them critical to the production sector as well. Without inventories, organizations could not hope to achieve smooth production flow, obtain reasonable utilization of machines and reasonable handling cost or expects to give reasonable service to customers. The basic function of inventories whether they are raw materials, work-in-progress or finished goods are that of decoupling the operations involved in converting inputs into outputs.
This allows the successive stages in the purchasing, manufacturing and distribution process to operate reliance on the schedule of output, of prior activities in the production process. Furthermore, the decoupling function allows both time and spatial separation between production and consumption of products in the operating system. Lastly, inventories can also be used for other purposes apart from the decoupling functions. For example, when inventories are displayed, they serve as promotional investment. Raw materials and finished inventories are frequently accumulated to wedge against price rises, inflation and strikes.
Inventories also serve to smooth out irregularities in supply. In essence, inventories act to decouple organizational activities, thereby achieving lower costs of operations. Inventories act to reduce procurement costs, and inventories act to provide good customer service and smooth production flow by providing onetime delivery and avoiding costly stock shortages. Inventories ordered in large quantities can result in lower freight charges and price discounts. On the other hand, inventory requires tying up capital that would otherwise be invested elsewhere.
Inventory also requires costly storage space; and such costs as insurance, spoilage obsolesce, pilferage and taxes must be incurred as a result of maintaining inventory. Hence, there is an appropriate opportunity cost associated with their value. It is therefore, the duty of the management to seek decision rules that will actually balance these controversies of costs for a given system. It is in response to this management quest for guidance in handling inventory decision situations that a number of techniques (models) have been developed to serve as aid to management in achieving optimal inventory solutions.
The objectives of materials management are to minimize inventory investments and to maximize customer service. It is a plan to see that, the goals can be inconsistent or even indirect conflicts the role of the materials management is thus to balance the objective in relation to the existing conditions and environmental limitations. The basic object of inventory management is to maximize customer service through maintaining appropriate amount of inventory with minimum possible cost. Inventory costs are costs associated with the operation of an inventory system. Thus the relevant costs included inventory are the following:
The purchase cost (P)The purchase costs of an item are the unit purchase it is obtained from an external source or the unit production costs it is produced internally. For the purchase items it is the purchase costless modified for different quantity levels manufacturing items the unit cost include direct labour or company overhead. Ordering or set up cost (C)This is the cost of placing an order. This cost directly with the number of order or setups placed and not at all weigh the size of the order. The ordering cost included making analysing materials inspecting materials follows up orders and doing the processing necessary to complete the transaction. Carrying costs or holding costs (H)There are costs of items (inventories) in storage.
These costs vary with the level of inventory and occasionally with the length of item an item is held. The greater the level of inventory overtime, the higher the caring cost caring casts can be included the costs of losing the use of funds field up in inventory like storages casts such as rent of building heating cooling righting security, record keeping, deprecation obsolescence, product deterioration etc. Stock out cost (shortage cost) This is the cost as a result of not having items in storage.
This can bring loses of good will profit loss of incur back order cost and delay in the customer service. Establishing the correct quantity to order from vendors or the size of lots submitted to the firms productive facilities involves a search for the minimum total cost resulting from the combined effects of fewer individual costs holding costs, setup costs ordering costs and storage costs (Tersine, R.J, 1994. PP. 13-15)
Inventory Costing Method
There are three methods of inventory costing method. These are:First – in First – out (FIFO)This method is based on the assumption that costs should be computed out in the order in which incurred. Inventory is thus stated in terms of recent costs. Last – in First – out (LIFO)is a method based on the assumption that goods should be charged out the latest cost be the latest cost be the first that are charge out. Inventories are thus stated in terms of earliest cost.Weighted average method is a method based on the assumption that goods should be charged out at an average cost such average being influenced by the number of unites acquired at the price. Inventories are stated at the same weighted average cost.