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DECISION MODEL FOR THE DESIGN AND OPERATION OF INVENTORY PROGRAMMES IN A MANUFACTURING INDUSTRY
CHAPTER ONE INTRODUCTION
1.1 Inventory Management
Various definitions have been given by different authors to inventory management. Black [1] described inventory as a buffer between supply and demand. Jonah et al [2] described it as stock of goods or material awaiting delivery or dispatch. While Monks [3] described it as stock of goods or item held for future use. From the foregoing one can see that good inventory management in a firm would lead to greater profits, minimized losses, greater customer satisfaction, stabilized employment, enhanced product quality and other latent benefits of inventory.
Failure to meet demand in any company usually compromises customer satisfaction and attracts high cost that characterizes emergency production. Efficient management of inventory system is therefore very critical in the operations of any firm.
Black [1] outlined the basic benefits of inventory management to the customer as off-the-shelf availability of products while to the management as reduced tied-up investment capital on inventory, reduced operating cost and carrying cost associated with warehousing and reduction in the accruing obsolescence of product.
From observations it can be said that a lot of failed investments did so as a result of inefficient inventory management.
In this work our emphasis is on backordering. As Fisher [4] observes, there may be some economic reasons for a company to decide not to satisfy all demand, but rather lose some sales in the interest of the company. We consider a situation where rather than accumulating a lot of buffer stocks and attracting spoilage, some stocks can be back-ordered, some lost and sufficient costumer and company satisfaction achieved.
Introduction Partial Back logging
On every research on inventory, it is always customary to establish optimal parameters which would ensure effective management of inventory. Two major parameters of interest are “optimal order quantity” and “optimal reorder point”. This would ensure a comfortable trade-off between the cost of inventory holding and the cost of shortage.
The phenomenon of shortage has been a recurring issue in modern inventory management. Another concept that is akin to it is the concept of “yield uncertainty, or “yield randomness”.
Yield uncertainty or yield randomness is simply a situation where the quantity of goods received does not equal the quantity requisitioned, due to factors like defective production, miscounting, breakage and pilferage.
Researchers in inventory theory and management have tried, to capture this situation through modeling, so as to enable inventory managers make well informed management decisions. One way this has been done is to consider the
possibility of keeping all the demands occurring within the time when there are shortages until a new consignment is received to fill the outstanding demands. This approach is known as complete Back-ordering or complete Backlogging. Another way to deal with this problem is to assume that all demands occurring within this period are lost which is known as “Total lost sales”. However a more dynamic situation is to realize that while some units of the demands occurring within the shortage period can be backordered others are permanently lost. This is an intermediate situation to the two mentioned above and is called Partial Backordering.
Partial Backordering posses one difficulty of complicated models which are not easy to handle. A major drawback of this system also is that the reorder point is not systematically determined. That is the reorder point because it is not included in the model is not determined by the conditions within the model.
Jonah et al (2) modeled the system using the length of stock-out period and the length of the inventory review period. They also tried to deal with the problem of “reorder point” by developing a closed form model parameters.
In this research a modification of the model by Jonah and Chukwu would be attempted, and an application of same to the Brewing industry would be explored.
1.3 Classification of Inventories
Types of inventories: Basically inventory can be classified into three different forms.
- Raw material inventory: This is the inventory of all the raw materials used in the production
- Work in progress inventory: This is the inventory of semi-
completed goods (work in progress) calculated at various points in the production process.
- Finished goods inventory: These are the inventory of the products of a They are frequently held throughout a firm‟s distribution channels even unto retail state.
1.4 Functional Classification of Inventories
Apart from classifying inventory according to its form, we can as well classify inventory according to its function, some of which are:
- Anticipatory Inventory: This inventory is accumulated when a firm produces or purchases more than its immediate requirements in low demand periods to anticipate the needs of high demand periods. By building up its anticipatory inventory the firm smoothes its production requirements. This type of inventory is very helpful when demand is seasonal.
- Cycle Inventory: This is when in order to reduce unit purchase cost (for increased production efficiency) the number of units purchased is greater than the firms immediate It may be more economical for purchasing to order a
large quantity of units and store some for future use than to make a series of small orders. With some items the firm may be forced to produce a minimum quantity. Production at sizes that exceed immediate requirements are normally chosen to offset the cost of lengthy process set-ups.
- Pipeline Inventory: These are items that have been ordered but not yet They are said to be created by materials moving forward through the value chain. It may be inventory moving from supplies to plants and from sub- contractors, from one operation to the next within the plant and from the plant to the firm‟s distribution channel.
- Decoupling Inventory: This inventory enables the synchronization between adjacent processes or operations whose production rates are not
- Safety or Buffer Inventory: This is inventory held to offset the risk of unplanned production stoppages or unexpected increases in customer
- Dependent and Independent Demand Inventory: Demand can be said to be dependent when it can be derived from the demand for other items produced by the firm whereas independent demand is when it is unrelated to the demand for other items produced by the firm.
- Classification by Quantities: This brings to bear the idea of ABC classification, where inventory are categorized according to quantities and
- A-class: These are items with higher values but with lower demand or usage in the Production machines and spares can be classified here.
- B-class: These are the items with intermediary demand and
- C-class: These are items with lower values but of regular The consumables are usually classified here.
- Deterministic/Probabilistic Demand Inventory: Inventory can further be divided into two areas: the deterministic inventory is a situation where the demand is known, such that for any given period of time the quantity to be ordered is known where as the probabilistic inventory is such where the demand is seasonal and stochastic and is described by probability
1.8 Background of the Work
Researchers for many years have studied the relations to various areas of inventory control, such as raw materials, work in process, finished goods and supplies inventory. Instruments for measurement of inventory like the ABC classification, Bar-coding, inventory counting, inventory turnover and quantity discounting have been established. Theories of precession like the just-in-time system, kanban system and the backlogging systems have also been established. Some of these theories have been made use of by researchers todevelop models which when applied to some specific areas are functional.
Harris et al [5] is one of the first to appear in print. He developed the basic and widely used Economic Order Quantity (EQQ) which is the reference point of most useful inventory theories today.
Oluyele et al [6] presented a system dynamic modeling of Nigerian automotive battery production organization, where policy runs of the system simulations were done to evaluate the impact of the size and pattern of demand.
Aderoba, et al [7] developed a model for progressive inventory management for job shops where the developed model incorporates salient characteristics like uncertainty of demand, limitations of space and funds and multiple materials.
Giri et al [8] presented a paper which considers an economic lot production quantity problem for an unreliable manufacturing system which the machine is subject to random failure (at most two failures in a production process). They established a model whereby shortages can be managed by accepting the existence of an on-hand inventory.
Mc Lachlin [9] established an EQQ model for deteriorating items where the supplier offers a permissible delay in payment. Their model allows not only the partial backlogging rate to be related to the waiting time but also the unit selling price to be larger than the unit purchase cost.
On the environs of this research work there are other models like that of Sheng [10] who defined a time dependent partial backlogging rate and introduced an opportunity cost due to lost sales. He established that the larger
the waiting time for the next replenishment the smaller the backlogging rate would be. Moreover the opportunity cost due to the lost sales should be considered since some customers would not like to wait for backlogging during the stockout period.
Faaland et al [11] addressed the economic lot scheduling problem where a manufacturer makes a variety of products types on a single facility or assembly line. The model accounts for the time to set up the facility and charges a penalty on each unit short regardless of whether shortages actually result in lost sales or not. The model considers a situation in which a cycle is complete when one batch of each product type has been set up, and produced. They assumed that production is at constant known rate and a profit maximization firm and also that some lost sales may be attractive in compromise with inventory carrying cost.
Netessine et al [12] presented the willingness of customers to backorder as a function of customer incentive that accompany the backorder. They analysed the impact of offering a monetary incentive on the optimal inventory policy by introducing an appropriate relationship between the proportion of backlogging customers and the incentive to backorder. They concluded that under some technical assumption other competitor‟s optimal inventory policy are monotone in the amount of incentive offered.
With this background, a further study on partial backordering stock and accepting some lost sale to arrive at a good inventory policy for a company will be made.
1.9 Problem Statement
Consider a firm that operates a random placement of orders on raw materials, upholds an infinite production process and delivers to customers when the customers is available. If supplies are made to a clone system of customers the firm may run into a problem of over-production and its attendant consequences. According to Ezema [13] the problem of most companies is that of inadequate planning and control of production activities. Many companies lack the technical know-how while others ignore the practice of inventory control entirely.
Another version of problem associated with inventory is the non- placement of order except there is requisition from customers. Akin to this are delays in supplies to customers and the likely losses of customers and sometimes permanently. This research seeks to establish a good inventory management policy that would bridge the gap between overstocking and under- stocking and also enhance quick delivery of orders.
1.10 Objectives of the Work
If it is possible it would rather be preferable for a company not to hold inventories since it may mean tying up cash in goods that would have rather improved the company‟s financial base. However, considering the fact that not holding inventories leads to incessant failures in production, the study of inventory management becomes inevitable. It is to enable a company to arrive at a point in its stock holding capacity where the holding cost will not be at the detriment of the company. In consideration of this fact we derive the objectives as:
- To capture prompt delivery to customers
- To reduce to the least possible the holding cost by choosing to rather backorder instead of accumulating
- To reduce buffer stocks to a known quantity such that even during uncertainties losses are
- To smoothen demand even when it is
1.11 Need and Importance of Work
A lot of companies operate without recognition o f the importance of inventory whereas good inventory management determines the wealth of any firm. This work would be important and applicable to companies that operate on either of two classes of inventory, the raw material inventory and finished product inventory. As usual it would be applied to a specific type of firm and if required in others firms, modification should be made to enable it fit into the
requirement of the given firm. It is therefore expected that good inventory control and infact the application of the model would go a long way to harness the wealth of the company of application.
1.12 Scope of the Work
In this research work a model which can be used to determine the total cost of inventory with backordering the quantity and the re-order point will be developed. The model will be tested with a given company and recommendations would be made following the results obtained.
1.13 Methodology
The work would be carried out through the following approach:
- The model by Jonah et al [2] will be slightly The research of Jonah and Chukwu is basically a theoretical analysis of a general situation, bringing both total back-ordering, total lost sales and partial backordering cases. In their analysis they made use of figures not obtained from real situation and also guessed some bias factors and variance which they used in their theoretical analysis. However this situation will endeavour to break down the case of partial back ordering by analyzing the development of the model and then employing same in the estimation of the Quantity and Recorder point making use of a real situation.
- Data will be collected from a given company in the brewing industry covering the following:
- Demand rate
- Set-up cost
- Variable costs
- Carrying or holding costs
- Shortage costs
- Backordering costs
- Profits
- The lower bound for the partial backordering rate will be
- The length of the inventory period (T), the fill rate (F) and consequently the order quantity (Q) and shortages (S) will be determined
- The re-order point will be established by applying the result above and the re-order point
1.14 Definition of Fundamental Terms
Demand: This is the sum total of customers requirements for a given time, usually per year.
Lead Time: This is the time limit between the placement of an order and the subsequent arrival of same to fill the inventory.
Base Stock Level: This is the maximum level that the replenishment should bring the stock level to.
Inventory Level: Is the instant level of on hand inventory.
Backorder: This is a given quantity of customer demand during stock-out of which he is prepared to wait and receive after replenishment.
Continuous Review: Is an inventory replenishment policy whereby replenishment is done at any point.
Economic Order Quantity (EOQ): The optimal replenishment level that would best minimize the holding cost and order of on hand inventory.
Fill Rate: This is the fraction of the demand that is filled from on hand inventory.
Holding Cost: This is the cost per unit of holding stock in inventory and comprises of rents, insurance and opportunity cost of tied up capital.
Inventory Level: This is the on-hand inventory less of backorders.
Lost Sales: These are sales that are lost due to non-availability of stock. If the waiting time for delivery of an order is too long.
Obsolescence: Where stock is no more usable for its intended purpose, by way of expiration, damage, contamination or shift of market.
On-hand Inventory: The instant available stock in inventory.
Lower Bound: This is the least value that partial backordering rate assumes for the partial backordering model to be applicable.
Yield Variance: Is the variance of the yield distribution. The quantity that makes the quantity ordered to differ from the quantity received.
Re-order Quantity: The number of items to be ordered during replenishment.
Safety Stock: Inventory which serves to promote continuous supply when unpredictable demand exceeds forcast, or the delivery of materials from the supplier is delayed.
Service Level: This demonstrates the fraction or percentage of order cycle during the year in which there are no stock-outs.
Set-up Costs: These are the costs of labour materials and marginal costs of machines or work station set-up.
Shortage Cost: The cost incurred when a sub-optimal inventory item must be used to produce an order, due to a stock out of the optimal inventory item.
Stationary Demand: Demand having a single probability distribution that does not change order time.
Stock: The items in the warehouse to support operations.
