This paper compares the two analytical methods with a selected situation to determine inventory policy and managerial insights.
Economic Order Quantity model: Cited in Whisler and Lapin (2002)
The purpose of the Economic Order Quantity model is to find the quantity of an item to order so as to minimize the total inventory cost.
In an EOQ model there are three component costs involved in the computation
- Fixed cost per order (denoted by the variable ‘k’)
- Cost of holding $1 of inventory for 1 time-period – usually one year – denoted by the variable ‘h’
- Procurement cost (denoted by the variable ‘c’)
The other two components involved are:
- Annual number of items demanded – denoted by the variable A
- Time between orders – denoted by the variable T
The main objective of the Economic Order Quantity model is to find the optimal order quantity denoted by Q*; the classical formula to obtain this value is presented by Wilson. The formula is:
Q* = (2Ak/hc) ^1/2
After Q* has been obtained, the corresponding reorder time and the total annual relevant cost is determined to be:
T* = Q*/A
AND
TC (Q) = [(A/Q) k] + [h c (Q/2)]
On the other hand the total cost can be determined by simulation. Simulation uses randomly fluctuating levels of demand to obtain an optimal inventory in cases where demand is uncertain and expected to fluctuate. These two methods are applied to a hypothetical case study, and their results are compared.
Problem Statement
One touch solution limited is a small-scale manufacturer of compact disc and mini CD’s. The demand for compact disc is growing due to the growth in the software industry.
The holding cost of CDs $ 0.39 for each dollars value held in inventory. The fixed ordering cost is $ 45 irrespective of the number of CDs ordered. When out of stock One touch solution ltd. purchases the required CDs from david jones at a price of $ 2 above the price which they receive from their wholesaler. The whole seller charges them is $ 4 per CD.
Over a year One-touch solution ltd. sell 3200 units. One-touch solutions’ wholesaler requires 1-month lead-time to fulfill a particular order. New order will be placed at the beginning of any month having and initial inventory of less than 250.
One touch solution ltd. sells each CD for $ 6 to the general public.
Based on the previous usage patterns, the following forecast usage applies for the next 12 months.
EOQ results
The perplexing and continuing questions for One Touch Solutions are how much to order, how much it will cost and when to reorder. The Economic Order Quantity model answers the above questions, giving the optimal inventory policy for One Touch Solutions Ltd. The present inventory policy as developed for One Touch Solutions Ltd shows the following results:
According to the EOQ (refer Appendix –I) the optimal quantity to be ordered is 430 units every month. The relevant cost associated with this order quantity is $ 13,470.28
- The optimal order quantity (Q*) is 430 units.
- The total relevant cost scaled to one year - TC (Q*) is $13,470.28
- The cycle time / time between orders (T) is 50 days.
With the above example, the following advantages make the scorecard for the EOQ model:
- The most important advantage is that it provides the optimal order quantity at the minimum possible cost.
- It provides an approximation of cycle time. A reorder point is arrived at with this model.
- It is easy and simple to implement in almost any kind of organization.
However, these advantages are counterbalanced by the disadvantages of the Economic Order Quantity model that arise because of its simplicity:
- The EOQ model is so simple that it cannot yield accurate results to fit real world situations.
-
The assumption of consistent demand is not true. Demand trends cannot be predicted, and can vary according to day-to-day happenings. For example, demand patterns were radically changed in the USA after the occurrences of September 11th.
- One of the main assumptions of the EOQ is that the cost of the product is fixed but in real world circumstances, the product cost is variable.
- The EOQ method does not take into account the lead-time in the movement of inventory. Lead times play a crucial role in inventory policy, as there is most often a gap in time between the fulfillments of orders.
In many industries demand is becoming more and more variable and uncertain. Such fluctuations of demand are sometimes due to quick changes in the final customer's preferences and taste, but quite often the supply chain is an important source of demand uncertainty. In supply chain inventory management, one of the challenges is how to manage demand uncertainty. In fact, demand uncertainty is the "root of evil" which accounts for the large supply chain inventory cost. Literature has discussed and analyzed this phenomenon called the Bullwhip Effect (e.g., Lee, Padmanabhan and Whang 1997), observing that, while moving towards the higher levels of the supply chain, orders show a more variable and uncertain pattern. The causes of this behavior are several: erroneous demand forecasting, supply shortages, long lead times, batch ordering, price variations and inconsistency of the customers located in the lower levels of the chain. Choosing an efficient inventory management policy for a generic product means gives the answer to the main issue of managing demand uncertainty.
In practice, it is found that underlying assumptions of the Economic Order Quantity model are so restrictive that it becomes limited in its application. Hence the need for simulation is increased.
A spreadsheet is used to simulate the identical example of One Touch Solution Ltd. (refer Appendix-II)
Results of the simulation are summarized as follows:
- The total cost is $ 12143.95
- The holding cost is $ 118.95
- The shortage cost is $ 2220.00
Comparing the results obtained from the first model Economic Order Quantity model the following differences are noticeable. The total cost under simulation is $ 12143.95; using largely the same parameters the corresponding Economic Order Quantity value is 13,470.28. The comparison displays one of the major advantage of simulation over Economic Order Quantity model that is simulation produces more effective inventory policy with reduced total cost for the optimal order quantity.
The major tangible benefit is the reduction in total inventory costs. The total inventory cost saving resulting from the increased efficiency and improved accuracy of the ordering policies can be observed from the comparison of EOQ and simulated ordering policies. A considerable amount of reduction in the total inventory costs was observed. This finding is also in a research work by Nagarur, Tai-san Hu, & Baid (1994)
One-month lead-time that was used in obtaining simulating results could not be incorporated in the Economic Order Quantity model. With the EOQ assumption of no lead-time it is assumed that there is instantaneous transfer of physical goods as well as possession. The uncertainty on lead-time is also a complicating factor – simulation can takes this into account. Stock outs are also assumed away in the EOQ model. Ideally this is never the case.
Perhaps the most important advantage is that it takes into account the varying demands. In EOQ model it is assumed that demand does not fluctuate but remains static. This assumption is highly unreasonable in most industries; demand usually fluctuates constantly and may not be distributed uniformly over the planning period. This underlying assumption of EOQ model makes it unrealistic and limits its acceptability.
Business Impact
Inventories are present in every business. If inventory level is high, maintaining the inventories is expensive and if the inventory level is low it will results in frequent orders to meet the demand, which in turn will lead to ordering expenses. Procuring and maintaining the right size of inventory is a primary concern of any organization while developing an inventory policy. Models like EOQ and simulation have a great impact on the business while answering such questions. Such models might be used in any kind of organization and for any kind of inventory. With managerial insights like optimal order quantity, total relevant cost and reorder point managers can plan well ahead not only the inventory but also other aspects like production cycle, financial, marketing and human resource. Effective inventory management gives the enterprise the means to ensure consistent delivery of the right product in the right quantity at the right time.
Different organization would have different demand patterns. Some organization would have fixed demand and some have fluctuating demands. For example a hostel cafeteria would have the same amount of students everyday but an organization selling computers or compact disc would have fluctuating demands.
The same inventory management techniques should not be applied to both constant and fluctuating demand items. With constant demand items, demand tends to be fairly constant and thus an EOQ system would be appropriate. However, items having varying demand would not fit with an EOQ model. Instead, a simulation model would be appropriate.
Conclusion
In this paper, the classical EOQ model and Simulation model were examined under identical problem situation. It can be seen that EOQ is the most basic model used for inventory control. Though it is not feasible and advisable for complex systems, it is the most fundamental inventory model. The results support that under situation where demand is uncertain or lead-time is prevalent the use of simulation produces better results than EOQ.
Every business has its own specific needs, constraints and demand trends; some have constant and some have fluctuating demands. Developing an inventory solution for a business is mainly affected by demands trends, lead time constraints and cost related to inventory. Thus, it may be essential for the organization to analyze their business environments before adopting any procedure or model to formulate an inventory policy.
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