Inventory control is a critical area in accountancy, especially for businesses managing stock to optimize costs and meet customer demand. Proper inventory control models enable accountants and managers to determine the optimal order quantity and timing, balancing ordering costs, holding costs, and stockout risks. This chapter focuses on formulating inventory control models, which are essential tools for financial planning and operational efficiency in Kenyan enterprises such as retail stores, manufacturing firms, and service providers.
Inventory control models involve specific technical terms that must be understood precisely to apply these models effectively. This section clarifies key terms such as Economic Order Quantity, Reorder Level, Lead Time, Safety Stock, and Carrying Cost, which form the foundation for formulating and analyzing inventory control decisions.
Economic Order Quantity (EOQ) is the optimal order quantity that minimizes the total inventory costs, which include ordering costs and holding costs. EOQ balances the trade-off between ordering frequently in small quantities and ordering less often in larger quantities.
$$EOQ = \sqrt{\frac{2DS}{H}}$$
Where:
\(D\) = Annual demand (units)
\(S\) = Ordering cost per order (Ksh)
\(H\) = Holding cost per unit per year (Ksh)
Example 1: A retail shop sells 12,000 units of a product annually. The ordering cost is Ksh 200 per order, and the holding cost is Ksh 5 per unit per year. Calculate the EOQ.
Given:
\(D = 12,000\) units
\(S = 200\) Ksh
\(H = 5\) Ksh
$$EOQ = \sqrt{\frac{2 \times 12,000 \times 200}{5}}$$$$= \sqrt{\frac{4,800,000}{5}}$$$$= \sqrt{960,000}$$$$= 979.8 \text{ units}$$ Answer: EOQ = 980 units
Example 2: A manufacturing firm has an annual demand of 50,000 units. The ordering cost is Ksh 500 per order, and the holding cost per unit per year is Ksh 10. Find the EOQ.
Given:
\(D = 50,000\) units
\(S = 500\) Ksh
\(H = 10\) Ksh
$$EOQ = \sqrt{\frac{2 \times 50,000 \times 500}{10}}$$$$= \sqrt{\frac{50,000,000}{10}}$$$$= \sqrt{5,000,000}$$$$= 2236.07 \text{ units}$$ Answer: EOQ = 2236 units
Example 3: A hospital pharmacy uses 24,000 units of a medicine yearly. Ordering cost is Ksh 150 per order, and holding cost is Ksh 8 per unit annually. Calculate EOQ.
Given:
\(D = 24,000\) units
\(S = 150\) Ksh
\(H = 8\) Ksh
$$EOQ = \sqrt{\frac{2 \times 24,000 \times 150}{8}}$$$$= \sqrt{\frac{7,200,000}{8}}$$$$= \sqrt{900,000}$$$$= 948.68 \text{ units}$$ Answer: EOQ = 949 units
Example 4: A SACCO distributes 15,000 passbooks per year. Ordering cost is Ksh 300 per order; holding cost is Ksh 6 per passbook annually. Determine EOQ.
Given:
\(D = 15,000\) units
\(S = 300\) Ksh
\(H = 6\) Ksh
$$EOQ = \sqrt{\frac{2 \times 15,000 \times 300}{6}}$$$$= \sqrt{\frac{9,000,000}{6}}$$$$= \sqrt{1,500,000}$$$$= 1224.74 \text{ units}$$ Answer: EOQ = 1225 units
Example 5: A county government office consumes 36,000 units of stationery annually. Ordering cost is Ksh 250 per order, holding cost is Ksh 4 per unit per year. Find EOQ.
Given:
\(D = 36,000\) units
\(S = 250\) Ksh
\(H = 4\) Ksh
$$EOQ = \sqrt{\frac{2 \times 36,000 \times 250}{4}}$$$$= \sqrt{\frac{18,000,000}{4}}$$$$= \sqrt{4,500,000}$$$$= 2121.32 \text{ units}$$ Answer: EOQ = 2121 units
Reorder Level is the inventory level at which a new order should be placed to replenish stock before it runs out. It depends on the lead time and average demand during that period.
$$ROL = d \times L$$
Where:
\(d\) = Average demand per day (units)
\(L\) = Lead time in days
Example 1: A retail store sells 100 units daily. Lead time is 5 days. Calculate the reorder level.
Given:
\(d = 100\) units/day
\(L = 5\) days
$$ROL = 100 \times 5$$$$= 500 \text{ units}$$ Answer: ROL = 500 units
Example 2: A school uses 60 textbooks per day. Lead time is 7 days. Find the reorder level.
Given:
\(d = 60\) units/day
\(L = 7\) days
$$ROL = 60 \times 7$$$$= 420 \text{ units}$$ Answer: ROL = 420 units
Example 3: A bank consumes 80 stationery items daily. Lead time is 4 days. Calculate the reorder level.
Given:
\(d = 80\) units/day
\(L = 4\) days
$$ROL = 80 \times 4$$$$= 320 \text{ units}$$ Answer: ROL = 320 units
Example 4: A retail business sells 150 units daily. Lead time is 3 days. Find ROL.
Given:
\(d = 150\) units/day
\(L = 3\) days
$$ROL = 150 \times 3$$$$= 450 \text{ units}$$ Answer: ROL = 450 units
Example 5: A cooperative uses 40 units daily with a lead time of 10 days. Calculate reorder level.
Given:
\(d = 40\) units/day
\(L = 10\) days
$$ROL = 40 \times 10$$$$= 400 \text{ units}$$ Answer: ROL = 400 units
Safety Stock is extra inventory held to prevent stockouts caused by uncertainties in demand or supply during the lead time. It acts as a buffer to ensure service continuity.
$$Safety\ Stock = Z \times \sigma_{L}$$
Where:
\(Z\) = Service factor (based on desired service level)
\(\sigma_{L}\) = Standard deviation of demand during lead time
Example 1: A retailer wants 95% service level (Z = 1.65). Standard deviation of demand during lead time is 20 units. Calculate safety stock.
Given:
\(Z = 1.65\)
\(\sigma_{L} = 20\) units
$$Safety\ Stock = 1.65 \times 20$$$$= 33 \text{ units}$$ Answer: Safety Stock = 33 units
Example 2: A school targets 99% service level (Z = 2.33). Standard deviation during lead time is 15 units. Find safety stock.
Given:
\(Z = 2.33\)
\(\sigma_{L} = 15\) units
$$Safety\ Stock = 2.33 \times 15$$$$= 34.95 \text{ units}$$ Answer: Safety Stock = 35 units
Example 3: A bank requires 90% service level (Z = 1.28). Standard deviation of demand during lead time is 25 units. Calculate safety stock.
Given:
\(Z = 1.28\)
\(\sigma_{L} = 25\) units
$$Safety\ Stock = 1.28 \times 25$$$$= 32 \text{ units}$$ Answer: Safety Stock = 32 units
Example 4: A retail store aims for 97.5% service level (Z = 2.0). Standard deviation is 10 units. Find safety stock.
Given:
\(Z = 2.0\)
\(\sigma_{L} = 10\) units
$$Safety\ Stock = 2.0 \times 10$$$$= 20 \text{ units}$$ Answer: Safety Stock = 20 units
Example 5: A cooperative has 85% service level (Z = 1.04). Standard deviation during lead time is 30 units. Calculate safety stock.
Given:
\(Z = 1.04\)
\(\sigma_{L} = 30\) units
$$Safety\ Stock = 1.04 \times 30$$$$= 31.2 \text{ units}$$ Answer: Safety Stock = 31 units
Carrying Cost, also known as holding cost, is the cost incurred to hold one unit of inventory for a year. It includes storage, insurance, deterioration, and opportunity costs.
$$Carrying\ Cost = (Storage + Insurance + Deterioration + Opportunity\ Cost) \text{ per unit per year}$$
Example 1: A retail company estimates storage cost at Ksh 2 per unit, insurance Ksh 1, deterioration Ksh 0.5, and opportunity cost Ksh 1.5 per unit annually. Find total carrying cost per unit.
Given:
Storage = Ksh 2
Insurance = Ksh 1
Deterioration = Ksh 0.5
Opportunity cost = Ksh 1.5
$$Carrying\ Cost = 2 + 1 + 0.5 + 1.5$$$$= 5 \text{ Ksh per unit per year}$$ Answer: Carrying Cost = Ksh 5 per unit per year
Example 2: A hospital has storage cost Ksh 3, insurance Ksh 2, deterioration Ksh 1, and opportunity cost Ksh 2 per unit annually. Calculate carrying cost.
Given:
Storage = Ksh 3
Insurance = Ksh 2
Deterioration = Ksh 1
Opportunity cost = Ksh 2
$$Carrying\ Cost = 3 + 2 + 1 + 2$$$$= 8 \text{ Ksh per unit per year}$$ Answer: Carrying Cost = Ksh 8 per unit per year
Example 3: A SACCO estimates storage cost Ksh 1, insurance Ksh 0.5, deterioration Ksh 0.2, and opportunity cost Ksh 1 per unit annually. Find carrying cost.
Given:
Storage = Ksh 1
Insurance = Ksh 0.5
Deterioration = Ksh 0.2
Opportunity cost = Ksh 1
$$Carrying\ Cost = 1 + 0.5 + 0.2 + 1$$$$= 2.7 \text{ Ksh per unit per year}$$ Answer: Carrying Cost = Ksh 2.7 per unit per year
Example 4: A retail firm records storage cost Ksh 4, insurance Ksh 1.5, deterioration Ksh 0.5, and opportunity cost Ksh 2 per unit yearly. Calculate carrying cost.
Given:
Storage = Ksh 4
Insurance = Ksh 1.5
Deterioration = Ksh 0.5
Opportunity cost = Ksh 2
$$Carrying\ Cost = 4 + 1.5 + 0.5 + 2$$$$= 8 \text{ Ksh per unit per year}$$ Answer: Carrying Cost = Ksh 8 per unit per year
Example 5: A cooperative estimates storage cost Ksh 2.5, insurance Ksh 1, deterioration Ksh 0.3, and opportunity cost Ksh 1.2 per unit annually. Find carrying cost.
Given:
Storage = Ksh 2.5
Insurance = Ksh 1
Deterioration = Ksh 0.3
Opportunity cost = Ksh 1.2
$$Carrying\ Cost = 2.5 + 1 + 0.3 + 1.2$$$$= 5 \text{ Ksh per unit per year}$$ Answer: Carrying Cost = Ksh 5 per unit per year
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Create a free accountThis chapter began by defining key terms related to inventory control, establishing a clear understanding of concepts such as reorder levels, safety stock, and lead time. It then explained how to set appropriate inventory control levels to balance supply and demand effectively. The focus shifted to methods for minimizing the total cost of inventories, including ordering costs, holding costs, and shortage costs. Various inventory control models were introduced, highlighting their application in managing stock efficiently. The chapter also covered how total inventory costs are determined using accurate records and reports. Finally, it explored probabilistic approaches to inventory control, accounting for uncertainties in demand and supply to optimize stock levels. Together, these topics provide a comprehensive framework for effective inventory management in practical settings.
A company holds an average inventory of 500 units. The ordering cost per order is Ksh 2,000 and the holding cost per unit per year is Ksh 50. Calculate the Economic Order Quantity (EOQ). (2 marks)
If the annual demand for an item is 12,000 units, the ordering cost is Ksh 1,500 per order, and the holding cost per unit per year is Ksh 30, find the EOQ. (2 marks)