# Inventory Control Models

Inventory control models are essential tools used by businesses to optimize their inventory levels and improve overall operational efficiency. These models provide a structured framework for managing inventory, ensuring that the right amount of stock is available when and where it is needed. Effective inventory control is crucial for businesses to balance the delicate trade-off between the costs of carrying excess inventory and the costs of stockouts, ultimately maximizing profitability and customer satisfaction. In this article, we will explore various inventory control models, their applications, advantages, and limitations, providing a comprehensive guide to optimizing inventory management.

## Understanding Inventory Control:

Inventory control, also known as stock control, refers to the processes and strategies employed by businesses to manage their inventory levels efficiently. It involves a range of activities, including forecasting demand, setting inventory targets, ordering stock, monitoring stock levels, and ensuring adequate inventory turnover. Effective inventory control is vital for businesses to meet customer demands, minimize costs, and maintain a positive cash flow.

Inventory control models are quantitative techniques that provide a systematic approach to making inventory-related decisions. These models use mathematical formulas, algorithms, and statistical analysis to determine optimal inventory policies, including when to order stock, how much to order, and when to replenish inventory.

## Types of Inventory Control Models:

Several inventory control models have been developed to address different inventory management scenarios. Each model makes specific assumptions and offers unique advantages. Here are some of the most commonly used inventory control models:

### Basic Inventory Control Models:

Economic Order Quantity (EOQ) Model: The EOQ model determines the optimal quantity to order that minimizes total inventory holding and ordering costs. It assumes constant demand, fixed ordering cost per order, and a known lead time. EOQ calculates the order quantity that results in the lowest total relevant costs.

Reorder Point (ROP) Model: The ROP model, also known as the reorder level model, determines the optimal time to place an order for inventory replenishment. It calculates the inventory level at which a new order should be placed to avoid stockouts. The ROP considers factors such as lead time, demand during lead time, and desired service level.

### Inventory Control Models with Variable Demand:

Probabilistic Inventory Models: These models account for variable and uncertain demand by using probability distributions. They include the Newsboy Model, which is suitable for non-replenishable inventory with a single selling period, and the Dynamic Programming Model, which optimizes inventory decisions over multiple periods.

Stochastic Inventory Models: Stochastic models incorporate random variables to represent demand uncertainty. Examples include the Stochastic Demand Inventory Model, which uses probability distributions to represent demand, and the Newsvendor Model, which optimizes inventory decisions for perishable items with uncertain demand.

### Inventory Control Models with Multiple Items:

Multi-Item Inventory Models: These models address inventory management for multiple items or products. They consider factors such as joint demand, shared resources, and interdependencies between items. Examples include the Joint Probabilistic Model and the Multi-Item Newsboy Model.

Inventory Routing Problems: These models optimize inventory decisions and delivery routes in scenarios where multiple locations or distribution centers are involved. They consider factors such as transportation costs, delivery time windows, and inventory constraints.

### Inventory Control Models with Backordering:

Backorder Inventory Models: These models consider the possibility of backordering, where customer orders can be fulfilled even if inventory levels are temporarily insufficient. The Wilson Model is a classic example, balancing the costs of carrying inventory, ordering, and backordering.

Continuous Review (CR) and Periodic Review (PR) Models: CR and PR models determine the optimal time to review and replenish inventory. CR involves continuous monitoring of inventory levels, while PR involves reviewing inventory at fixed intervals. Both models can incorporate backordering.

### Inventory Control Models with Lead Time Considerations:

Inventory Models with Deterioration: These models account for inventory deterioration or obsolescence during lead time. They are applicable in industries with perishable or time-sensitive items, such as food, fashion, or technology.

Inventory Models with Variable Lead Time: Some industries experience variable lead times due to supply chain dynamics or production complexities. These models optimize inventory decisions considering lead time variability, helping businesses manage uncertainty.

## Integrated Inventory and Production Control Models:

Just-In-Time (JIT) Inventory Control: JIT aims to minimize inventory levels by aligning production or procurement with actual demand. This model reduces waste, improves cash flow, and enhances responsiveness to customer needs.

Materials Requirement Planning (MRP): MRP is a production planning and inventory control system that determines the quantity and timing of material purchases to support production schedules. It considers bill of materials, lead times, and inventory levels.

## Inventory Control Models with Multiple Objectives:

Multi-Objective Inventory Models: These models optimize inventory decisions based on multiple objectives, such as minimizing costs, maximizing service levels, or achieving sustainability goals. They involve trade-offs and decision-making under uncertainty.

## Applying Inventory Control Models:

The application of inventory control models involves several steps, including data collection, model selection, parameter estimation, and implementation. Here’s an overview of the process:

Identify Inventory Management Goals: Define the specific objectives of your inventory control system, such as minimizing costs, maximizing profitability, or ensuring a certain service level.

Collect Relevant Data: Gather historical data on demand patterns, lead times, ordering costs, holding costs, and relevant price fluctuations. Clean and analyze the data to identify patterns and trends that will inform your model selection and parameter estimation.

Select an Appropriate Inventory Control Model: Choose a model that aligns with your inventory management goals and the characteristics of your inventory items. Consider factors such as demand variability, perishability, lead time, and the number of items managed.

Estimate Model Parameters: Use historical data to estimate the parameters required by the chosen model, such as demand rate, ordering cost, holding cost, lead time, and desired service level.

Implement the Model: Utilize the selected model to calculate optimal inventory levels, reorder points, and order quantities. Consider any practical constraints, such as storage capacity or budget limitations.

Monitor and Adjust: Regularly review the performance of your inventory control system. Compare actual outcomes with expected results, and make adjustments as necessary. Feedback loops are essential for refining the model and improving its accuracy over time.

## Advantages of Using Inventory Control Models:

Cost Optimization: Inventory control models help minimize inventory holding costs, ordering costs, and stockout costs. By determining the optimal quantity and timing of orders, businesses can reduce waste, improve cash flow, and enhance profitability.

Improved Customer Service: Inventory control models ensure that sufficient stock is available to meet customer demands, reducing the risk of stockouts and improving customer satisfaction. This can lead to increased sales, market share, and customer loyalty.

Efficient Resource Allocation: Inventory control models provide insights into the optimal allocation of resources, helping businesses manage their inventory investment effectively. This includes optimizing storage space, labor utilization, and transportation costs.

Reduced Waste and Obsolescence: By optimizing inventory levels, businesses can reduce the risk of excess inventory becoming obsolete or deteriorating. This minimizes waste, improves sustainability, and enhances environmental performance.

Enhanced Decision-Making: Inventory control models provide a quantitative framework for making inventory-related decisions. They enable businesses to make data-driven choices, reducing reliance on intuition or guesswork.

Improved Financial Planning: Inventory control models facilitate accurate financial planning and budgeting. By understanding inventory costs and requirements, businesses can better manage cash flow, forecast expenses, and secure financing if needed.

## Limitations and Challenges of Inventory Control Models:

Despite their benefits, inventory control models also have limitations and challenges:

Assumptions and Simplifications: Inventory control models often make simplifying assumptions, such as constant demand or known lead times, which may not always hold true in practice. Deviations from these assumptions can impact the accuracy of the model.

Data Quality and Availability: The effectiveness of inventory control models relies on accurate and comprehensive data. In some cases, data may be limited, incomplete, or subject to errors, affecting the reliability of model outputs.

Dynamic Market Conditions: Markets are often dynamic, with demand patterns, prices, and lead times fluctuating over time. Inventory control models may struggle to capture these dynamics, requiring frequent updates and adjustments.

Limited Consideration of Strategic Factors: Inventory control models typically focus on operational efficiency rather than strategic considerations. They may not fully account for factors such as customer behavior, competitive dynamics, or market trends.

Implementation Complexity: Some inventory control models can be complex to implement, especially in organizations with diverse product portfolios or complex supply chains. This complexity may require specialized software or expertise.

Behavioral and Organizational Challenges: Implementing inventory control models may involve changing existing processes, behaviors, and organizational structures. Resistance to change or a lack of buy-in from stakeholders can hinder successful implementation.

## Best Practices and Recommendations:

To maximize the benefits of inventory control models, consider the following best practices:

Start with a Clear Objective: Define the specific goals of your inventory control system, such as cost minimization, service level improvement, or sustainability enhancement. This clarity will guide model selection and parameter estimation.

Embrace Data-Driven Decision-Making: Leverage data analytics and technology to collect, clean, and analyze inventory-related data. Data-driven insights will improve the accuracy and reliability of your inventory control models.

Select the Right Model for Your Context: Choose inventory control models that align with the unique characteristics of your industry, inventory items, and business objectives. Consider demand variability, perishability, lead time dynamics, and the number of items managed.

Regularly Review and Update Models: Inventory control models should be dynamic and responsive to changing market conditions. Regularly review and update models to reflect shifts in demand patterns, costs, or other relevant factors.

Integrate with Other Business Functions: Ensure that your inventory control models are integrated with other business functions, such as sales, marketing, production, and finance. This holistic approach enhances decision-making and aligns inventory management with overall business objectives.

Monitor Performance and Adjust: Continuously monitor the performance of your inventory control system, comparing actual outcomes with expected results. Be prepared to adjust models, processes, or parameters as necessary to improve accuracy and effectiveness.

Foster a Culture of Continuous Improvement: Encourage a culture of learning and adaptation within your organization. Embrace feedback loops, learn from successes and failures, and continuously seek opportunities to optimize your inventory control processes.

## Conclusion:

Effective inventory control is a critical aspect of business operations, and inventory control models provide a quantitative framework for optimizing stock levels. By applying these models, businesses can strike a balance between carrying costs and stockout costs, ultimately improving profitability and customer satisfaction. The choice of inventory control model depends on the specific characteristics of the industry, inventory items, and organizational goals.

Through the exploration of various inventory control models, it is evident that there is no one-size-fits-all solution. Businesses must carefully consider their unique context, including demand patterns, lead times, cost structures, and strategic objectives, when selecting and implementing an inventory control model.

Additionally, the dynamic nature of markets and supply chains underscores the importance of flexibility and adaptability in inventory control. Regular reviews, updates, and adjustments to inventory control models are essential to align with changing market conditions, technological advancements, and customer expectations.

By embracing data-driven decision-making, integrating inventory control with other business functions, and fostering a culture of continuous improvement, businesses can maximize the benefits of inventory control models. Ultimately, effective inventory control contributes to operational efficiency, financial health, and long-term sustainability, positioning organizations for success in a competitive marketplace.

## SUMMARY:

Entity needs to maintain inventory at appropriate level keeping balance in contrasting factors inventory levels e.g if large amount of inventory is ordered ordering cost is reduced but opportunity cost is much increased , money tied could be used for other profitable investments. So keeping all factors in mind entity needs appropriate models to be used for inventory management to save from irrelevant costs , help profits to boost up

Let’s study different systems showing to   manage inventory in best ways.  Prominent methods include:

## EOQ Without Discounts

Example

Acompany utilizes 5000 units per year,

Purchase price of each unit is \$2,

Cost of placing order (ordering cost) =\$10

Holding cost =10% of unit cost

Find

• EOQ
• Total Co
• Total Ch

SLOUTION

=√2.10.5000/ 10%* 2

707.10

Annual Ordering Cost

D/ EOQ * Co per unit

= 5000/707.10*10

\$14.14

Annual Holding Cost

EOQ/2*Ch per unit

=707.10/2* 0.2

=\$71

## EOQ with dicounts

In case of purchase of large quantities, supplier offers discounts So its necessary to calculate EOQ considering those discounts, so can decision can be  regarding acceptance or rejection of those large orders with discounts(keeping in mind high holding costs for large quantities order)

STEPS TO FOLLOW

• Calculate EOQ in normal circumstances(without discounts)
• Calculate total COSTS without discounts on basis of EOQ calculated
• Now calculate total costs on basis of large orders quantities(with discounts)
• In case of more than one offers, calculate costs with each offer and choose the best one

###### EXAMPLE # 1         ACCA DEC 2010

WQZ Co is considering making the following changes in the area of working capital management

It has been suggested that the order size for Product KN5 should be determined using the economic order quantity model (EOQ).WQZ Co forecasts that demand for Product KN5 will be 160,000 units in the coming year and it has traditionally ordered 10% of annual demand per order. The ordering cost is expected to be \$400 per order while the holding costis expected to be \$5·12 per unit per year. A buffer inventory of 5,000 units of Product KN5 will be maintained, whether orders are made by the traditional method or using the economic ordering quantity model.

SOLUTION

Cost of the current ordering policy

Order size = 10% of 160,000 = 16,000 units per order

Number of orders per year = 160,000/16,000 = 10 orders per year

Annual ordering cost = 10 x 400 = \$4,000 per year

Holding cost ignoring buffer inventory = 5·12 x (16,000/2) = \$40,960 per year

Holding cost of buffer inventory = 5·12 x 5,000 = \$25,600 per year

Total cost of current policy = 4,000 + 40,960 + 25,600 = \$70,560 per year

###### Cost of the ordering policy using the EOQ model

Order size = (2 x 400 x 160,000/5·12)0·5 = 5,000 units per order

Number of orders per year = 160,000/5,000 = 32 orders per year

Annual ordering cost = 32 x 400 = \$12,800 per year

Holding cost ignoring buffer inventory = 5·12 x (5,000/2) = \$12,800 per year

Holding cost of buffer inventory = 5·12 x 5,000 = \$25,600 per year

Total cost of EOQ policy = 12,800 + 12,800 + 25,600 = \$51,200 per year

Change in costs of inventory management by using EOQ model

Decrease in costs = 70,560 – 51,200 = \$19,360

###### EXAMPLE #2       ACCA DEC2012

KXP Co  orders 15,000 units per month of Product Z, demand for which is constant. There is only one supplier of Product Z and the cost of Product Z purchases over the last year was \$540,000. The supplier has offered a 2% discount for orders of Product Z of 30,000 units or more. Each order costs KXP Co \$150 to place and the holding cost is 24 cents per unit per year. KXP Co has an overdraft facility charging interest of 6% per year

Calculate whether the bulk purchase discount offered by the supplier is financially acceptable and comment

SOLUTION

Cost of current inventory policy

Cost of materials = \$540,000 per year

Annual ordering cost = 12 x 150 = \$1,800 per year

Annual holding cost = 0·24 x (15,000/2) = \$1,800 per year

Total cost of current inventory policy = 540,000 + 1,800 + 1,800 = \$543,600 per year

Cost of inventory policy after bulk purchase discount

Cost of materials after bulk purchase discount = 540,000 x 0·98 = \$529,200 per year

Annual demand = 12 x 15,000 = 180,000 units per year

KXP Co will need to increase its order size to 30,000 units to gain the bulk discount

Revised number of orders = 180,000/30,000 = 6 orders per year

Revised ordering cost = 6 x 150 = \$900 per year

Revised holding cost = 0·24 x (30,000/2) = \$3,600 per year

Revised total cost of inventory policy = 529,200 + 900 + 3,600 = \$533,700 per year

Evaluation of offer of bulk purchase discount

Net benefit of taking bulk purchase discount = 543,600 – 533,700 = \$9,900 per year

The bulk purchase discount looks to be financially acceptable. However, this evaluation is based on a number of unrealistic assumptions. For example, the ordering cost and the holding cost are assumed to be constant, which is unlikely to be true in reality. Annual demand is assumed to be constant, whereas in practice seasonal and other changes in demand are likely.

## IMPORTANT FORMULAE OF MATERIALS

#### Re-Order Level:

“Minimum level set by entity at which order is made “

Maximum Usage * maximum Lead Time  (IN CASE OF WITHOUT SAFETY STOCK)

OR

Safety Stock + Lead Time Consumption

“Time lap between placement of order and delivery of order at warehouse by supplier”

Average Lead Time * Average Consumption

#### Maximum level:

ROL+ROQ-(Minimum Usage*Minimum Lead Time)       (absolute maximum inventory)

ROL+ROQ-(Average Usage*Average lead Time)  (Normal maximum inventory)

#### Average Level:

1/2(Maximum Level+ Minimum Level)

OR

Minimum Level + 1/2 ROQ

Danger Level:       Minimum Usage Rate * Minimum Lead Time

OR

Average Usage Rate * Minimum Lead Time

OR

Minimum Usage Rate * Average Lead Time

EOQ/ROQ              Square  Root of √ 2D.Co/Ch

Material T/O Ratio              Consumption / Average Stock

Average Stock      1/2(Maximum Stock+ Minimum Stock)