M6- economies of scale

Business Process Management (BPM)

Economies of Scale

• Focus on inventory management

• Consideration of flow units

  • Flow Unit: The item being analyzed within a process.

• Importance of managing the supply chain to align demand with supply.

• Key aspects of inventory management:

  • Managing waiting times for materials.

  • Analyzing costs vs. benefits of maintaining inventory.

Inventory and Supply Chain Management

Costs of Mismatch

• Over-stocking issues:

  • Results in liquidation, holding costs, and potential obsolescence.

• Under-stocking concerns:

  • Leads to lost sales and subsequently lost margins.

Inventory Categories

• Input Inventory: Flow units waiting to be processed.

• In-process Inventory: Flow units actively being worked on.

• Output Inventory: Flow units that have been processed but are still within the process boundaries; may not always be necessary.

Managing Inventory Metrics

Inventory Equations

• Total Inventory (I):

  • I = Ii + Ip + Io

    • Ii = Average input inventory

    • Ip = Average in-process inventory

    • Io = Average output inventory

• Time Metrics (T):

  • T = Ti + Tp + To

    • Ti = Average time spent in input inventory

    • Tp = Average time spent in in-process inventory

    • To = Average time spent in output inventory

• Relationships:

  • I = R * T

    • Ii = R * Ti

    • Ip = R * Tp

    • Io = R * To

Reasons for Holding Inventory

Buffer Build-up

• Economies of Scale (EoS):

  • Fixed costs related to production batches.

  • Potential for quantity discounts.

• Uncertainties:

  • Fluctuations in supply and demand.

  • Seasonal variability leading to the need for:

    • Cycle/Batch Stock.

    • Safety Stock.

    • Seasonal Stock.

Costs Associated with Inventory

Holding Costs

• Physical Holding Cost: hC

• Financial Holding Cost (Opportunity Cost): rC

• Total Holding Cost (per unit): H = (h + r)C

• Total Inventory Holding Cost (per unit of time): H * I

Order and Inventory Management

Batch Orders and Costs

• Batch Size (Order Size): Q

• Annual Order Frequency: R / Q

• Fixed Cost of Order: S

• Total Annual Fixed Cost of an Order: S * (R / Q)

• Average Cycle Inventory:

  • Icycle = Q / 2

• Total Annual Cost Formula:

  • TC = (S * (R / Q)) + (H * (Q/2)) + (C * R)

Retail Inventory Management Example

Coats-R-Us Store Case Study

• Sells coats at an average price of $325 (30% markup over cost).

• Costs associated with a full truckload shipment (1500 coats, $2200 fee).

• Annual sales around $1 million.

Recommended Order Size (Batch Size)

• Annual Demand Rate (Throughput): R

• Number of Coats per Order: Q

• Average Inventory (Icycle): Q / 2

• Orders per Year: R / Q

Economic Order Quantity (EOQ) Concept

• EOQ Formula: Q* = EOQ = ( \sqrt{\frac{2SS}{H}} )

• Total Annual Cost Formula: ( TC* = 2SS + (C * R) )

Continuing the Coats-R-Us Example

Calculation Details

• Sales Price: $325

  • Unit Cost: C = $325 / 1.3 = $250 per unit.

• Annual Sales: $1,000,000

  • Throughput (R) = 3077 units.

• Fixed Cost per Order (S): $2,200.

• Opportunity Cost of Capital (

  • r = 20% per year.

Required Calculations for Q*

• Total Holding Cost per Unit Based on Cost, H:

  • H = (0 + 0.2) * $250 = $50/year.

• EOQ Calculation:

  • Q* = EOQ = ( \sqrt{\frac{2(2200)(3077)}{50}} ) = 520.36 or approximately 520 units.

Order Frequency and Additional Metrics

• Annual Order Frequency: R/Q* = 3077 / 520 = 5.92 orders per year.

• Interval Between Batch Orders: 52 weeks / 5.92 = 8.8 weeks.

• Total Annual Fixed Cost Calculation: S * (R/Q*) = $2,200 * (3077/520) = Approximately $13,018.

• Average Inventory Calculation (in coats): Q* / 2 = 520/2 = 260 coats.

• Total Inventory Holding Cost (per year): H * (Q*/2) = $50 * 260 = $13,000.

• Flow Time in Store: T = I / R = 260 / 3077 = 0.084/year or about 4.4 weeks.