exam-courseactive3 Yrs Solved PYQs

Logistics & Supply Chain Management

Value creation, adaptability, and sustainability across multi-echelon networks. Covers Fisher strategic fit, deterministic EOQ/EPQ, stochastic safety stocks, warehouse workflows, and 2023–2025 solved examinations.

Curriculum Faculty

Prof. Ajit MauryaProf. ManojProf. Praful More

KaTeX Mathematical EngineRigorous Proofs & Arithmetic Derivations

Formula & Proof Directory

A standardized repository of all mathematical models in Supply Chain Management. Includes deterministic inventory optimization (EOQ/EPQ), stochastic safety stock under dual demand and lead-time volatility, facility location Center of Gravity mechanics, and financial Cash-to-Cash operating cycle formulations.

Economic Order Quantity (EOQ)

Finds the exact order batch size that minimizes the sum of annual ordering setup costs and annual inventory holding costs under constant demand.

Inventory

$$Q^* = \sqrt{\frac{2DS}{H}}$$

Variable Dictionary & Parameters

Symbol	Economic Definition	Standard Unit
$Q^*$	Optimal Economic Order Quantity	units
$D$	Annual demand volume	units/year
$S$	Fixed administrative and transport setup cost per order	₹ or $ per order
$H$	Annual carrying cost per unit (H = i * C)	₹ or $ per unit-year

Step-by-Step Arithmetic WalkthroughNumerical Example

Given Parameters:

D: 12,000 unitsS: ₹1,500C: ₹250i: 20% (H = ₹50)

→Numerator = 2 * 12,000 * 1,500 = 36,000,000

→Divide by H = 36,000,000 / 50 = 720,000

→Square root = sqrt(720,000) = 848.53 units

Calculated Output:Q* = 849 units

Economic Production Quantity (EPQ)

Determines the optimal production run quantity when materials are manufactured internally and consumed simultaneously at daily rates p and d.

Inventory

$$Q_{EPQ}^* = \sqrt{\frac{2DS}{H\left(1 - \frac{d}{p}\right)}}$$

Variable Dictionary & Parameters

Symbol	Economic Definition	Standard Unit
$Q_{EPQ}^*$	Optimal production lot size	units
$d$	Daily demand rate	units/day
$p$	Daily manufacturing capacity	units/day
$I_{max}$	Peak inventory accumulated (I_{max} = Q * (1 - d/p))	units

Step-by-Step Arithmetic WalkthroughNumerical Example

Given Parameters:

D: 50,000 unitsS: ₹2,500H: ₹10d: 200 units/dayp: 500 units/day

→(1 - d/p) = 1 - 200/500 = 0.60

→Denominator = 10 * 0.60 = 6.0

→Numerator = 2 * 50,000 * 2,500 = 250,000,000

→Quotient = 250,000,000 / 6 = 41,666,666.67

→Square root = sqrt(41,666,666.67) = 6,455 units

Calculated Output:Q_{EPQ}^* = 6,455 units

Safety Stock under Dual Uncertainty

Calculates the necessary buffer stock to maintain a specified Cycle Service Level when both customer demand and vendor lead time are stochastic variables.

Inventory

$$SS = Z \cdot \sqrt{\bar{L} \cdot \sigma_d^2 + \bar{d}^2 \cdot \sigma_L^2}$$

Variable Dictionary & Parameters

Symbol	Economic Definition	Standard Unit
$Z$	Standard normal distribution factor for target service level	dimensionless
$\bar{L}$	Average replenishment lead time	days
$\sigma_d$	Standard deviation of daily demand	units/day
$\bar{d}$	Average daily demand rate	units/day
$\sigma_L$	Standard deviation of lead time	days

Step-by-Step Arithmetic WalkthroughNumerical Example

Given Parameters:

d_bar: 150 unitssigma_d: 20 unitsL_bar: 16 dayssigma_L: 3 daysCSL: 98% (Z = 2.054)

→Demand variance component = L_bar * sigma_d^2 = 16 * (20)^2 = 16 * 400 = 6,400

→Lead time variance component = d_bar^2 * sigma_L^2 = (150)^2 * (3)^2 = 22,500 * 9 = 202,500

→Combined variance = 6,400 + 202,500 = 208,900

→Standard deviation = sqrt(208,900) = 457.06 units

→Safety Stock SS = 2.054 * 457.06 = 938.8 units

Calculated Output:Safety Stock = 939 units; ROP = (150 * 16) + 939 = 3,339 units

Center of Gravity Facility Location

Calculates the optimal geographical coordinates for a central distribution center or warehouse to minimize total ton-kilometer freight hauling costs.

Transportation

$$X^* = \frac{\sum W_i X_i}{\sum W_i}, \quad Y^* = \frac{\sum W_i Y_i}{\sum W_i}$$

Variable Dictionary & Parameters

Symbol	Economic Definition	Standard Unit
$X^, Y^$	Optimal Cartesian coordinates of new facility	grid units / km
$X_i, Y_i$	Coordinates of customer market or supplier source i	grid units / km
$W_i$	Volume, weight, or annual freight shipments at point i	tons/year

Step-by-Step Arithmetic WalkthroughNumerical Example

Given Parameters:

NodeA: (100, 200) W=500tNodeB: (400, 100) W=800tNodeC: (300, 500) W=700t

→Total Weight = 500 + 800 + 700 = 2,000 tons

→Sum(W * X) = (500*100) + (800*400) + (700*300) = 50,000 + 320,000 + 210,000 = 580,000

→X* = 580,000 / 2,000 = 290

→Sum(W * Y) = (500*200) + (800*100) + (700*500) = 100,000 + 80,000 + 350,000 = 530,000

→Y* = 530,000 / 2,000 = 265

Calculated Output:Optimal DC Coordinates: (290, 265)

Cash-to-Cash (C2C) Operating Cycle

Measures the time span (in days) required for an enterprise to convert cash invested in raw material procurement back into cash received from customer accounts.

Forecasting

$$C2C = DIO + DSO - DPO$$

Variable Dictionary & Parameters

Symbol	Economic Definition	Standard Unit
$C2C$	Cash-to-Cash Cycle time	days
$DIO$	Days Inventory Outstanding (Inventory / COGS * 365)	days
$DSO$	Days Sales Outstanding (Accounts Receivable / Revenue * 365)	days
$DPO$	Days Payables Outstanding (Accounts Payable / COGS * 365)	days

Step-by-Step Arithmetic WalkthroughNumerical Example

Given Parameters:

DIO: 45 daysDSO: 30 daysDPO: 60 days

→C2C = DIO + DSO - DPO = 45 + 30 - 60 = 15 days

→If company extends vendor payment terms to 80 days: C2C = 45 + 30 - 80 = -5 days (Negative Working Capital)

Calculated Output:C2C = 15 days (Standard); C2C = -5 days (Negative Working Capital)