Scope — Applied management science to six practical problems in retail, manufacturing, and services.
Methods — Queues (M/M/c), payoff & regret, Monte Carlo, LP, decision tree (EMV), BILP.
Tools — Excel (Solver), LINGO.

Project overview

Course: Operations & Supply Chain Management (Fall 2023)
This project applied a range of operations research (OR) and optimization techniques to solve six real-world challenges. These include customer queue optimization, inventory stocking under uncertainty, new product profitability simulation, copier selection using LP, lawsuit decision modeling, and machinist assignments using BILP.

Techniques Applied

  • Queueing Theory (M/M/c): Optimized customer service levels.
  • Decision Analysis: Expected value, regret, pessimistic/optimistic strategies.
  • Monte Carlo Simulation: Modeled cost variability for a new product.
  • Linear Programming (LP): Determined optimal copier selection for cost savings.
  • Decision Tree (EMV): Assessed financial outcomes in legal disputes.
  • Binary Integer Linear Programming (BILP): Minimized production time via optimized assignments.

Tools used: Excel with Solver and LINGO.

Problems and Solutions

A) Customer Checkout Optimization

Objective: Reduce customer balking by optimizing cashier allocation using queueing theory.
Approach:

  • Modeled customer arrivals with a Poisson process and service time as Exponential.
  • Simulated scenarios with 1, 2, and 3 cashiers using M/M/c logic.
  • Calculated utilization, probability of waiting >5 min, and balking impact.

Result: Using 3 cashiers significantly reduced wait times and met the operational target.

B) Specialty Steak Stocking

Objective: Determine the best weekly stocking level to maximize profit.
Approach:

  • Developed payoff and regret tables across demand levels.
  • Used Expected Value, Optimistic, and Pessimistic criteria.
  • Ran sensitivity analysis to assess robustness under demand changes.

Result: Ordering 35 lbs optimized expected profit at $79/week.

C) New Product Profitability (Monte Carlo)

Objective: Simulate profit per unit given variable input costs.
Approach:

  • Conducted 20 trials of Monte Carlo simulation.
  • Calculated profit per unit as:
    [ ext{Profit} = ext{Price} - ext{Purchase} - ext{Labor} - ext{Transport} ]

Result:

  • Mean: $6.90, Standard Deviation: $2.27
  • 95% CI: [$4.46, $9.34]
  • Product is viable pending risk appetite.

D) Copier Selection (Linear Programming)

Objective: Choose the more cost-effective copier.
Approach:

  • Built LP model with copier speeds, costs, and constraints.
  • Objective function minimized daily cost.

Result: High-speed copier saved $11.20/day compared to regular copier.

E) Patent Infringement Decision (Decision Tree / EMV)

Objective: Decide whether to settle or go to trial.
Approach:

  • Constructed a decision tree modeling win/loss outcomes, costs, and probabilities.
  • Calculated Expected Monetary Value (EMV) for both paths.

Result: Go to trial yielded higher EMV ($1.8M) over settling ($1.5M).

F) Machinist Assignment (BILP)

Objective: Assign machinists to machines minimizing total production time.
Approach:

  • Used Binary Integer LP to assign 4 machinists to 4 machines.
  • Constraint: Machinist 3 cannot operate Turning machine.

Result:

  • M3 → Metal Lathe
  • M1 → Turning
  • M2 → Milling
  • M4 → Radial Drill
  • Total Time: 100 minutes

How to Run

Requirements: Excel with Solver, LINGO

Instructions:

  1. Download Excel workbook and LINGO scripts.
  2. Adjust parameters for each module (costs, rates, demand).
  3. Run:
    • Excel: Data → Solver on each tab
    • LINGO: Execute models; customize constraints
  4. Review results, validate with sensitivity tests.

Testing & Validation

  • Constraint checks: Infeasibles flagged and resolved.
  • Sensitivity: Stress-tested decisions against input variability.
  • Repeatability: Documented seeds and solver settings for reproducibility.

Contribution Guidelines

Code of Conduct: Respectful, constructive collaboration is expected.
Workflow: Fork-pull-request model. Branches for features/improvements.
Style Guide: Clear naming, consistent formatting, inline documentation.

Licensing: Educational use under course guidelines.

Future Work

  • Automate modules for web dashboard integration.
  • Integrate predictive modeling for dynamic inputs.
  • Expand scope to include stochastic optimization.

Updated: December 1, 2023

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