A six-part operations and supply chain portfolio that applies queueing theory, linear programming, mixed and binary integer programming, Monte Carlo simulation, and decision tree analysis to real business scenarios. Each model moves from structured data to clear recommendations supporting cost control, service quality, and risk-aware decision making.
Project overview
This portfolio sits at the intersection of operations research and managerial decision making. Over the semester worked through six structured business problems that mirror real situations in retail checkout lines, grocery inventory planning, new product launches, legal strategy, and manufacturing shop floors.
Key deliverables
Phase 1
Problem framing
Interpreted narrative case descriptions and clarified objectives, decision levers, and constraints.
Phase 2
Model selection
Chose appropriate structures including queueing, LP, BILP, Monte Carlo, and decision trees.
Phase 3
Implementation
Implemented models in Excel and LINGO with clean input, calculation, and output blocks.
Phase 4
Scenario testing
Ran what-if analysis and sensitivity checks on key parameters and assumptions.
Phase 5
Managerial insight
Translated model outputs into staffing, stocking, investment, and legal recommendations.
The six problems fall into three major categories of management science: optimization models, simulation models, and decision models. Together they create a compact but powerful toolkit for reasoning about capacity, uncertainty, and tradeoffs.
These models use queueing theory, linear programming, and binary integer programming to recommend staffing levels, equipment choices, and assignments that minimize cost or time while respecting real-world constraints.
Using an M/M/c queue to balance staffing cost and customer waiting time
A retail manager worried that long checkout lines were causing customers to abandon purchases. The question: how many cashiers should be staffed so that a typical customer does not wait more than a few minutes, without overspending on labor.
ρ = λ / (c · μ) -- server utilization
Lq ≈ function(λ, μ, c) -- expected number in queue
Wq = Lq / λ -- expected waiting time in queue
W = Wq + 1 / μ -- total time in system
Choose the smallest c such that Wq stays below
the target waiting time (for example 5 minutes).
The model showed that one cashier leads to very high utilization and long queues. Two cashiers reduce the problem but still miss the target during busy periods. With three cashiers, expected waiting time stays under the five-minute goal and the probability of a visible line collapses, justifying the additional staffing cost.
Modeling arrival rates, service rates, and queueing parameters that drive checkout system performance.
Modeling daily operating cost of copier options in a law office
A law office needed to choose between a regular copier and a high-speed copier. Each option had different lease payments, speeds, and operating costs, and the firm wanted a structured comparison instead of intuition about which machine "felt" faster.
Let:
V = required pages per day
rate_A = pages per hour for Copier A
rate_B = pages per hour for Copier B
cost_hrA = hourly cost for A
cost_hrB = hourly cost for B
Then:
hours_A = V / rate_A
hours_B = V / rate_B
TotalCost_A = hours_A · cost_hrA
TotalCost_B = hours_B · cost_hrB
Choose the copier with the lower TotalCost.
The high-speed copier completed the workload in fewer hours and generated an estimated daily savings of around eleven dollars versus the regular copier. Over a multi-year lease this compounds into a meaningful reduction in operating cost and staff time.
Cost comparison showing the high-speed copier delivers lower combined operating and labor cost.
Assigning machinists to machines to minimize total processing time
A small manufacturing operation had four machinists and four machines. Each machinist had different processing times on each machine, and one machinist lacked certification on a specific machine. The goal: choose assignments that minimize total time.
Minimize Σᵢ Σⱼ ( time[i,j] · x[i,j] )
Subject to:
Σⱼ x[i,j] = 1 for each machinist i
Σᵢ x[i,j] = 1 for each machine j
x[3,turning] = 0 machinist 3 not certified
x[i,j] ∈ {0,1}
The optimal assignment sent Machinist 3 to the metal lathe, Machinist 1 to the turning machine, Machinist 2 to the milling machine, and Machinist 4 to the radial drill. The minimum total time of 100 minutes was lower than any intuitive pairing the manager had considered.
LINGO solution confirming the optimal machinist-machine pairing and 100-minute total processing time.
The simulation component focuses on modeling uncertainty explicitly, generating a distribution of outcomes instead of a single "best guess." This is especially helpful when both upside and downside risk matter.
Monte Carlo simulation for per-unit profit and confidence intervals
A firm evaluated whether to introduce a new product with a known selling price but uncertain cost components such as purchase cost, labor, and transportation. Rather than rely on one point estimate, management needed to understand the distribution of profit per unit.
For each trial i:
purchase_cost[i] ~ Dist_purchase(...)
labor_cost[i] ~ Dist_labor(...)
transport_cost[i] ~ Dist_transport(...)
profit_per_unit[i] = SellingPrice
- purchase_cost[i]
- labor_cost[i]
- transport_cost[i]
After n trials:
μ = mean(profit_per_unit)
σ = sd(profit_per_unit)
CI = μ ± 1.96 · σ / √n -- 95% CI
The simulation produced an average profit of roughly $6.90 per unit with a standard deviation of about $2.27. The 95% confidence interval ranged from roughly $4.50 to just over $9.00. This gave leadership a clear sense of both upside and downside.
Simulation trials showing mean profit, variability, and confidence interval bounds for the new product.
The decision models translate uncertainty and payoffs into structured comparisons using payoff tables, regret tables, and decision trees. These tools help managers move from gut feeling to transparent, defensible choices.
Perishable inventory decision making under demand uncertainty
A grocery manager needed to decide how many pounds of a specialty steak to stock each week. Demand is uncertain, the product is perishable, and unsold meat must be marked down or discarded. Ordering too little leaves profit on the table, while ordering too much wastes product and margin.
Expected Profit(Q) = Σ over demand levels d [
P(D = d) · Profit(Q, d)
]
Regret(Q, d) = BestProfit(d) - Profit(Q, d)
Choose:
Q* that maximizes Expected Profit(Q)
and performs well under minimax regret.
The analysis indicated that ordering about 35 pounds of steak per week produced the highest expected profit (around $79) and remained attractive across alternative decision criteria. This turned a gut-level stocking guess into a documented, data-supported policy.
Expected monetary value comparison of settling versus going to trial
A firm facing a patent infringement dispute had two main options: accept a settlement or proceed to trial. Each path involved different probabilities and very different financial outcomes. Management needed a transparent way to compare the options.
EMV(Settle) = Payoff_settlement
EMV(Trial) = P(win) · Payoff_win
+ P(lose) · Payoff_lose
+ P(partial)· Payoff_partial
Choose the option with the higher EMV,
then test it against risk appetite and strategy.
The decision tree showed that pursuing trial produced an EMV of roughly $1.8M, versus about $1.5M for accepting the settlement. From a purely financial standpoint, litigation created more expected value, assuming the firm was comfortable with increased variability.
Decision tree payoff and probability table used to calculate EMV for settling versus trial.
Quantitative decision modeling transforms messy business questions into clear, actionable recommendations across operations, finance, and strategy.
Converts vague complaints about "long lines" into quantified staffing recommendations.
Reveals cost and time savings that are not obvious from intuition alone.
Clarifies the range and likelihood of profit outcomes under uncertain costs.
Provides structured, auditable basis for inventory and legal strategy.
Optimizes discrete assignments respecting skill constraints and certifications.
Turns messy business questions into clear, actionable decisions.
This quantitative decision modeling portfolio shows how classical management science techniques move beyond textbook exercises into real business decisions. By combining queueing models, inventory analysis, Monte Carlo simulation, linear and integer programming, and decision trees, the work demonstrates a practical toolkit for choosing staffing levels, setting stocking policies, evaluating new products, selecting equipment, planning legal strategy, and assigning scarce skilled labor. The consistent pattern is taking messy, qualitative questions and turning them into structured, data-driven recommendations that managers can confidently act on.