economic-order-quantity

What it does

Instructs the agent to optimize order quantities to minimize total inventory costs by balancing ordering/setup costs and holding costs using EOQ models. It covers classic EOQ, a Python implementation, cost components, and extensions like quantity discounts and reorder-point calculations.

How it works

• It defines the Classic EOQ problem: minimize TC(Q) = Purchase Cost + Ordering Cost + Holding Cost, with TC(Q) = DC + (D/Q)S + (Q/2)H, and EOQ = sqrt(2DS/H).
• It computes key outputs: EOQ, orders per year, cycle time, total annual cost, purchase cost, ordering cost, holding cost, relevant cost, average inventory and value, and max inventory.
• It provides a Python implementation class EOQModel that initializes with annual_demand, unit_cost, ordering_cost, and holding_cost_rate. It derives H = unit_cost * holding_cost_rate and returns a dictionary with EOQ metrics via calculate_eoq().
• It includes a sensitivity_analysis method to vary a parameter (demand, ordering_cost, holding_rate, unit_cost) and produce a DataFrame of outcomes.
• It includes a plot_cost_curve to visualize cost versus Q and mark the EOQ.
• It offers a reorder_point method to compute reorder point given lead time and safety stock.
• It includes an example function example_basic_eoq that demonstrates creating the model, computing EOQ, printing a cost breakdown, computing a reorder point for a 14-day lead time, and plotting the cost curve.
• It extends to EOQ with quantity discounts (All-Units Discount Model). The class EOQWithQuantityDiscounts evaluates price breaks, computes EOQ at each price, determines feasible quantities, and returns candidate options with costs and orders per year, selecting the optimal by total cost. It also computes savings vs. no discount against the highest price.

When to use it

Use when the user wants to calculate optimal order quantities to minimize total inventory costs or determine the economic lot size. It is applicable when the user references EOQ, Wilson formula, economic lot size, order quantity optimization, production batch size, quantity discounts, EPQ, backorder models, or reorder point calculations.

What it can touch

• Variables and parameters in the formulations:
  • Annual demand (D)
  • Unit cost (C)
  • Ordering cost per order (S)
  • Holding cost rate (r) and derived H = C * r
• Outputs including EOQ, orders_per_year, cycle_time_days, total_annual_cost, purchase_cost, ordering_cost, holding_cost, relevant_cost, avg_inventory, avg_inventory_value, max_inventory, reorder_point.
• For discount model: price_breaks as [(min_qty, unit_price), ...] and calculations of feasible quantities, total costs, and optimal candidate.

Caveats

• The model assumes constant demand and known parameters; baseline EOQ assumptions include constant demand, constant lead time, no stockouts, instantaneous replenishment, and no quantity discounts unless the discount model is used.
• The provided Python code uses imports (numpy, pandas, matplotlib) and includes example usage; ensure dependencies are available in the environment where the skill runs.
• The All-Units Discount model depends on the defined price breaks and may require handling of edge cases if breaks are not well-ordered or if EOQ calculations yield non-feasible quantities.