Balance holding, shortage, and ordering costs under stochastic demand & lead times. Find robust reorder points.
1) Why It Matters — The Cost of Poor Replenishment
Fixed rules that ignore variability cause both overstock and stockouts. In continuous-review systems these show up as unnecessary holding costs, lost sales/backorders, and too many small rush orders.
Goal: choose reorder points \(r_i\) (with given policies) to minimize average cost per period while maintaining strong service.
Multi-product (up to 5)Continuous-review(r,Q) & (s,S)Stochastic
2) System Model — What We Simulate
Core assumptions
Demand: Poisson arrivals × discrete demand size per customer.
Lead time: exponential per order.
Policy: per-product (r,Q) or (s,S) with fixed Q or S.
Shortage handling: backorders or lost sales (fixed per product).
Costs: holding, shortage, and ordering (setup + per unit).
What you control
Decision variables: reorder points \(r_i\) for selected products.
Evaluation settings: horizon (periods) and number of replicates.
Everything else (prices, demand/lead distributions, Q/S) is static and reasonable by design.
We review every period (e.g., daily); deliveries arrive at sampled lead times; demand hits stock; costs accrue each step.
3) Simulation Mechanics — One Loop
Inventory position: \(IP_t = \text{on hand}_t + \text{outstanding}_t\).
Reorder rule: if \(IP_t \le r_i\), place order of size \(Q_i\) (r,Q) or up to \(S_i\) (s,S).
Average cost: \(\;\bar C = \frac{1}{H}\sum_{t=1}^{H}(C^{hold}_t + C^{short}_t + C^{ord}_t)\).
Per period: receive due orders → draw demand → update stock & costs → possibly reorder.
Run for horizon \(H\); repeat over replicates and average to reduce Monte-Carlo noise.
4) Optimization — Genetic Algorithm (GA)
Chromosome: \(x = (r_1,\dots,r_m)\) over selected products. Objective: minimize summed average cost across products.
