📘 operations research

1. The Economic Order Quantity (EOQ) model is designed to find the optimal order quantity that minimizes the total inventory costs. 2. These total costs include two main components

1. **Problem Statement:** Calculate the safety stock, reorder point, and economic order quantity (EOQ) for a part with given demand, lead time, and cost parameters.

1. **State the problem:** We need to find the Economic Order Quantity (EOQ) for glass units, given the annual demand, ordering cost, and holding cost per unit. 2. **Given data:**

1. **State the problem:** We have three discount options for ordering skateboards with different quantity discounts and fixed order costs. We want to find the most cost-effective o

1. **Problem Statement:** We need to assign 3 jobs (A, B, C) to 4 machines (W, X, Y, Z) minimizing the total cost, given the cost matrix:

1. **State the problem:** We want to maximize the total profit from producing two components, C1 and C2, given constraints on costs, production capacity, and available resources.

1. Тодорхойлж байна: Диагоналийн аргаар хуваарилалт хийхэд i-р агуулахын ачаа дууссан үед дараагийн ачаа хуваарилах нүдийг олох шаардлагатай. 2. Диагоналийн аргын үндсэн зарчим: Ху

1. **Problem Statement:** Fill in the blanks for queuing system concepts, identify variables and events, complete probability tables, create CDFs, simulate interarrival and service

1. **Problem Statement:** A firm produces two products A and B. Each unit of A requires 2 kg raw material and 4 labor hours. Each unit of B requires 3 kg raw material and 3 labor h

1. **Problem Statement:** A firm produces two products A and B. Each unit of A requires 2 kg of raw material and 4 labor hours. Each unit of B requires 3 kg of raw material and 3 l

1. **Problem Statement:** A firm produces two products A and B. Each unit of A requires 2 kg raw material and 4 labor hours. Each unit of B requires 3 kg raw material and 3 labor h

1. The problem is to maximize or minimize a linear objective function subject to a set of linear inequalities or equations called constraints. 2. A typical linear programming probl

1. **Problem statement:** We have a linear programming (LP) problem (P) and its integer programming (IP) version with integer constraints on $x_1, x_2$. 2. **Part (a):** What can b

1. **Problem statement:** We analyze the multi-objective optimization problem (P) with objectives $$w_1 = -2x_1 + x_2$$ and $$w_2 = -x_1 - 3x_2$$ subject to constraints $$x_1 + x_2

1. **Problem Statement:** We have a transportation problem with origins San Jose, Las Vegas, Tucson and destinations Los Angeles, San Francisco, San Diego. The goal is to minimize

1. **Problem Statement:** A company transports units from three factories (F1, F2, F3) to four warehouses (W1, W2, W3, W4). Given transportation costs, supplies, demands, and a fea

1. **State the problem:** We have an annual demand $D=5000$ packs, ordering cost per order $S=12000$, holding cost per pack per year $H=4000$, and lead time of 3 weeks. We need to

1. **State the problem:** Calculate the Economic Order Quantity (EOQ), ordering frequency, total costs, and reorder level for an inventory system with given demand, ordering cost,

1. **State the problem:** We want to determine how many units of products A and B to produce weekly to maximize profit.

1. **Problem statement:** We have a duplicating machine with a Poisson service rate of mean $\mu = 10$ jobs/hour and arrivals at rate $\lambda = 5$ jobs/hour over an 8-hour workday

1. **State the problem:** Mossaic Tiles, Ltd. wants to maximize profit by deciding how many batches of large tiles ($x$) and small tiles ($y$) to produce weekly, subject to constra