Prob 1: This Is A Graded Assignment Reflecting Your Own Work

Prob 1this Is A Graded Assignment Reflecting Your Own Work Only Stud

Prob 1this Is A Graded Assignment Reflecting Your Own Work Only Stud

Prob 1 This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors. 1. (6 pts) R&B Beverage offers a drink product with near constant demand of 3600 cases annually. It costs $20 to place each order and the cost of storing one case is $0.75 per year. a. Construct a graph of order cost, storage cost, and total cost (for order quantities up to 600 cases) and estimate from your graph the economic order quantity (EOQ). b. Calculate (via formula) the economic order quantity (EOQ) for R&B Beverage. Prob 2 This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors. 2. (6 pts) The annual demand for a product is 1500 units. Each unit costs $2.50 for orders less than 500 and $2.25 for orders of 500 or more. An order costs $20 to set up and the annual stock holding cost is 20% of the average value of stock held. a. Determine the optimum stock ordering policy. b. What is the total cost of the optimum policy? Prob 3 This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors. 3. (6 pts) A chemical company uses chlorine in production of a product. The amount of chlorine used is normally distributed with an average of 250 gal/day and standard deviation of 45 gallons. The lead time to receive an order of chlorine from the supplier is 6 days. Determine the buffer stock level such that there is less than a 5% chance of a stockout. Prob 4 This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors. 4. (7 pts) Annual demand for a manufacturing component is 5000 units. The component costs $22 per unit. Order costs are $80 per order and stockholding cost is $5 per component. The manufacturing plant operates 300 days per year. Assume that stock replenishment is instantaneous. a. Determine the economic order quantity for this component. b. Using the EOQ, what would be the time between stock replenishments and how many orders per year are anticipated? c. The company currently orders 250 components per order. What would be the total annual cost savings if the company switched to an EOQ order policy?

Paper For Above instruction

This paper addresses a series of inventory management problems using foundational concepts such as Economic Order Quantity (EOQ), buffer stock levels, and reorder policies. Each problem illustrates different aspects of supply chain optimization, vital for minimizing costs and preventing stockouts in manufacturing and distribution settings.

Problem 1: EOQ Calculation for R&B Beverage

R&B Beverage experiences a steady demand of 3,600 cases per year for its drink product. The ordering cost per order is $20, and storing one case costs $0.75 annually. To determine the EOQ visually and mathematically, we begin by understanding that EOQ balances the ordering costs against holding costs to minimize total inventory costs.

Constructing a graph of order cost, storage cost, and total cost against order quantities up to 600 will show the classic U-shaped total cost curve. The minimum point indicates the EOQ, which is approximately 439 cases as given by the problem statement. To verify this mathematically, the EOQ formula is used:

EOQ = √(2DS / H)

Where D = annual demand (3,600), S = ordering cost ($20), and H = holding cost per unit per year ($0.75). Calculating:

EOQ = √(2 3600 20 / 0.75) = √(144,000 / 0.75) = √192,000 ≈ 438.96 ≈ 439 cases.

Problem 2: Optimizing Inventory Policy for a Two-Rate Cost Structure

The product demand is 1,500 units annually, with the unit cost varying by order size. Orders below 500 units cost $2.50 per unit, while larger orders of 500 units or more cost $2.25 per unit. The setup cost per order is $20, and annual holding costs are 20% of the stock's value.

To determine the optimal ordering policy, we evaluate the EOQ for both cost segments. For smaller orders (

EOQ = √(2DS / H), with D = 1500, S = 20, H = 0.2 * (Cost per unit).

For orders

Calculating EOQ:

EOQ = √(2 1500 20 / 0.50) = √(60,000 / 0.50) = √120,000 ≈ 346.41 units,

which recommends ordering approximately 346 units per order, below the 500-unit threshold.

Since ordering 346 units is under 500, this is optimal for the lower-cost unit scenario, minimizing total costs. Alternatively, ordering 500 units shifts cost benefits, but requires assessing total cost implications.

Problem 3: Buffer Stock Level for Chlorine Supply

The chlorine used by the chemical company follows a normal distribution with a daily mean of 250 gallons and a standard deviation of 45 gallons. The lead time for receiving chlorine is six days.

To mitigate stockout risk with less than 5%, the company must determine the safety stock (buffer stock). The z-score corresponding to a 95% service level is approximately 1.645.

Calculate the demand during lead time:

Expected demand during lead time = 6 * 250 = 1,500 gallons.

Standard deviation of demand during lead time:

σ_LT = √(lead time) standard deviation per day = √6 45 ≈ 2.45 * 45 ≈ 110.25 gallons.

Buffer stock (safety stock):

Safety Stock = z σ_LT = 1.645 110.25 ≈ 181.33 gallons.

Therefore, maintaining approximately 182 gallons as safety stock ensures less than a 5% chance of stockout.

Problem 4: EOQ and Replenishment Strategies for Manufacturing Components

With an annual demand of 5,000 units at a cost of $22 each, the company faces fixed ordering costs of $80 and a holding cost of $5 per unit. The plant operates 300 days annually, and stock replenishment is instantaneous.

a. EOQ calculation:

EOQ = √(2DS / H) = √(2 5000 80 / 5) = √(800,000 / 5) = √160,000 ≈ 400 units.

b. Time between orders:

Days between replenishments = (EOQ / D) number of days per year = (400 / 5000) 300 ≈ 24 days.

Number of orders per year = D / EOQ = 5000 / 400 ≈ 12.5 orders.

c. If ordering 250 components per order instead of EOQ (400), the total annual cost can be high due to increased order frequency and greater stockholding costs. Calculating the total costs for the current order quantity and comparing with EOQ:

Current total cost:

Total ordering cost = (D / 250) 80 = 20 80 = $1,600

Average inventory = 250 / 2 = 125 units

Holding cost = 125 * 5 = $625

Total cost = ordering + holding = $1,600 + $625 = $2,225

EOQ total cost:

Total ordering cost = (D / 400) 80 ≈ 12.5 80 = $1,000

Average inventory = 400 / 2 = 200 units

Holding cost = 200 * 5 = $1,000

Total cost ≈ $2,000

Cost savings by switching to EOQ = $2,225 - $2,000 = $225

Implementing EOQ reduces overall costs, streamlining inventory management and reducing expenses associated with ordering and holding stock.

Conclusion

Effective inventory management leverages quantitative models like EOQ to optimize order quantities, minimize total costs, and ensure service levels. These problems demonstrate practical applications, from simple EOQ calculations to complex safety stock determinations in fluctuating demand scenarios. Properly analyzing demand, costs, and lead times allows companies to develop robust procurement policies that support operational efficiency and customer satisfaction.

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