Question

Underlying replenishment policies. 1. Wilson's formula 2. Order point method 3. Impact of discounting on replenishment I. Base Case Summary Getributes fully equipped bathrooms, as well as bathroom items (soap For a bathroom shelf, the supplier offered the following price the quantities ordered, with a replenishment period of usually The company Alsatian bathrooms distributes fu dishes, towel rails, tablets, etc.). For a bathr conditions: € 20 per unit, regardless of the quantitie one month. roduct is stable at 2,500 units. The holding rate of inventory items costs 150 €. This product is managed by an order point system. The projected annual demand for the product is stable at is 25% per year. Placing an order costs 150 €. This II. Questions 1 Calculate the base case optimal order quantity, minimizing the annual o this year's annual negotiation, the bathroom shelf supplier offers the following conditions for discounts on the quantities of shelves purchased: • Less than 500 units, price: 20.00 €, • Between 500 and 1499 units, price: 18.50 €, • More than 1500 units, price: 17.50 €. These prices are for all quantities ordered, as long as the respective thresholds are exceeded. 1. Using the diagram below, graphically reconstruct the total cost function associated with the proposed rebate mechanism. 2. From this function, find the optimal order quantity (mathematically and graphically).

Answer 1

Optimal order quantity = [2*Annual usage(in units)*Setup costs/Annual carrying cost per unit]^(1/2) In the given question, annual demand is 2500 units Ordering costs = 150 Euro Holding cost per unit per year = 25%*20 = 5 Euro Applying the given data in the above formula, we get Optimal order quantity 387 units No.of orders 6.5 Caculation of total cost if the order quantity is Ordering cost Holding cost Purchase cost Total cost (Annual usage/Order (Order No.of units * quantity) *Ordering quantity/2)*Holding Purchase cost cost il cost per unit per year per unit Less than 500 units 938 1,000 8,000 9,938 We have considered 400 units, so purchase price of 20 Euro would be applicable Between 500 & 1499 units 375 2,313 18,500 21,188 We have considered 1000 units, so purchase price of 18.5 Euro would be applicable More than 1500 units 188 4,375 35,000 39,563 We have considered 2000 units, so purchase price of 17.5 Euro would be applicable