The Economic Order Quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model are holding cost per unit, ordering cost and the cost of goods ordered. The assumptions forthat model are that only a single item is considered, that the entire quantity ordered arrives at one time, that the demand for the item is constant over time, and that no shortages are allowed.Suppose we relax the first assumption and allow for multiple items that are independent except for a restriction on the amount of space available to store the products. The following model describes this situation:Let D; = annual demand for item jC; unit cost of item jS; = cost per order placed for item ji = inventory carrying charge as a percentage of the cost per unitW = the maximum amount of space available for all goodsw; = space required for item jThe decision variables are Q;, the amount of item j to order. The model is:Minimizes.t+8+ic, 1]Σκ,,;D; +'ΣwQ ≤ Wj = 1, 2, ... NIn the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D;/Q; is the number of orders), and the last term is the annual inventory holding cost (Q;/2 is the average amount of inventory).Set up a spreadsheet model for the following data:Item 1Item 2Item 3Annual Demand2,5002,5002,000Item Cost ($)905070Order Cost ($)150135125Space Required (sq. feet)502540W = 4,000i = 0.3Solve the problem using Excel Solver. Hint: You will need to start with decision variable values that are greater than 0 for Solver to find a solution.If required, round your answers to two decimal places.Optimal Solution:Q1 =Q2Q3=If required, round your answer to the nearest dollar. Do not round intermediate calculations.Total cost =$

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Answered: The Economic Order Quantity (EOQ) model…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Henrique Correa's bakery prepares all its cakes between 4 A.M.and 6 A.M.so they will be fresh when customers arrive. Day-old cakes are virtually always sold, but at a 50% discount off the regular $8 price. The cost of baking a cake is $5,and demand is estimated to be normally distributed, with a mean of 25 and a standard deviation of 7. What is the optimal stocking level?
ESTRELLA is a bike retailer located in the outskirts of Bacolod City. ESTRELLA purchases bikes from STORAGEHUB in orders of 250 bikes which is the current economic order quantity. STORAGEHUB is now offering the following bulk discounts to its customers: Price 0% discount on orders less than 499 P3,500 10% discount on orders above 500 units - 999 3,150 15% discount on orders above 1,000 units 2,975 ESTRELLA is wondering if the EOQ model is still the most economical and whether increasing the order size would actually be more beneficial. Following information is relevant to forming the decision: Annual demand is 5000 units Ordering cost is $100 per order Annual holding cost is 25% How much is the EOQ for each quantity discount? How much should be the EOQ?
Pam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers is 16,000. The annual holding cost per unit per year is $2.50 and the cost to place an order is $50. There are 300 working days in a year. What is the optimal order quantity? 80 units 800 units 40 units 400 units How many orders in a year? 20 orders 40 orders 20 units 40 units How many days between orders? 20 days 40 days 18.25 days 15 days How much is the total inventory cost? $1000 $2500 $2000 $3000
Martina is in charge of ordering brake pads for an auto shop. The daily demand for brake pads is normally distributed with an average of 40 brake pads and a standard deviation of 8 break pads. Currently, it takes 4 days between when Martina places an order for new brake pads and when the order is received. Currently, Martina orders new break pads when there are 184 break pads left in stock. 1) What is the average demand during lead time? 2) What is the standard deviation of demand during lead time? 3)What is the service level provided by Martina's auto shop?
Surge Electric uses 4,000 toggle switches a year. Switches are priced as follows: 1 to 499, 90cents each; 500 to 999, 85 cents each; and 1,000 or more, 80 cents each. It costs approximately$30 to prepare an order and receive it, and carrying costs are 40 percent of purchase price perunit on an annual basis. Determine the optimal order quantity and the total annual cost.
1. Suppose the demand of a product in a retail store is 800 per year and it occurs at a constant rate. Placement of an order of this product to an outside supplier by the store is 40 Dollar. The super market authority has calculated the inventory holding cost per unit per year as 90 cents. Assuming no occurrence of shortages of the product, find a) i. the minimal order quantity of the product from the outside supplier if the product is not allowed to sell during production. ii. the minimal number of orders per year. Explain whether the nearest integer number of orders per year is justified. iii. the cycle time of a lot in months. iv. the annual minimal total cost of ordering and inventory holding for that minimal order quantity. v. the reorder point if the lead time of delivering a lot is 2 days,? b) If the production rate of processing the product is 1200 per year and the set up cost per set up is 65 Dollar. If the selling of the product is allowed during production, determine i) the…
Suppose a certain company has a product for which the assumptions of the inventory model with backorders are valid. Information shows that: 1 = 100 units/year h = 5/unit/year PhP 25/unit C = K = PhP 15/order The company is considering the possibility of allowing backorders to occur for the product. Find the optimal order policy and the optimal total inventory cost given that the annual backorder cost per unit is estimated to be PhP 30. (Q* – S*)² + h- 2Q* S*2 + b + Ac 2Q* G(Q", S*) = K{
True or False: Single-Period inventory model makes the assumption that the demand follows a standard normal distribution.
Problem 20-39 (Algo) CU, Incorporated (CUI), produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity, Q, to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price-break and other data for the problem: Price of copper 0.80 per pound up to 2,499 pounds 0.79 per pound for orders between 2,500 and 4,999 pounds %24 0.77 per pound for orders 5,000 pounds or greater 51,000 pounds per year 30 percent per unit per year of the price of the copper Annual demand Holding cost Ordering cost 30 Which quantity should be ordered? Quantity pounds

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