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.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 22P

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The Cove at UP recently hired Ray Bones as the new inventory replenishment manager. Ray is a recent Accounting graduate from the University of Portland and learned all about managing inventory in BUS 457. Ray needs to determine the length-of the build up and sell thru periods associated with an optimal ordering policy for an item with constant annual demand of 2200 units, unit cost $3790.5, annual unit holding cost percentage 0.28, and aggregate order placement cost $425 for an item with a production rate of 3820 (units/year). What are the cost minimizing order quantity and build up and sell thru periods? (specify answer as a whole number) (specify answer to 3 decimal places). (specify answer to 3 decimal places).
The TransCanada Lumber Company and Mill processes10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, the logging company’ssupplier begins delivery to the lumber mill at the rate of 60logs per day. The lumber mill has determined that the ordering cost is $1600 per order, and the cost of carrying logsin inventory before they are processed is $15 per log on anannual basis. Determine the following:a. The optimal order sizeb. The total inventory cost associated with the optimalorder quantityc. The number of operating days between ordersd. The number of operating days required to receive anorde
Company ABC utilizes an inventory system in which order gets placed after uniform time duration. Which of the following represents the inventory policy used by the Company? a) (0, x) Model b) EOQ Model c) Fixed period model d) Fixed quantity model
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 for that 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 Dj = annual demand for item j Cj = unit cost of item j Sj = cost per order placed for item j i = inventory carrying charge as a percentage of the cost per unit W = the maximum amount of space available for all goods wj = space required for item j The decision variables are Qj , the amount of item j to order. The model is: In…
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 for that 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 = annual demand for item j = unit cost of item j S₁ = cost per order placed for item j W, = space required for item j W = the maximum amount of space available for all goods ¡ = inventory carrying charge as a percentage of the cost per unit. The decision variables are Q₁, the amount of item j to order. The model is $ [50, +501 +10,21] j=1 N…
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 for that 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 = annual demand for item j Cj = unit cost of item j S; = cost per order placed for item j = space required for item j W; W = the maximum amount of space available for all goods i = inventory carrying charge as a percentage of the cost per unit. The decision variables are Q₁, the amount of item j to order. The model is Minimize s.t. N j = 1 [c₂p₁ +…
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 Annual demand Holding cost Ordering cost $ 0.82 per pound up to 2,999 pounds 0.81 per pound for orders between 3,000 and 5,999 pounds $ 0.79 per pound for orders 6,000 pounds or greater 48,000 pounds per year 30 percent per unit per year of the price of the copper 30 Which quantity should be ordered? Quantity pounds
The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 35,000 yards of denim per year to make jeans. The cost of ordering denim from the textile company is $500 per order. It costs Western $0.35 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.
A manufacturer of exercise equipment purchases the pulley section of the equipment from a supplier who lists these prices: Less than 1000 $5.00 each 1000 to 3999 $4.95 each 4000 to 5999 $4.90 each 6000 or more $4.85 each Ordering costs are $50, annual carrying costs per unit are 40 percent of purchase cost, and annual usage is 4900 pulleys. Determine the order quantity that will minimize total cost.
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?
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 for that 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 Dj = annual demand for item j Cj = unit cost of item j Sj = cost per order placed for item j i = inventory carrying charge as a percentage of the cost per unit W = the maximum amount of space available for all goods wj = space required for item j The decision variables are Qj, the amount of item j to order. The model is:…
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 for that 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 Dj = annual demand for item j Cj = unit cost of item j Sj = cost per order placed for item j i = inventory carrying charge as a percentage of the cost per unit W = the maximum amount of space available for all goods wj = space required for item j The decision variables are Qj, the amount of item j to order. The model is: (view…

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