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).
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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
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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 C₁ = unit cost of item j S;= cost per order placed for item j ¡ = inventory carrying charge as a percentage of the cost per unit W = the maximum amount of space available for all goods W;= space required for item j The decision variables are Q₁, the amount of item j to order. The model is: Minimize Σ s.t £% [C,D, +²…
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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