Question

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 arc allowed. Suppose we relax the first assumption and allow for multiple items that are independent except for a budget restriction. 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 B- the maximum amount of investment in goods N-number of items The decision variables are, the amount of item j to order. The model is In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost is the number of orders), and the last term is the annual inventory holding cost (is the avcrage amount of inventory) 1 Sct up a spreadshcect model for the following data Item 1 Item 2 Item 3 2,000 2,000 1,000 $100 $50 $80 $150 $135 $125 Annual Demand Item Cost Order Cost 2. Solve the problem using Excel Solver. (Hint: For Solver to find a solution, you need to start with decision variable values that are greater than 0.)

Answer 1

1. Spreadsheet model is following:

Item 1 Item 2 Item 3 2 Annual Demand 3 Item Cost 4 Order Cost 5 Inventory carrying charge0.2 6 7 Order Quanti Dj 2000 Cj 100 Sj 150 2000 50 135 0.2 1000 80 125 0.2 9 Total investment 10 11 Total Cost/Item 12 13 Total Cost 14 15 16 17 18 -SUMPRODUCT(C3:E3,C7:E7 S -SUM(C11:E11)

2. Inventory carrying charge (I) and maximum amount of investment in goods (B) is not specified in the question.

However, a hypothetical value of 0.2 for I and 12000 for B is taken to demonstrate the solution

Initialise the model by entering non-zero values in Qj (range C7:E7)

Enter Solver parameters as below:

S Solver Parameters SCS1B Set Objective: To: O Max ⓔMín O Value Of: By Changing Variable Cells: SCS7:SES7 Subject to the Constraints: Add Change Delete Reset AllI Make Unconstrained Variables Non-Negative Select a Solving Method: IPOPT Nonlinear Options Solving Method Select the IPOPT Nonlinear engine for Solver Problems that are smooth nonlinear.Select the LP Simplex engine for linear Solver Problems Solve Close

Click Solve button to generate the optimal solution:

Item 1 2000 100 150 0.2 Item 2 Item 3 1000 2 Annual Demand 3 Item Cost 4 Order Cost 5 Invento 2000 S Solver Results 135 0.2 125 0.2 ing chargeI Solver found a solution. All constraints and optimality conditions are satisfied. Reports 7 Order Quantit 53.39 71.80 38.39 Answer Keep Solver Solution 9 Total investment 10 11 Total Cost/Item 12000 12000 В Restore Original Values $206,153 104,12083,56:3 Return to Solver Parameters Dialog 13 Total Cost 14 15 16 17 18 19 393,836 Canceled Solver found a solution. All constraints and optimality conditions are satisfied. When Simplex LP is used, this means Solver has found a global optimal solution. 21 23 24