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Consider the Economic Order Quantity (EOQ) Model for Multiple Products

question 10

Essay

Consider the economic order quantity (EOQ) model for multiple products that are independent except for a budget restriction. The following model describes this situation
Let Dk = annual demand for product k
Ck = unit cost of product k
Sk = cost per order placed for product k
i = inventory carrying charge as a percentage of the cost per unit
B = the maximum amount of investment in goods
N = number of products
The decision variables are Qk, the amount of product k to order. The model is:  Minimize k=1N[CkQk+SkDkQk+iCkQk2]\text { Minimize } \sum _ { k = 1 } ^ { N } \left[ C _ { k } Q _ { k } + \frac { S _ { k } D _ { k } } { Q _ { k } } + i C _ { k } \frac { Q _ { k } } { 2 } \right] s.t. k=1NCkQkB\sum _ { k = 1 } ^ { N } C _ { k } Q _ { k } \leq B Qk0 for k=1,2,NQ _ { k } \geq 0 \text { for } k = 1,2 , \ldots N
a. Set up a spreadsheet model and for the following data:  Product 1  Product 2  Product 3  Annual Demand 125015501450 Product Cost $120$90$105 Order Cost $110$175$140B$30,000i0.3\begin{array} { | l | c | c | c | } \hline & \text { Product 1 } & \text { Product 2 } & \text { Product 3 } \\\hline \text { Annual Demand } & 1250 & 1550 & 1450 \\\text { Product Cost } & \$ 120 & \$ 90 & \$ 105 \\\text { Order Cost } & \$ 110 & \$ 175 & \$ 140 \\B & \$ 30,000 & & \\i & 0.3 & & \\\hline\end{array}
b. 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.)

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Definitions:

Nation

A large group of people united by common descent, history, culture, or language, inhabiting a particular country or territory.

Total Employment

The total number of people employed in an economy at a given time, including both full-time and part-time workers.

Absolute Number

A value expressed without comparisons, adjustments, or relations, representing a distinct, precise figure.

Farm Employment

Farm employment refers to the work and jobs related to agriculture, including the cultivation of crops and livestock management.

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