Question

A manufacturing firm is determining the production and inventory plan to meet demand in the next three months. The production facility can produce at most 400 units in one month. The cost of producing one unit in the next three months are respectively 28, 30, and 40 dollars. The cost of carrying one unit of inventory in the next three months are respectively are 2, 3, and 3 dollars. Assume that the firm has a starting inventory of 20 units. The demand for the next three months are respectively 200, 250 and 400 units. Build a mathematical formulation that will minimize the production and inventory costs while ensuring that monthly demands are met.

a. Define the decision variables using complete sentences

b. Write down the objective function in words

c. Write down the constraints using complete sentences

d. Express the objective function mathematically using the decision variables defined in part a

e. Express the constraints mathematically using the decision variables defined in part a; see slides for an example

f. Input the mathematical formulation into an Excel worksheet in an organized fashion. Once done organizing the worksheet then copy paste the table from Excel into Word showing the setup of your worksheet. DO NOT turn in the EXCEL worksheet. All homework answers should be in one file formatted as pdf.

g. What is the optimal solution? (Use solver to determine the solution)

h. What is the optimal objective function value? (use solver to determine the optimal objective function value)

Answer 1

(a) Decision variable shall be how much to produce per month (g) so that demand is met as well as units are produced with lowest possible production cost (i) and units carry forward (h) after demand is fulfilled lead to least carrying cost (j).

(b) Objective function is to minimize the production cost and inventory carrying cost by ensuring demand is fulfilled. Where

1. d is production cost per unit per month
2. g is produced units in corresponding month
3. e is carrying cost per unit per month
4. h is carry forward units in each month

(c) Constraints are Maximum units that can be produced in a month is 400. That is ,

(d) Objective Function :- Minimize : d * g + e * h
(e) Constraint for maximum production units per month is a

Model is as below :-