Quantitative Methods
The Wade Co. is a manufacturer of Product X which is an important ingredient for the hightech industry. Each month, the company can produce up to 27 units of Product X by usingregular time labour at the cost of $40 per unit. In addition, the company can produce as many
Product X as they need by hiring overtime labour at the cost of $60 per unit. For the nextthree months, the company must satisfy the demands of 30 units, 20 units and 40 units for thefirst, the second and the third month, respectively.
The process has 20% of defective rate. In other words, if Wade Co produces 30 units of
Product X, 20% of them are defective and cannot be used to meet the monthly demand. Inaddition, 10% of all units on hand at the end of a month get spoiled and cannot be used tomeet the demand of next month. To reflect the spoilage effect, $15 is charged for every unitof inventory at the end of the month.
The inventory checking shows that 20 usable units of Product X are on hand at the beginningof the first month.
(a) Develop a LP model to minimise the total cost for the Wade Co. to meet the demands for the next three months. Use a suitable computer software to solve the LP problem.
Hint: The Ending Inventory of the Month = The beginning Inventory of the Month
The demand of the month + The quantity produced during the month.
(b) Interpret the compute solution output that you obtained in 3(a) and answer the following questions.
There were 20 available units at the beginning of the first month. If arequirement is added in that 20 units should be available at the beginning ofthe fourth month, how will it affect your formulation in Question 3(a)? Inaddition, discuss how this new requirement will affect the objective functionvalue.
Spoilage charge has been increased from $15 per unit to $17 per unit. Howwill it impact the optimal solution?
Thanks to the special arrangement with the labour union, 10 more units can beobtained at the regular time cost in the third month. What will be the impact ofthis arrangement on the total cost?