Imperial Stone Manufacturing is a company from Perak, Malaysia, that imports marble, granite, and limestone from around the world. It has several facilities in both Peninsular Malaysia (in Perak and Selangor) and Borneo (Sarawak) for manufacturing the rock.

It cuts, shapes, and profiles the rock in slabs and tiles, which are ready to be used in construction and furniture factories both domestically and abroad.

The company, which prides itself on producing its products in compliance with international standard ISO 9001:2000/DIN EN 9001:2000, has been able to sell high-quality marble and granite outputs to customers from sophisticated markets such as Japan, Australia, and South Korea.

To continue its expansion into other overseas markets, the company has decided to embark on a major investment campaign and substitute its Taiwanese machines with new, expensive, stateof-

the-art European marble-cutting machines.

After some research, the chief executive officer (CEO) has determined that, to suit the company’s manufacturing needs, he will buy Italian marble-cutting machines, which are reputed to be the best in the world. With the machines, his company will be able to process raw stones all the way to the finished product, including milling and polishing and getting them ready for packing and export.

However, given the high price of the machines, the CEO decides to start buying only one machine for each of the company’s main plants and to complete the equipment upgrade only when profits grow. He knows he needs to be able to pay not only for the machines, but also for the additional handling costs of the machines, including postal service assistance and spare parts shipment from Europe.

However, the CEO has a major dilemma. Because of differences both in the machine models and in the kind of slabs and tiles manufactured in each of Imperial Stone’s plants, the expected costs of adding a machine to a plant are not the same in every plant; the additional handling costs will vary by plant, making each allocation more or less expensive.

As a first solution to decrease costs, the CEO decides to not upgrade the company’s factories in Selangor and Sarawak, which are far away from the headquarters, and to upgrade with new machines only the plants located in Sitiawan, Ipoh, Kampar, and Gopeng. Because these plants are all based in Perak, he reckons that this will minimize the additional handling costs and that these plants represent, as a whole, the best possible combination.

To further fine-tune his solution, he also played with single costs/plant possibilities and, after trying some machine–plant allocations, he created a table with likely handling costs in different scenarios.

Sitiawan Ipoh Kampar Gopeng Machine 1 7 4 1 4 Machine 2 4 6 7 2 Machine 3 8 5 4 6 Machine 4 6 7 6 3 The CEO, who has some knowledge of linear programming, has decided to choose the best allocation for costs by modeling and solving the problem as a normal transportation problem.

However, one engineer in the company observes that the problem cannot be considered a real transportation problem because at least two unusual characteristics make it special;

these are:

●● The number of sources is the same as the destinations.

●● Both supply and demand = 1.

Accounting for these (correct) considerations, the CEO will have to determine:

a. In what way this problem can be better formulated.

b. The optimal cost solution (using Excel Solver or other software). LO.1