BioPharma $$ pp$.184-187,$ Chopra and Meindl $(2016)$ Write a mathematical formulation for the production network of Biopharma. $1)$ Define sets $2)$ Define parameters $3)$ Define decision variables $4)$ Write the model together with the explanation of the constraints photos are below BioPharma, Inc. In $2009,$ Phillip $($Phil$)$ Landgraf faced several glaring For $2009,$ sales of each product by region and problems in the financial performance of his company, the production and capacity at each plant are shown in BioPharma, Inc. The firm had experienced a steep Table $6-18.$ The plant capacity, measured in millions of decline in profits and very high costs at its plants in kilograms of production, can be assigned to either Germany and Japan. Landgraf, the company's president chemical as long as the plant is capable of producing for worldwide operations, knew that demand for the both. BioPharma has forecast that its sales for the two company's products was stable across the globe. As a chemicals are likely to be stable for all parts of the result, the surplus capacity in his global production world, except for Asia without Japan, where sales are network looked like a luxury he could no longer afford. expected to grow by $10$ percent annually for each of the Any improvement in financial performance was next five years before stabilizing. dependent on having the most efficient network in place, The Japanese plant is a technology leader within because revenues were unlikely to grow. Cutting costs the BioPharma network in terms of its ability to handle was thus a top priority for the coming year. To help regulatory and environmental issues. Some developdesign a more cost$-$effective network, Landgraf assigned ments in the Japanese plant had been transferred to other a task force to recommend a course of action. plants in the network. The German plant is a leader in terms of its production ability. The plant has routinely Background had the highest yields within the global network. The BioPharma, Inc., is a global manufacturer of bulk Brazilian, Indian, and Mexican plants have somewhat chemicals used in the pharmaceutical industry. The company holds patents on two chemicals that are called Highcal and Relax internally. These bulk chemicals are outdated technology and are in need of an update. used internally by the company's pharmaceutical After considerable debate, the task force identified the cost division and are also sold to other drug manufacturers. structure at each plant in $2009$ as shown in Table $6-19.$ There are distinctions in the precise chemical specifica$-$ Each plant incurs an annual fixed cost that is independent tions to be met in different parts of the world. All plants, of the level of production in the plant. The fixed cost however, are currently set up to be able to produce both includes depreciation, utilities, and the salaries and fringe chemicals for any part of the world. benefits of employees involved in general management, Table $6-18$ Sales by Region and Production$/$Capacity by Plant of Highcalscheduling, expediting, accounting, maintenance, and so BioPharma transports the chemicals in specialized forth. Each plant that is capable of producing either containers by sea and in specialized trucks on land. Highcal or Relax also incurs a product$-$related fixed cost The transportation costs between plants and markets are as that is independent of the quantity of each chemical shown in Table $6-20.$ Historical exchange rates are shown produced. The product$-$related fixed cost includes depreci$-$ in Table $6-21$ and the regional import duties in Table $6-22.$ ation of equipment specific to a chemical and other fixed Given regional trade alliances, import duties in reality vary costs that are specific to a chemical. If a plant maintains based on the origin of the chemical. For simplicity's sake, the capability to produce a particular chemical, it incurs however, the task force has assumed that the duties are the corresponding product$-$related fixed cost even if the driven only by the destination. Local production within chemical is not produced at the plant. each region is assumed to result in no import duty. Thus, The variable production cost of each chemical production from Brazil, Germany, and India can be sent to consists of two components: raw materials and production Latin America, Europe, and the rest of Asia excluding costs. The variable production cost is incurred in propor$-$ Japan, respectively, without incurring any import duties. tion to the quantity of chemical produced and includes Duties apply only to the raw material, production, and direct labor and scrap. The plants themselves can handle transportation cost component and not to the fixed cost varying levels of production. In fact, they can also be idled component. Thus, a product entering Latin America with a for the year, in which case they incur only the fixed cost, raw material, production, and transportation cost of $ $10$ none of the variable cost. incurs import duties of $ $3.($continued$)$ Table $6-22$ Import Tariffs $($Percentage of Value of Product Imported, Including Transnortation$)$ Network Options Under Consideration Questions The task force is considering a variety of options for $1.$ How should BioPharma have used its production network its analysis. One option is to keep the global network in $2009?$ Should any of the plants have been idled? What is with its current structure and capabilities. Other the annual cost of your proposal, including import duties: options include shutting down some plants or limiting $2.$ How should Landgraf structure his global production the capability of some plants to producing only one network? Assume that the past is a reasonable indicator of chemical. Closing down a plant eliminates all variable the future in terms of exchange rates. costs and saves $80$ percent of the annual fixed costs $3.$ Is there any plant for which it may be worth adding : $($the remaining $20$ percent accounts for costs that are million kilograms of additional capacity at a fixed cost or incurred related to the plant shutdown$).$ Similarly, if a $ $3$ million per year? plant is limited to producing only one chemical, the $4.$ How are your recommendations affected by the reduction plant saves $80$ percent of the fixed cost associated with of duties? the chemical that is no longer produced. The two $5.$ The analysis has assumed that each plant has a $100$ percent options being seriously considered are shutting the yield $($percent output of acceptable quality$).$ How woulc Japanese plant and limiting the German plant to a you modify your analysis to account for yield differences single chemical. across plants? $6.$ What other factors should be accounted for when making your recommendations?