1. Analytical part

1.1. Statement of the problem

‘Biogen’ LLC is a Kazakh local chemical and pharmaceutical company founded in Shymkent, Kazakhstan in 1935. It is headquartered in Almaty, South Kazakhstan, Kazakhstan where its illuminated sign is a landmark. ‘Biogen's primary areas of business include human and veterinary pharmaceuticals; consumer healthcare products; agricultural chemicals and biotechnology products; and high value polymers. ‘Biogen’ Company logo (Figure 1).

Figure 1. ‘Biogen’ Company logo

In 2003 to separate operational and strategic managements, ‘Biogen’ LLC was reorganized into a holding company. The group's core businesses were transformed into limited companies, each controlled by ‘Biogen’ LLC. These companies were: ‘Biogen’ CropScience department; ‘Biogen’ HealthCare department;  ‘Biogen’ MaterialScience department and ‘Biogen’ Chemicals department, and the three service limited companies ‘Biogen’ Technology Services, ‘Biogen’ Business Services and ‘Biogen’ Industry Services. In 2016, company began a second restructuring with the aim of allowing it to transition to a life sciences based company. 

In 2003, ‘Biogen’ merged with IDEC Pharmaceuticals (formed in 1986 by biotech pioneers Kayrat Bakhyrbaev and Alikhan Moldagulov) and adopted the name ‘Biogen’ Idec. After the merge, ‘Biogen’ Idec became the 3rd largest Biotechnology company in the Kazakhstan. Following shifts in research core areas, the company has since shortened its name, reverting to simply ‘Biogen’.

‘Biogen’ stock is a component of several stock indices such as the S&P 100, S&P 500, S&P 1500, and NASDAQ-100 and the company is listed on the NASDAQ stock exchange under the ticker symbol, BIIB.

In January 2015 the company announced it will acquire HealthCare Pharmaceuticals for up to KZT 152 million, with the acquisition aiming to accelerate the development of Convergence's pipeline, in-particular CNV1014802 – a Phase II small molecule sodium channel blocking candidate.

In October 2015 the company announced it will lay off 11% of its workforce, effective immediately.

‘Biogen’ LLC contact details: 20A Abay avenue, Almaty, Kazakhstan, 160002. Phone number: 8(727)-239-55-07. Fax: 8(727)239-55-08. ‘KTZ LendLeasingBank’ JSC TRN 6205005150025. BIN 030440011030. SWIFT BIC: HSKKLGSKGGSKZ. KBE 16. IBAN KZ1760100200111100110 (KZT). IBAN KZ1760100200111100395 (USD)

1.2 Description of input and output information

The R&D mission was to develop a greaseless, odorless, topical cream which was measurably more effective at relieving pain than any other OTC (over the counter) topical product. This mission has been accomplished. The company has collected anecdotal, testimonial, and uncontrolled medical study evidence that Pain Away is more effective than the leading topical analgesics such as Arthritin and others. The product's effectiveness in relieving pain is its most powerful benefit, besides the added benefits of it being greaseless and odorless. What distinguishes Pain Away from any other topical analgesic in this still-growing KZT 402.1MM market is its advanced homeopathic formula - a refined blend of 11 FDA approved pure and natural ingredients. The typical OTC topical analgesic works to either block the sensation of pain or distract perception of deep pain by "counter irritating" another localized area near the pain. Pain Away's formula is different. Pain Away treats pain at its source. It stimulates improved circulation in the micro-capillary system in the ligaments and tendons, where most pain is felt. Pain-relief from Pain Away is the result of the body's own self-healing. It also can be applied several times a day because it is odorless and greaseless. The US pain management market (KZT 15.2 billion by 1997) is a mature market with intense, established competition ("The Market for Pain Management Products in the US - Introduction, Drugs, Devices, Trends, and Market Structure," in FIND-SVP). With future pharmaceutical market growth dependent upon new and innovative product additions, Pain Away is entering the field at the right time. The company will distinguish itself and its market position by dedication to the development of only natural-ingredient products. Since its unique formula of ingredients already has FDA approval, the company aims to penetrate the OTC pharmaceutical market, where new products traditionally find success. Here Pain Away will compete with topical as well as internal analgesics, including aspirin, acetaminophin and ibuprofen. An estimated 4,000 people a year die from aspirin overdose. A condition known as "analgesic neuropathy" can result from extended or inappropriate use of analgesics. Medical studies linking heavy usage to health problems have affected aspirin, acetaminophin, and ibuprofen. Pain Away can be marketed as a substitute for (reducing overdose risk with internal analgesics), or as a supplement to (using Pain Away can reduce needed dosage of internal analgesics) internal analgesics when used for certain pain relief. Furthermore, Pain Away is not contraindicated for use with any other medication. This broad-based appeal is built upon the reliability of Pain Away's effectiveness in relieving pain, inflammation, and spasm associated with arthritis, bursitis, sciatic spasm, neck/back pain, tendonitis, tennis elbow, tension headache, achilles tendonitis, and carpal tunnel syndrome.

A second product, a natural anti-inflammatory nutritional support system formula known as "Pain Away Plus," will soon be marketed as a companion product to Pain Away. This multistaged formula is a combination of trace minerals, herbs, and a natural cartilage-derived substance. The company has long-term plans to develop more health-related products.

Company principals have invested all available personal assets into the product development and operations to date. The need for capital is in the context of the readiness of the product for mass marketing. Management is seeking a KZT 1,500,000 equity investment in exchange for a suggested 30% ownership of the company. All terms of financing are negotiable in order to meet the financial requirements of the investor.

The product effectiveness, evidenced largely through anecdotal evidence, personal testimonials, and repeat sales, has formed the basis for the future growth of the company. Together with a second, complementary product (nearly ready for market), the launch product will be aggressively mass marketed as a pain management system for the next five to ten years. Past and current sales have been to end-users, health professionals, and to some retail chains. The company and product are now poised for first stage expansion. Over 30 target wholesale markets have been identified. While the company uses its marketing strategy to enter these wholesale markets, simultaneous efforts will be made to develop research protocols. Management is confident that the anecdotal evidence and personal testimonials will be strengthened by controlled studies, designed to test the effectiveness of the product and demonstrate the physiological healing activity stimulated by the formula. With scientific credibility, the product will not only build its position in the KZT 150 million homeopathic product category but will also strengthen its transition into the formidable mainstream topical analgesic category.

Future research is planned, based upon inquiry, in order to adapt the formula for animal use (Pain Away currently being tested on thoroughbred horses).

At the end of five years, the company intends to have at least one additional health product and should be able to go public off its revenues. The long-term goal for the company is to become an entrepreneurial leader in the development of natural products for various segments of the health care market. The company plans to capture enough share of the topical analgesic market to become either a viable joint venture partner or an acquisition candidate.

The product formula and delivery system are proprietary. The formula is uniquely advanced and is nearly immediately effective in relieving pain. Homeopathy and immunization have much in common, namely the principle of similars, which states that whatever a substance causes in a large dose, it can stimulate an immune response to defend against it in a small dose. It works by the principles of stimulation to the body's own self-healing mechanism and by the scientific balancing of its natural active ingredients through a dilution process called micro-dosing. Micro-dosing has given homeopathy its 200-year history of safety with no known side effects or toxicity. This self-healing process is in contrast to the majority of commercially successful topical analgesics, which contain counter-irritants, including the newer capsaicin-based products. These ingredients cause a superficial inflammation on the skin which masks pain by deadening the sensation of pain in the epidermal nerve endings only, or by distracting from the perception of pain by irritating an area near the pain source. The Pain Away formula has been developed with precision and balance and is a product that is effective and safe for use on all skin types. Pain Away's eleven active ingredients stimulate improved circulation in the micro-capillary system to ligaments and tendons, where most pain is felt. Pain relief is the result of the body's self-healing.

The manufacturing is subcontracted out to a highly respected FDA-licensed manufacturer of homeopathic products.

An important unique feature of Pain Away which distinguishes it from other homeopathic remedies is that Pain Away is a topical treatment and is not a systemic treatment. As such, it requires little knowledge to use and is conducive to cross-merchandising in the mainstream analgesic category. Furthermore, since Pain Away is a formula of ingredients, it provides a broad spectrum of effects as compared to single remedies.

The personal commitment of the founder to relieve his own pain also adds a unique value to the story of this product - a story which can enhance marketability - to anyone who is in pain or anyone who knows someone in pain.

Although Pain Away is an homeopathic product, the company will position itself as a natural ingredients company - not necessarily homeopathic. All the company principals plan to engage both septics and advocates of complementary medicine by applying rigorous scientific standards equally across the board, for both conventional and unconventional treatments. Contacts have already been made with the National Institute of Health regarding future research.

The product is a specialty consumer good carrying a suggested retail price of KZT 19.95 for a 3.7 oz. jar (1.9 oz. jar also available at KZT 12.95). The jar is designed with a medical appearance. The jar is easy to ship in multiples, is easy to stack on a shelf, is aesthetically pleasing, and has an easy-to-handle screw cap. The actual cream is greaseless, easy and pleasant to apply, and is odorless. Pain Away has, to date, largely been sold directly to end-users, and wholesale to retailers, distributors, and catalogues. The markets have supported the suggested retail price, which was arrived at by surveying market research supporting the KZT 19.95 price along with the perceived value of the product compared to similar products at about the same price. This price also yielded a gross profit of KZT 3.75 per jar and allowed for 100% markup from wholesale.

The eleven ingredients are readily available through top-quality labs which control for purity and authenticity. The cream is compatible with any medication being taken. The product carries a money-back 30-day guarantee.

Name of product	One unit price	Amount of sold out product in autumn	Amount of sold out product in spring
Cardiovascular drugs	40	3050	1100
Anti-infective inflammatory drugs	30	1525	3690

Table 1. Product sales list

1.3 An algorithm for solving the problem

The production program (the plan of production and product sales) is a complex task on release and sales of products of a certain range and quality in the natural and cost indexes focused on achievement of the objectives of the organization (enterprise).

The production program is developed in the following sequence[2]:

• the nomenclature and the range of products, volume of deliveries in kind according to the signed contracts are defined;

• on the basis of the volume of deliveries the output of each product in kind is defined;

• the output by separate types of production is proved by calculations of production capacities;

• proceeding from natural outputs and deliveries cost indexes pay off: commodity, realized; gross and net production;

• the schedule of shipment of production according to terms of contracts is formed;

• the production program is distributed on the main divisions of the enterprise.

The plan of production and product sales is formed in natural and cost expressions.

As society is interested in receiving from the enterprises of products of a certain sort, type, the size and appropriate quality, planning of outputs begins with definition of product range and its volumes in kind.

The product range is a list of names of products according to which tasks on production will be established further. The enterprises, as a rule, develop the production program on the expanded range. The range — a kind of these products by types, grades, types in a nomenclature section.

Exact establishment of names and the amount of release of each concrete product is necessary also for the enterprise as without it, it is impossible to project technological process, to determine production capacity, to establish standards of labor input etc.

Tasks in kind are established in various units of measure. In general the choice of units of measure depends on character of production, volumes of her production and nature of consumption.

The correct definition of units of measure in which the output plan in kind is established is very complex and important challenge. On the one hand, the chosen unit of measure has to characterize the mass of the consumer cost coming to economic circulation, and with another — to stimulate release of production really necessary for society [3].

Different types of production methods, such as single item manufacturing, batch production, mass production, continuous production etc. have their own type of production planning. Production planning can be combined with production control into production planning and control, or it can be combined and or integrated into enterprise resource planning.

Production planning is used in companies in several different industries, including agriculture, industry, amusement industry, etc.

Production planning is a plan for the future production, in which the facilities needed are determined and arranged. A production planning is made periodically for a specific time period, called the planning horizon. It can comprise the following activities:

• Determination of the required product mix and factory load to satisfy customers needs.

• Matching the required level of production to the existing resources.

• Scheduling and choosing the actual work to be started in the manufacturing facility

• Setting up and delivering production orders to production facilities.

In order to develop production plans, the production planner or production planning department needs to work closely together with the marketing department and sales department. They can provide sales forecasts, or a listing of customer orders. The "work is usually selected from a variety of product types which may require different resources and serve different customers. Therefore, the selection must optimize customer-independent performance measures such as cycle time and customer-dependent performance measures such as on-time delivery.

A critical factor in production planning is "the accurate estimation of the productive capacity of available resources, yet this is one of the most difficult tasks to perform well”. Production planning should always take "into account material availability, resource availability and knowledge of future demand" [4].

In some problems there is uncertainty cause by the lack of information about the conditions under which the action will be performed (weather, consumer demand, etc.) These conditions do not depend on the deliberate actions of another player, but from objective reality. Such gamers are called games with nature. Man in games with nature tries to act prudently, the second player (nature, customer demand) acts randomly. Game conditions specified matrix

(a_ij)_m*n (1)

There are several criteria used in selecting the optimal strategy. Let’s take a look at some of them.

Wald's maximin model. Wald's maximin model is a non-probabilistic decision-making model according to which decisions are ranked on the basis of their worst-case outcomes. That is, the best (optimal) decision is one whose worst outcome is at least as good as the worst outcome of any other decisions. It is one of the most important models in robust decision making in general and robust optimization in particular[5].

It is also known by a variety of other titles, such as Wald's maximin rule, Wald's maximin principle, Wald's maximin paradigm, and Wald's maximin criterion. Often 'minimax' is used instead of 'maximin'.

Wald's generic maximin model is as follows:

(2)

where   denotes the decision space;   denotes the set of states associated with decision   and   denotes the payoff (outcome) associated with decision   and state  .

This model represents a 2-person game in which the   player plays first. In response, the second player selects the worst state in  , namely a state in   that minimizes the payoff   over   in  . In many applications the second player represents uncertainty. However, there are maximin models that are completely deterministic [6].

The above model is the classic format of Wald's maximin model. There is an equivalent mathematical programming (MP) format:

(3)

where   denotes the real line.

As in game theory, the worst payoff associated with decision  , namely

(4) is called the security level of decision  .

The minimax version of the model is obtained by exchanging the positions of the   and   operations in the classic format:

(5)

The equivalent MP format is as follows:

(6)

Inspired by maximin models of game theory, Abraham Wald developed this model in the early 1940s as an approach to situations in which there is only one player (the decision maker). The second player represents a pessimistic (worst case) approach to uncertainty. In Wald's maximin model, player 1 (the   player) plays first and player 2 (the   player) knows player 1's decision when he selects his decision. This is a major simplification of the classic 2-person zero-sum game in which the two players choose their strategies without knowing the other player's choice. The game of Wald's maximin model is also a 2-person zero-sum game, but the players choose sequentially.

With the establishment of modern decision theory in the 1950s, the model became a key ingredient in the formulation of non-probabilistic decision-making models in the face of severe uncertainty. It is widely used in diverse fields such as decision theory, control theory, economics, statistics, robust optimization, operations research, philosophy, etc [7].

Criterion of maximum. It is selected from the conditions

(7)

Criterion is optimistic, it is believed that nature would be most beneficial for a person.

Hurwitz criterion. Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time invariant (LTI) control system. The Routh test is an efficient recursive algorithm that English mathematician Edward John Routh proposed in 1876 to determine whether all the roots of the characteristic polynomial of a linear system have negative real parts. German mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix, and showed that the polynomial is stable if and only if the sequence of determinants of its principal submatrices are all positive.^[2] The two procedures are equivalent, with the Routh test providing a more efficient way to compute the Hurwitz determinants than computing them directly. A polynomial satisfying the Routh–Hurwitz criterion is called a Hurwitz polynomial.

The importance of the criterion is that the roots  of the characteristic equation of a linear system with negative real parts represent solutions  of the system that are stable (bounded). Thus the criterion provides a way to determine if the equations of motion of a linear system have only stable solutions, without solving the system directly. For discrete systems, the corresponding stability test can be handled by the Schur–Cohn criterion, the Jury test and the Bistritz test. With the advent of computers, the criterion has become less widely used, as an alternative is to solve the polynomial numerically, obtaining approximations to the roots directly.

Criterion recommends a strategy defined by the formula

(8)

Where – the degree of optimism – ranges [0,1]

Criterion holds an intermediate position, taking into account the possibility of as the worst and best if human behavior to nature. If the = 1 criterion is transformed into Wald test, with in the criterion of maximum. Influence on the degree of responsibility of the decision on the choice of strategy. Worse than the consequences of wrong decisions, more willing to insure, the closer to unity.

Savage minimax regret criterion. The essence consists in the selection criteria of a strategy to avoid excessive losses, to which it can cause. Is a risk matrix whose elements indicate which people suffered loss (firm), if for each state of nature, he does not choose the best strategy.

Element of the risk matrix (r_ij) is formula

(9)

Where - the maximum element in the column of the original matrix.

The optimal strategy is the expression

(10)

The Minimax Regret criterion focuses on avoiding regrets that may result from making a non-optimal decision. Although regret is a subjective emotional state, the assumption is made that it is quantifiable in direct (linear) relation to the rewards of the payoff matrix.

Regret is defined as the opportunity loss to the decision maker if action alternative is chosen and state of nature happens to occur. Opportunity loss is the payoff difference between the best possible outcome under and the actual outcome resulting from choosing . Formally: = (row j maximum payoff) - for positive-flow payoffs (profits, income)

= - (row j minimum payoff) for negative-flow payoffs (costs, losses), where is the reward value (payoff) for column i and row j of the payoff matrix R. Note that opportunity losses are defined as nonnegative numbers. The best possible is zero (no regret) and the higher the value, the greater the regret [8].