Global supply chain planning for pharmaceuticals

Abstract

The shortening of patent life periods, generic competition and public health policies, among other factors, have changed the operating context of the pharmaceutical industry. In this work we address a dynamic allocation/planning problem that optimises the global supply chain planning of a pharmaceutical company, from production stages at primary and secondary sites to product distribution to markets. The model explores different production and distribution costs and tax rates at different locations in order to maximise the company's net profit value (NPV).

Large instances of the model are not solvable in realistic time scales, so two decomposition algorithms were developed. In the first method, the supply chain is decomposed into independent primary and secondary subproblems, and each of them is optimised separately. The second algorithm is a temporal decomposition, where the main problem is separated into several independent subproblems, one per each time period. These algorithms enable the solution of large instances of the problem in reasonable time with good quality results.

Introduction

In the past 30 years, the operating context of the pharmaceutical industry has evolved and become much more challenging. The establishment of regulatory authorities and market maturity have led to an increase in the costs and time to develop new drugs, decreasing the productivity of the research and development (R&D) stage and shortening the effective patent lives of new molecules. These two factors, in conjunction with the appearance of many substitute drugs in several therapeutic areas, have led to the reduction of the exclusivity period of new products. Another factor having an impact on the operation of this industry was the transition of the paying responsibilities from individuals to governmental agencies and insurance companies, which in association with high demands for pharmaceuticals, due to aging populations, put strong pressure on prices and prescription policies (Shah, 2004).

From the point of view of manufacturing, the global pharmaceutical industry can be divided into five sub-sectors: large R&D based multinationals, generic manufacturers operating in the international market, local companies based in only one country, contract manufacturers without their own portfolio and biotechnological companies mainly concerned with drug discovery. The first group, the intensive R&D based industries, is economically the most important and tends to have large and complex supply chains due to the global nature of its activity. In addition, these companies are the most vulnerable to the global financial, regulatory and social changes so this work will focus on their supply chains.

The industry's preferred mechanism to overcome the productivity crises has been to increase investment in current business activities, primarily R&D and sales, the two extreme ends of the supply chain. This has been implemented by organic growth or by mergers and acquisitions (M&A) to exploit economies of scale. However, statistics show that productivity continues to decline after a decade of vigorous growth in investments on these areas (Coe, 2002). There are no significant economies of scale in sales activities. The revenues generated by a pharmaceutical company are directly proportional to its sales, general and administrative (SG&A) expenditure, suggesting that two merged companies will not necessarily be more profitable than they would be separately, i.e. there is no improvement on the return rates. Further more, despite the theoretical higher probability of successful product development with greater scale in R&D, in reality it does not translate into improved pipeline value. Companies will only improve their profit margins if they change the relationship between volume and costs, which can be achieved through productivity gains in the supply chain.

Supply chain optimisation is an excellent way to increase profit margins and is becoming current practice, not only in pharmaceutical industries but also in other areas of business. Arntzen et al. (1995) described the restructuring of the supply chain at Digital Equipment Corporation with savings of over US$ 100 million. They developed a large mixed integer linear programming (MILP) model that incorporates a global, multi-product bill of materials for supply chains with arbitrary structure and a comprehensive model of integrated global manufacturing and distribution decisions. Camm et al. (1997) described a project related to P&G's supply chain in North America. The main objective of the study was to streamline the work processes to eliminate non-value added costs and duplication. The study involved hundreds of suppliers, over 50 product lines, 60 plant locations, 10 distribution centres and hundreds of customer zones. It allowed the company to save $200 million before taxes. Kallrath (2000) reported on a project in BASF where a multi-site, multi-product, multi-period production/distribution network planning model was developed, aiming to determine the production schedule in order to meet a given demand. Neiro and Pinto (2004) described a petroleum supply chain planning problem of Petrobras in Brazil, which comprises 59 petroleum exploration sites, 11 refineries and five terminals, with 20 types of supplied petroleum and 32 products to local markets. Sousa et al. (2008) considered an industrial global supply chain of a multinational agrochemicals company, comprising two subsystems: US network and worldwide formulation network.

Supply chain management in the process industries has long been used as a tool to define production and distribution policies, as well as product allocation. This is the case of Cohen and Lee (1988) who described the modelling of a supply chain composed of raw material vendors, primary and secondary plants (each one with inventories of raw materials and finished products), distribution centres, warehouses and customer areas. Later, Cohen and Moon (1991) used supply chain optimisation to analyse the impact of scale, complexity (the operating costs are a function of the utilisation rates and number of products being processed in each facility) and weight of each cost factor (e.g. production, transportation and allocation costs) on the optimal design and utilisation patterns of the supply chain systems.

Timpe and Kallrath (2000) described an MILP model, which combined production, distribution and marketing and involved plants and sales points, to cover the relevant features required for the complete supply chain management of a multi-site production network. Jayaraman and Pirkul (2001) developed a Capacitated Plant Location Problem (CPLP) type model for planning and coordination of production and distribution facilities for multiple commodities, comprising raw materials suppliers, production sites, warehouses and customer areas. The authors followed a holistic approach to the supply chain, resulting in a deterministic, steady-state, multi-echelon problem.

Park (2005) considered both integrated and decoupled production and distribution planning problem, consisting of multiple plants, retailers, items over multiple periods. The author proposed mixed integer optimisation models and a two-phase heuristic solution to maximise the total net profit. Oh and Karimi (2006) highlighted the importance of duty drawback regulations in the production-distribution planning problem, and incorporated three main regulatory factors: corporate taxes, import duties and duty drawbacks, in the proposed linear programming (LP) model.

Tsiakis and Papageorgiou (2008) considered the optimal configuration and operation of multi-product, multi-echelon global production and distribution networks, integrating production, facility location and distribution with financial and business issues such as import duties, plant utilisation, exchange rates and plant maintenance. An MILP model was formulated and applied to a case study for the coatings business unit of a global specialty chemicals manufacturer. Verderame and Floudas (2009) proposed a discrete-time multisite planning with production disaggregation model to provide a tight upper bound on the true capacity of daily production and shipment profiles between production facilities and customer distribution centres. Salema et al. (2010) presented a general dynamic model for the simultaneous design and planning of multiproduct supply chains with reverse flows, where time is modelled along a management perspective to deal with the strategic design and the tactical planning simultaneously. The applicability of the model is proved in an example based on Portuguese glass industry. You et al. (2010) addressed a simultaneous capacity, production, and distribution planning problem for a multisite supply chain network including a number of production sites and markets and propose a multiperiod MILP model and two decomposition approaches for solution.

When performing long term process planning, uncertainty factors (e.g. in product demand) have to be taken into account in order to produce robust models whose output decisions will perform well in a variety of scenarios (Verderame et al., 2010). Tsiakis et al. (2001) addressed a strategic problem of stochastic planning for multi-echelon (although with rigid structure) supply chains.

Iyer and Grossmann (1998) extended the work of Liu and Sahinidis (1996), a specific problem of long-range capacity expansion planning in the chemical industry. The inputs were a set of available chemical processes, an established production and distribution network and demand forecasts affected by uncertainty leading to an MILP, multi-period planning model with multiple scenarios for each time period. Ahmed and Sahindis (2003) considered forecast uncertainty parameters by specifying a set of scenarios in a stochastic capacity expansion problem. A multistage stochastic mixed integer programming formulation with fixed-charge expansion costs was formulated.

Oh and Karimi (2004) developed a deterministic MILP model for the capacity-expansion planning and material sourcing in global chemical supply chains with the introduction of two important regulatory factors, corporate tax and import duty. Guillen et al. (2005) proposed a two-stage stochastic optimisation approach to address a multiobjective supply chain design problem. The Pareto-optimal solution was obtained by the ɛ-constrained method. Puigjaner and Laínez (2008) proposed a scenario-based MILP stochastic model considering both process operations and finance decisions with an objective of maximising the corporate value. A model predictive model strategy was integrated with the stochastic model for solution.

Several authors addressed the issue of supply chain optimisation and long-term process planning in the pharmaceutical industry. Rotstein et al. (1999) started a series of papers dedicated to the specific problem of supply chain optimisation in the pharmaceutical industry. Later, Papageorgiou et al. (2001) published a paper based on the previous one, where the production stage is formulated with high degree of detail and including the trading structure of the company. The proposed deterministic model considers up to 8 possible products in the company's portfolio. Levis and Papageorgiou (2004) extended this work to account for uncertain demand forecasts, dependent on the results of the clinical trials for each product. Gatica et al. (2003) proposed an MILP approach for the problem of capacity planning under clinical trials uncertainty, where four clinical trial outcomes for each product are considered as is typical in the pharmaceutical industry. Amaro and Barbosa-Póvoa (2008) considered the integration of planning and scheduling of generalised supply chains with the existence of reverse flows. The developed approach was applied to the solution of a real pharmaceutical supply chain case study.

So far, most of the problems referred in this review concern detailed or very detailed descriptions of supply chains of relatively small systems (i.e. 1 or 2 sites, and up to 8 products). The long term strategic planning of large pharmaceutical companies has not been addressed in any of the previous works. In this work we build a model of the global supply chain of a large pharmaceutical company, with a long list of products in its portfolio and an extensive network of manufacturing sites with locations all over the world. The allocation policy of products to sites also differs from previous works. In each time period, each product will be produced at a single location (single sourcing policy), however the product/site assignment may change along the time horizon reflecting actual practice. This feature increases significantly the binary variables space.

In order to keep the model size within reasonable limits, it cannot be too detailed in its description of the supply chain. Nevertheless, even with this approach, it is necessary to use decomposition algorithms. The development of decomposition approaches is a promising research direction in the area (Grossmann, 2005, Maravelias and Sung, 2009).

To solve a typical large MILP model, Iyer and Grossmann (1998) used a bi-level decomposition (hierarchical) algorithm to solve the original model. In the first step, the design stage, the capacity expansion variables were aggregated in a new variable set, time independent, and the processes to develop are chosen. In the second level model (operation model), only the processes chosen to be developed are subjected to investment. Bok et al. (2000) proposed a bi-level decomposition. The relaxed problem making the decisions for purchasing raw materials generates an upper bound to the profit, while the subproblem yields a lower bound by fixing the delivery from the relaxed problem. Levis and Papageorgiou (2004) solved an aggregated model, computationally less expensive, although detailed enough to make the “here-and-now” decisions. In the second step, the values of the corresponding variables were fixed and the detailed model is solved. Üster et al. (2007) used a Benders decomposition approach for a multi-product closed-loop supply chain network design problem. Three different approaches for adding multiple Benders cuts are proposed. Li and Ierapetritou (2009) formulated the integrated production planning and scheduling as bilevel optimisation problems with one planning problem and multiple scheduling problems. A decomposition approach based on convex polyhedral underestimation was proposed and successfully applied to the integrated planning and scheduling problem of multipurpose multiproduct batch plants.

Some authors solved the large models resulting from supply chain optimisation problems through Lagrangean decomposition. In their work, Gupta and Maranas (1999) formulated an extension of the “economic-lot-sizing” problem, characterised by determination of the production levels of multiple products, in multiple sites, with deterministic demands and multiple time periods. Jayaraman and Pirkul (2001) relaxed three blocks of constraints concerning assignment of customers to warehouses, raw materials availability and material flows balance. This allowed them to decompose the original problem in three different sets of subproblems. Maravelias and Grossmann (2001) introduced a good example of a model composed of two (or more) independent sub-models with one linking constraint.

Jackson and Grossmann (2003) built a multiperiod optimisation model for the planning and coordination of production, transportation and sales for a network of geographically distributed multiplant facilities supplying several markets. Two Lagrangean decomposition methods were adopted to tackle the problem, spatial and temporal decompositions. In both cases, the authors followed the regular algorithm of Lagrangean decomposition to reach the optimal solution of the original problem, as described in Reeves (1995). The numerical examples show the temporal decomposition to work significantly better than the spatial decomposition.

Eskigun et al. (2005) developed a Lagrangean heuristic for the proposed large-scale integer linear programming model for supply chain network design problem of an automotive company with capacity restriction on vehicle distribution centres. Shen and Qi (2007) embedded Lagrangean relaxation in branch and bound to solve an integrated stochastic supply chain design problem which is formulated as a nonlinear programming (NLP) model. The Lagrangean relaxation subproblems are then solved by a low-order polynomial algorithm.

Chen and Pinto (2008) proposed several various decomposition strategies for the continuous flexible process network model by Bok et al. (2000), including Lagrangean decomposition, Lagrangean relaxation, and Lagrangean/surrogate relaxation. Among the four decomposition strategies, it was proved that the solutions generated from Lagrangean relaxation are better, although its CPU time is lower. Hinojosa et al. (2008) proposed an MILP formulation for a dynamic two-echelon multi-commodity capacitated plant location problem with inventory and outsourcing aspects. The authors solved the resulting, independent subproblems from a Lagrangean relaxation scheme and a dual ascent method to find a lower bound on the optimal objective value. Nishi et al. (2008) used an augmented Lagrangean decomposition and coordination approach for the proposed framework for distributed optimisation of supply chain planning for multiple companies. An augmented Lagrangean approach with a quadratic penalty function was used to decompose the original problem into several subproblems for each company to eliminate duality gap.

Puigjaner et al. (2009) used the optimal conditional decomposition (OCD), a particular case of Lagrangean decomposition, for the supply chain design-planning model extended from the work by Puigjaner and Laínez (2008). In the OCD, the difference from the classic Lagrangean decomposition is its automatic updating process of Lagrange multipliers. You and Grossmann (2010) proposed a spatial decomposition algorithm based on the integration of Lagrangean relaxation and piecewise linear approximation to solve mixed integer nonlinear programming (MINLP) model for large-scale joint multi-echelon supply chain design and inventory management problems.

From the literature discussed above, there is a gap in the research on supply chain planning taking both primary and secondary manufacturing in the pharmaceutical industry into account. This paper aims to fill this gap.

The rest of our paper is organised as follows. Section 2 introduces a brief description of the typical supply chain and its components in the pharmaceutical industry. Section 3 is concerned with the problem description. The mathematical formulation of the model is presented in section 4. In Section 5, two decomposition algorithms are conceived to solve the large model resulting from the problem formulation. In Section 6, the model as well as the performance of the developed algorithm is tested with two illustrative examples. Some concluding remarks are drawn in Section 7.