ADVANCED SUPPLY CHAIN OPTIMIZATION. TRADITIONAL & STATE-OF-THE-ART MODELS

LARGE SCALE OPTIMIZATION APPLIED TO SUPPLY CHAIN & SMART MANUFACTURING: THEORY & REAL-LIFE APPLICATIONS. Main Editor of the book to be published in the series Springer Optimization and Its Applications https://www.springer.com/series/7393

White papers related:

SCIENTIFIC MARKETING: ADVANCED DEMAND CHAIN OPTIMIZATION

https://www.dhirubhai.net/pulse/scientific-marketing-advanced-demand-chain-jesus-velasquez/

PDF version of this document: https://goo.gl/jsTKhR

1. INTRODUCTION

To improve the competitive advantage, reduce costs and increase profits, managers seek to integrate planning activities of its value chain, which can be understood as the sum of the supply chain and demand chain. Because of its complexity, from a conceptual point of view, the problem is divided into two: in the bottom of the chain, related to the transformation of raw materials into commercial products, is determined the best way to industrial production, focusing analysis in minimizing the costs of serving an aggregate market consumption centers; at the top, sale and delivery of commercial products to individual consumers, the analysis focuses on the study of the end customer in a way to optimize the price and the place to sold the products. The methodologies and technologies used in each case differ in their details, but they are always supported in the fundamental concepts of operations research: optimizing decisions once studied and characterized the random behavior of the environment of decisions.

OPCHAIN-Supply Chain Optimization (OPCHAIN-SCO) is a system of technical and economic planning tools that exploits the latest computer technologies coupled with the advanced mathematical modeling of value chains, supply and demand, integrated vertically and horizontally. The power of algorithms used for optimization, joint with the ability to represent precisely the relation of cost and volume, provides confidence in optimal results that cannot be provide by simpler approaches. It services for generation of models, coupled with spreadsheets, databases, multidimensional analysis tools, visualization software and simulation models to generate probabilistic scenarios; providing an ideal place to develop quickly and comprehensively optimization studies of the supply chain environment. OPCHAIN-SCO is designed to allow its users to parameterize the model according to the complexity of its supply chain and optimization requirements thereof.

Some benefits of the implementation of mathematical models OPCHAIN-SCO are:

• Explicit cost reduction or profit increase;
• Clarification of the goals of the organization, the decision options and environmental constraints;
• Processes more rational and systematic planning;
• Improvements in the communication process; and
• Better focus of the process of data collection and interpretation.

?OPCHAIN-SCO allows people to study the behavior of the supply chain into a multi-sectoral/multi-business value chain, in which the objectives are to design and operate industrial infrastructure and relationships with their environment in ways that minimize the sum of the total investment and the costs of raw materials, production, transport and distribution; while not only the levels of customer service are met, in many cases they are exceeded, achieving expand market share and growth sustained over time,

2. TYPICAL APPLICATIONS

OPCHAIN-SCO provides the solution to a wide range of strategic and tactical problems considering many aspects of the different types of chains and its components. OPCHAIN-SCO can be used to support consultancy work, home or end customer, or in the "cloud" on an optimization server to directly support their decision making processes.

OPCHAIN-SCO integrates a set of mathematical optimization models with its corresponding information system; the models are aggregate for strategic and tactical planning, and detailed for scheduling of industrial and logistics operations.

For distribution companies, wholesale and retail, the goal of the analysis is the distribution network; for manufacturing companies, the goal is the planning and scheduling of industrial operations integrated with the transport of products that covers all the links of the chain. The comprehensive modeling integrates multiple industries/businesses allowing optimization from a holistic point view.

At the strategic level, OPCHAIN-SCO supports the optimal design of the network infrastructure that is required to meet the objective of the supply chain market share. Tactically and operationally OPCHAIN-SCO supports:

• Weekly/monthly aggregate operations plan
• Definition of dynamic inventory policies with a planning horizon of several months
• Daily and weekly programming of industrial operations (production and distribution)
• Optimization of purchasing processes
• Assignment of products in distribution centers will trade commitments
• Projecting of endogenous demand for medium and short-term

2.1. PRODUCTION PLANNING

?OPCHAIN-SCO optimizes supply chains of different types:

• Batch: in which predefined set of product batches are produced at each stage of the process. Examples are: food industry, beverages, pharmaceuticals, paints, cement, steel, ....
• Continuous: corresponds to processes that operate permanently, or for long periods, producing a product or set of products. Some examples are: electric power, chemical/petrochemical industry, solid waste treatment, paper, cement, ...
• ?Discrete: based manufacturing and assembly of parts, products and goods. Some examples are: manufacture and assembly of parts and components (auto parts, electronics, plastics, … ).
• Agroindustry: based on the integration of agricultural, livestock processes and/or fish with added value industrial processes taking living beings as raw material. Optimization coordinates two links: the primary link that occurs in farms and the industrial link, taking place in industrial plants.

2.2. PLANNING FOR DISTRIBUTION NETWORK

The analysis of the distribution network is one of the most common applications of the OPCHAIN-SCO. Given that suppliers and markets are geographically dispersed, the companies want to determine the distribution strategy that minimizes the total cost to meet demand, while meeting the service level requirements (delivery time) to customers, which can be measured against the cost of the network topology and the inventory policies.

OPCHAIN-SCO allows to describe the total cost as the sum of multiple costs; such as: costs of selling the products, transportation costs (in own fleet or in fleets of third party), including distribution centers or direct consumers, packaging costs, handling costs and capital associated with inventories, and indirect costs based on the "throughput" of the company.

?OPCHAIN-SCO generates and solves the optimization models of a spatially distributed network that can be static, one time, or dynamic, multiple periods and provide a solution to the following questions:

• How can clients minimize the total cost of investment and operation of the network?
• What is the commitment, or opportunity cost, including delivery times and total costs?
• How many, when and where should distribution centers be located?
• How many, when and where you cross-docking centers be placed?
• How should the client operate cross-docking centers?
• How the product must flow through the distribution network?
• Which is the optimal mix between own fleet and third-party fleet?
• How inventories should be handled in each distribution center?
• Which distribution center must meet a consumer?
• Which one, is the most efficient mode of transportation?
• Which is the optimal policy of maintaining the fleet of vehicles?
• Which is the optimal management policy of cross-docking centers?

2.3 INTEGRATED PLANNING PRODUCTION AND DISTRIBUTION

?This type of problem is of permanent interest to those responsible for planning the supply chain. A company with multiple plants serving a geographically dispersed market is looking to optimally allocate demand for its products from all its plants. The goal is to minimize the sum of the costs associated with raw materials, manufacturing and distribution, based on demand to the extent that it is profitable; it can also be determining the optimal mix of products to be produced to maximize their profits.

The modeling capacity of OPCHAIN-SCO allows detailed description of costs, resources, production processes, production formulas and qualities of products. To make this description no limits exists, because OPCHAIN-SCO can mix any number of types of processes, or process steps describing a plant, which can be represented as rigid units, with fixed production formulas, or flexible units where quality constraints are respected and the model provides the optimal mix of raw materials.

The optimization models from OPCHAIN-SCO can help solve simultaneously, among others, the following questions:

• How many, when and where they should locate production plants?
• How many, when and where you should place the packing plants?
• How many, when and where you should place the packaging lines?
• What infrastructure must be owned and which must be rented to third parties?
• Which products and how much should be produced at each plant and/or equipment?
• What technological processes should be used on each floor?
• What forms of production should be used on each computer and/or process?
• What supplier, and in what quantities, should serve each plant?
• What intermediate products must be produced and which should be obtained from a third party?
• What services are to be provided with its own force and which should be obtained from third parties?
• What plant, and how much should meet each distribution center?
• What is the value added by the offices intra-product plants in processes?
• The level of inventories of raw materials, goods in process and/or finished products that should be kept in each chain storage?
• What are the transfer prices between regions in global supply chains?
• Who should bear the freight on transfers between global chains?
• Is it necessary to have contingency plans to deal with (strikes, attacks) in the links of the chain?
• What is the level of risk associated with operations in the chain?
• What long-term contracts must be signed with third parties to manage market risks (price risk and volume risk)?

The above questions, together with questions about the distribution network integrated chain, can be resolved by OPCHAIN-SCO; the result: a detailed description of the optimal structure of the chain and how it should operate.

2.4. DECISION SUPPORT

OPCHAIN-SCO integrates mathematical models for decision support, from different hierarchical levels related to the problem of network design of supply chain synchronization of industrial facilities, production scheduling and distribution of products, optimizing purchasing and demand planning in the short, medium and long term. The set of mathematical models needed to optimally perform the planning and programming of a supply chain depends on it and cannot be specified in general.

Conceptually OPCHAIN-SCO supports the following types of models, a process related to product demand and others with the offer:

• DEM:????Statistical models (S-ARIMAX-GARCH) to forecast demand, including the impact of marketing events and sales promotions.
• SCD:????Optimal design of the supply chain network using binary non-anticipative stochastic optimization models, including risk analysis
• S&OP:??Tactical planning of aggregate industrial operations for short and medium term.
• INV:?????Optimization of the parameters for inventory management policies.
• SOO:?Sourcing optimization through detailed modeling of the negotiation and clearance and import of products under ordinary and special customs regimes.
• PSH:????Scheduling of daily/weekly production operations at the level of process units, work cells and machines.
• ATP-D:??Available-to-Promise, assignment of products for business commitments and travel schedules for delivery.
• DIS:?????Daily schedule of distribution operations and/or collection of products, citywide and nationwide.

OPCHAIN-SCO supports all levels of planning and programming of industrial and collateral, at different hierarchical levels and in different functional areas of operations; this is supported in all models involved; however, they provide specific service models to different areas of the organization decision makers.

Below possible applications OPCHAIN-SCO are described:

• Supply Chain Planning: corresponds to the main support work OPCHAIN-SCO which generates information for the remaining areas of the organization. At the strategic level this work is done through model SCD, at the tactical level it is performed by S&OP and INV models that receive information from DEM model.
• Production Scheduling: production models in the different places where the supply chain operates; this is done through POD family models, which consists of specialized models for each site. The production managers are the end users of the POD.
• Logistic and Transport (Distribution Scheduling): Planning distribution/pick-up of products, through the ATP and DIS-D models, which together account for the allocation of products to orders/contracts and planned trips for delivery.
• Purchases (Sourcing Optimization): Optimize the procurement process and import of raw materials and other products required by the supply chain, it is done by the POD model; which is designed to make easy the bids from suppliers, while it develops analytical ability to find the best alternative within all offers made.
• Commercial: OPCHAIN-SCO provides the following supports:

-??Projection of demand ("Demand Planning") using the model DEM

-??Assessment of commitments (Available-to-Promise, ATP): analysis of whether or not, to accept an order to impact, positively or negatively, the supply chain. It is performed by a specialized version of S&OP-ATP.

• Product Development (R&D): at this level OPCHAIN-SCO provides support for the evaluation of alternatives in the process of designing production processes for new products; it is carried out by a specialized version S&OP-R&D.

2.5. ANALYTICAL CAPABILITIES

2.5.1. TRADITIONAL ANALYTICAL CAPABILITIES

OPCHAIN-SCO is a computer system of industrial mathematical modeling, competitive at the level of state of art of the supply chain optimization, that has the capacity to:

?Describe arbitrarily complex supply chains. This is required because the elements of the chain are dependent on each other. To be precise and comprehensive, holistic model should allow detailed representation of the facilities that integrate horizontally and vertically, all levels of the chain: raw material suppliers, processing plants, packaging plants, plants producing resources, facilities of third party, transport fleets, storage facilities/distribution and markets (end customers).

?Describe the distribution network with an arbitrary number of levels of complexity. This is required because the distribution networks integrate different types of facilities whose structure and links involve strong dependencies. The user must create realistic models that integrate production plants, cross-docking centers, distribution centers, storage warehouses and delivery points to end users, interconnected in multiple ways and multiple modes. It must also coordinate events occurring throughout the network so as to ensure operational feasibility.

Representing decisions through multiple planning horizons periods associated with the strategic and tactical decisions that involve problems related to the investment, location and operation of industrial facilities in the long or medium term to represent accurately the costs associated to future decisions.

?Represent precisely the relationships of cost-volume processes. The actual cost structures include variable costs, which depend on each process and can include economies or diseconomies of scale, such as those derived from processes start/stop times and change in production lines, allowing the inclusion of fixed costs, investment and operation, which are independent of the volume.

?Shaping the time and cost of multi-objective optimization criteria. The underlying problem in optimizing the distribution network is the competition between the time the network (service level) and the associated cost. Therefore, models must allow management time and costs so that they can be part of the objective of optimizing and/or some of the restrictions of the system function. OPCHAIN-SCO, through stochastic optimization models (by scenarios), determines the optimal curves relating the probabilities of "stock out" with costs.

Modeling complex industrial processes involving nonlinearities. The amount produced is the result of the multiplication of the production rate for the time used. When these two technical aspects are part of the decision-making process, the models are nonlinear so it requires careful in their modeling. OPCHAIN-SCO has multiple alternatives, mathematics and/or modeling, to address this situation and ensure optimality of the solutions.

?Maximize total profits or alternatively the total cost of operation. Depending on the view you have of the market/demand management may seek to clarify the product mix that maximizes its net profit, which equals sales revenue minus production costs, so as to determine the bid offer to the market. In other cases, management may take the demand as an exogenous factor to determine the productive way to satisfy the minimum possible cost.

?Optimize decisions along the production chain. The number of possible solutions exist for the operation of a supply chain is infinite, as it is determined by, among other factors, the combination of the number of investment options, links between facilities, and mixtures and qualities of products. OPCHAIN-SCO generates production plans in all dimensions (facilities-products) in the way of the productive system moves.

?Synthesize complex manufacturing processes. In many supply chains products are created from materials acquired from suppliers through activities in multiple processing centers, each with their own recipes/formulas, skills, technologies, efficiency factors, cash, fixed costs, variable costs and direct and indirect variable costs.

Integrate the chain of decisions associated with strategic planning and tactics. The wealth of modeling OPCHAIN-SCO allows developing integrated models based on overlapping strategic and tactical decisions. At the strategic level, they can create static to determine decisions regarding the location of facilities, products models to be made there, and the equipment to be used to manufacture; tactically optimal operation that should be given to industrial infrastructure is simulated.

?Integration of production processes with energy and industrial services. The large-scale industrial production is always tied to heavy use of industrial services, various forms of energy, which make the process feasible. Allows simultaneous optimization of both industrial and consumer/energy conversion (industrial services) services.

Supporting negotiation processes. The new Internet-based economy, "e-economy" implies profound changes in the speed of transactions between companies and between customers and companies. Mathematical models of OPCHAIN-SCO provide the appropriate information to determine the possibility and desirability of a given transaction (a purchase or a sale). This process is performed by the models called ATP (Available-To-Promise)

?Product assignment to business commitments. While all activities chain planning aims to deliver products to end customers, the final process is not simple because the products exist in large quantities in many warehouses to be assigned to multiple orders, or bilateral agreements, each one with its own conditions. OPCHAIN-SCO facilitates this process by performing simultaneous allocation processes displayed around the problem, including the distribution of assigned orders.

?Programming/scheduling of activities, production and/or distribution, respecting complex allocation rules. OPCHAIN-SCO coordinates different types of processes whose timing is essential to ensure the feasibility and profitability of industrial operations. It is possible to optimally coordinate multiple production equipment (cells/workstations, machines) or transport fleets-trailers-truck drivers, distribution or mixed-production activities such as those occurring in a specialized port, all complying its own special allocation rules of each business.

Quantify the risk associated with decisions. The modern financial engineering has focused its efforts on identifying alternatives for quantitative measurement and assessment of the risks associated with a decision under uncertainty. The ultimate goal is making decisions to ensure the financial health of the organization, while "maximizing" profits by the "optimal" management of their investments in accordance with the expected return and the risk management decision alternatives.

2.5.2.?TRADITIONAL ANALYTICAL CAPABILITIES?

Fully optimize the different functions of the organization. Current computing power coupled with the speed of high performance mathematical algorithms can extend the coverage of OPCHAIN-SCO to integrate models of "forecast" demand and/or financial models so that the optimal plans develop coherent ensuring financial results that meet the expectations of "stakeholders".

Production and demand models. Traditionally, the integration demand (DEM) and production tactical planning (S&OP) models is carried out through two input files (parameters) that contain: i) the predictions made by DEM (adjusted by the sales team) and ii) inventory policies; this implies that the demand is defined exogenous to S&OP model and may be sub-optimal.

However, under the concept of driven demand, it is possible to improve performance (demand optimization); this implies: i) replace the demand input file by the algebraic equations of the statistical models of demand, ii) include the definition of inventory policy in the S&OP model, iii) characterize the probabilistic model based on the demand model errors and iv) use a stochastic optimization model for the integrated problem.

Financial & Production Optimization. The Management of Asset Liability Management (ALM) has evolved from financial sector, just before the beginning of the 1980's. to cover the industrial sector; this fact generate the connection of ALM models with supply chain models (SCD & S&OP) producing, as minimum gain, the automatic generation of financial statements which is usually make in an independent post-processing, that consumes time and effort of planners. As a substantial improvement to the decision-making process, this linkage may be possible to optimize: i) fiscal management (dividends, capital repatriations, payment or down-payment of liabilities,...), ii) corporate risk analysis and iii) capital structure.

Additionally, due to the regional difference between the tax policies, tariff regimes, exchange control policies and exportation promotion policies, the integrated OPCHAIN-SCO-ALM-S&OP modeling is necessary for global supply chains, since it is the only way to determine the optimal transfer prices and the amounts of products to be transferred between subsidiaries.

Treasury & Working Capital Optimization. The Optimal Cash Flow (OCF) considered a predefined flow of passive during a planning horizon; the financial decisions are the cover financial movements with respect to: bills, bonds, shares, currencies and other assets, that can meet the requirements imposed by the liabilities. The S&OP model determines the requirements of working capital and the sales to recover the investment and expenses; then ALM-S&OP vision is holistic of the financial problem that affect the cash flow.

Quantify the risk associated with decisions. The financial engineering focusses its efforts on identifying measurement of the financial risks. The goal is making decisions under uncertainty to ensure the financial health of the organization, while "maximizing" profits by the "optimal" management of their investments in accordance with the expected return and the risk management decision alternatives.

Preventive Maintenance Optimization. Traditionally, the maintenance planning is independent of the S&OP activities, which is carried out previously and becomes an input parameter. However, it is now possible to integrate in the S&OP model the maintenance activities, so that the integrated planning produces lower cost that coordinated planning; in general, it seeks to: i) optimize use of resources of the , ii) minimize the impact of maintenance, iii) Define dates for carrying out maintenance (months, weeks, days) and iv) minimize production plus maintenance costs.

3. OPCHAIN-SCO: MATHEMATICAL METHODOLOGIES

3.1. STRUCTURED MATHEMATICAL MODELING

OPCHAIN-SCO integrates a set of mathematical optimization models with its corresponding information system; the models are aggregate for strategic and tactical planning and detailed for scheduling operations.

OPCHAIN-SCO is built based on the concepts of Structured Mathematical Modeling in which the constraints, and all algebraic elements (indexes, sets, parameters, variables, objective functions), are stored in a Mathematical Modeling Information System (MMIS); subsequently the mathematical models are built as a set of optimization problems and the problems, in turn, are defined as a set of constraints. OPCHAIN-SCO has a set of basic equations (core) are those that represent the physical system, these equations are added the specific equations of each problem.???

3.2. NON-LINEAR MODELING

Traditionally electrical systems planning models are based on stochastic optimization and are solved using Nested Benders Decomposition (NBD), this is the case of SDDP model (Stochastic Dual Dynamic Programming). Due to limitation of Benders Theory, NBD only can solve linear problems, which becomes an important constraint to multiple cases of real-life that require discrete and/or non-linear models; then linearized solutions do not correspond to the optimal solutions real-life system. The G-SDDP methodology (Generalized Stochastic Dual Dynamic Programming) used by OPCHAIN-SCO can solve real-life (discrete and/or non-linear) problems providing optimal solutions.

3..3. STOCHASTIC OPTIMIZATION

The power of the optimization solvers (GUROBI, IBM CPLEX, XPRESS) and the power of current computers, allows the analysis of problems based on stochastic optimization models, leaving aside the traditional deterministic models. The modeling of random events in optimization models is supported in:

• We don’t know what will happen
• We know what can happen

Random events are modeled based on scenarios, which are assigned to probabilities of occurrence.

While several decades ago to solve problems of stochastic optimization of large size using lots of scenarios seemed unattainable, technological advances in all directions (speed of the processor, cache memory capacity and memory RAM, "solvers" speed, networks of high-speed communications,...) made the stochastic optimization a viable methodology to face the problem of handling uncertainty in decision-making process.

Stochastic optimization is necessary when we want to manage financial risks related to the investment and operation of industrial systems; a case known is related to the management of resilient supply chains to face disasters, which cannot be achieved with deterministic models.

Traditionally, Multi-Stage Stochastic Programming (MS-SP) has been part of the mathematical methods used to optimize the dispatch of electricity generation plants; initially, Stochastic Dynamic Programming models were the most used; later, the models based on Nested Benders Stochastic Decomposition (NBD) are the “standard”.

All models of OPCHAIN-SCO can be modeled using MS-SP, this is a decision of the end-user, no a decision of the mathematical modeler.

The use of MS-SP implies the definition by the user of five fundamental aspects:

1.??The “core” deterministic model, all E&G models can be converted in a stochastic optimization model.

2. The dimensions of uncertainty (the number of random parameters, i.e. water inflows, demand, oil prices, …) that define the random environment of decisions (scenarios). The user can select many uncertainty dimensions, according to the situation or to the model.

3. The decision-making process is represented by a multi-stage tree that is configured by the user.

4. The policy of risk management, financial or operational, that the user wants to include in the analysis.

5. The methodology of mathematical problem solution, which can be: i) default or ii) selected the user according to the format of the problem.

3.4. LARGE-SCALE OPTIMIZATION METHODOLOGIES

In the future, the real-life solution based on Mathematical Programing, applied to large physical and social structures/organizations, must be based on multilevel parallelism using the modern computational architectures, then, Large-Scale Optimization Methodologies (LSOM) are the fundamental to atomize an optimization mathematical problem in multiple types of sub-problems that can be solve using the concepts of: i) Asynchronous Parallel Optimization and ii) Real-Time Distributed Optimization.

The table presents a summary of benchmarks made by the researchers to compare Benders Theory (BT) with IBM-CPLEX, one of the best solvers in the optimization market. The conclusions are clear: LSOM speed-up the solution time of large problems.

All models supported by OPTEX may use LSOM like Benders Theory (BT), Lagrangean Relaxation (LR), Dantzig-Wolfe Decomposition (DW-D), Stochastic Optimization (SO), Column Generation (CG), Cross Decomposition (CD), Disjunctive Programming (DP), Parallel and/or Distributed Optimization …?and its variations.

?The image shows the control parameters of BT in OPTEX; it allows to the user of OPCHAIN-SCO to select the LSOM more convenient.

All mathematical problems of OPCHAIN-SCO may be resolved using LSOM and stochastic optimization.

3.4. G-SDDP: GENERALIZED STOCHASTIC DUAL DYNAMIC PROGRAMMING

To speed-up the solution time of large-scale problems, DW created the GDDP (Generalized Dual Dynamic Programming) oriented to solve dynamic optimization problems, integrating the Benders Theory (BT) and Dynamic Programming (DP) approaches (Velasquez, 2002, 2018).?Based on the DP approach, GDDP makes a distinction between state variables and control variables, this distinction permits a more detailed algorithm in which the sub-problems are smaller than in the NBD. The NBD has been widely used in the economic dispatch of power systems. The main limitation of NB, including Dual Dynamic Programming (DDP), is that they only solve linear models, then GDDP is more robust than NBD.

The next tables present a DW benchmark between standard GDDP and standard NBD using a “little” determinist linear economic electricity dispatch (variables 1057, constraints 337 and no-Ceros 2245). The conclusions are: i) the case complexity doesn’t justify the large-scale methodologies, ii) the experiments show that GDDP is 7.69 times faster than NBD and iii) the integrated coordinator is 3.37 faster that NBD coordinator.

The next tables present a DW benchmark between standard G-SDDP and standard SNBD (Stochastic Nested Benders Decomposition, like SDDP) using a stochastic linear economic electricity dispatch. The conclusions are: i) The complexity of the case does not justify the large-scale methodologies, ii) the experiments show that the best G-SDDP is, approximately, 100 times faster than SNBD and iii) the experiments show that the best G-SDDP with NBD coordinator is, approximately, 15 times faster than SNBD.

The following table and the image resume the study of behavior of G-SDDP for a stochastic mix-linear economic electricity dispatch. The decrease in the solution time per scenario, when increase the number of scenarios, is a measure of the learning capacity of the G-SDDP.

3.5. RISK MANAGEMENT

Risk Management (RM), financial and operational, is the true profit provided by stochastic optimization models. The complexity of this problem lies in its bi-criterion nature: i) the desire to maximize the expected payoff and ii) the desire to minimize the risk assumed in decisions under uncertainty.

The risk management using neutral risk models, that optimize the expected value of the objective function, excluding the risk management methodologies based on risk measures (like CVaR, Conditional Value-At-Risk), lead to system to vulnerable positions (high risk positions).

OPTEX facilitates the inclusion of multiple types of criteria to measure the risks and introduce such measures as part of the decision-making process, the following may be appointed: i) income expected value, ii) mean-variance, iii) minimax, iv) maximum regret, v) down-side risk, vi) minimum risk plus expected income constrains and vii) expected value plus risk constraints. The user can select which criteria must include in the stochastic models.

4. TECHNOLOGY PLATFORM

4.1. CONCEPTUALIZATION

OPCHAIN-SCO provides the solution to a wide range of strategic, tactical and operational problems considering many aspects of the different types of problems and its components. OPCHAIN-SCO can be used to support consultancy work, end customer studies, or in the "cloud" on an optimization server to directly support decision-making processes.

OPCHAIN-SCO was implemented using OPTEX Optimization Expert System, it can produce program algorithms in various optimization technologies (GAMS, AMPL, AIMMS, C-GUROBI, … ). This implies that it inherits all the characteristics of OPTEX. For more information: https://goo.gl/S2TV8T.

4.2. ALGORITHMS

OPTEX separates completely the mathematical models of optimization technologies, storing the models in normalized database, allows the user to interact with OPCHAIN-SCO models to update the equations according to the changes in its modeling environment. OPCHAIN-SCO may include services to design, to implement, to support and to solve quickly optimization models in multiples optimization technologies like GAMS, IBM ILOG CPLEX OPTIMIZATION STUDIO, MOSEL, C, AMPL, GMPL … .

Next image presents a GAMS computer programs generated by OPTEX.

Next image presents a IBM-CPLEX-OPL computer programs generated by OPTEX.

Next image presents a C computer programs generated by OPTEX.

Next image presents a G-SDDP-GAMS programs generated by OPTEX.

4.3. INFORMATION SYSTEMS

As a complement to other computer systems that require organizations, OPCHAIN-SCO architecture is open (the user knows the data-model) to facilitate their integration with other solutions and/or existing technological tools in organizations (ERP, TMS, WMS, GIS).?

OPCHAIN-SCO integrate input-output data models around a common data-model, it permits to connect them automatically through the database.

The data base may be installed any SQL (Standard Query Language) database, including DBF, EXCEL and .csv text files.

OPCHAIN-SCO takes advantage of the facilities of visual environments found in personal computers, the ever-greater speed offered by the new family of servers and technological advances in mathematical optimization. The basic user interface (generate by OPTEX) provides an easy environment and the ability to integrate OPCHAIN-SCO with the requirements of each client.?

The OPCHAIN-SCO utilities provide automatic generation of prototype for shell, data and dialog windows to capturing and maintaining the input data required by models.

The results of the models are stored in SQL tables, generated automatically by OPTEX, the structured if know by the user. The scenario comparison reports allow users to view the results from multiple viewpoints, and net differences between scenarios.?

OPCHAIN-SCO includes a tools system that allows easily detect the differences, and possibly the causes, of the actual decisions and the decisions proposed by the models; it includes a feasibility analyzer to detect problems in the models or in the input data.

Finally, the user can connect the results of the models to its Business Intelligence (BI) system.?

4.4. CLIENT-SERVER ARCHITECTURE

OPCHAIN-SCO can operate in a single computer or in a Wide Area Network (WAN) using reference standards intranet/internet. complies with the coordination of tasks and communication between operational modules of OPCHAIN-SCO on different computers on the network. The optimization server facilitates the use of the licenses of the optimization technologies.

5. ABOUT DECISIONWARE

DECISIONWARE maintains permanent lines of research methodologies large scale optimization and modeling decision problems. Its "know how", through its professionals, has more than forty years working on solving real problems using mathematical programming methodologies.

?OPCHAIN-SCO is a suite of mathematical optimization models, designed and produced by DecisionWare includes solutions to fully optimize multi-business supply chains. Its components have been implemented in many countries and customers in its open structure allow communication with ERP transactional systems. For More information on opchain@doanalytics.net

• ?From their specific expertise, DW has developed the following specialized vertical solutions:
• OPCHAIN-SCO-FOOD: oriented food industry
• OPCHAIN-SCO-BEV: oriented to the beverage industry
• OPCHAIN-SCO-BEER: oriented beer industry
• OPCHAIN-SCO-A&M: oriented to the manufacturing and assembly industry
• OPCHAIN-SCO-PHARMA: oriented pharmaceutical sector
• OPCHAIN-SCO-OIL: oriented to the oil sector
• OPCHAIN-SCO-GAS: oriented to the natural gas industry
• OPCHAIN-SCO-ELE: oriented to the electricity sector

The following topics may be complementing the information about DW:

1.????The course ADVANCED ANALYTICS & OPTIMIZATION APPLIED TO SUPPLY AND TO DEMAND CHAINS are related with all topics including in this document (https://goo.gl/EAXTCg)

2.????The course OPTEX Optimization Expert System include lessons related with large-scale optimization technologies and included a license of OPTEX: https://goo.gl/sAai9T

3.????More information about:

• OPTEX Optimization Expert System: https://goo.gl/S2TV8T.
• GDDP (Generalized Stochastic Dual Dynamic Programming):?https://goo.gl/xVjHCn?

4.????DW has developed the OPCHAIN-OIL oriented to the oil sector.?

5.????For more information on OPCHAIN the reader is invited to consult the following documents:

https://www.doanalytics.net/documents/DW-PPT-OPCHAIN-SCO-IND.pdf

https://www.doanalytics.net/documents/DW-OPCHAIN-SCO-BIO-Resumen.pdf

https://www.doanalytics.net/documents/DW-OPCHAIN-SCO-BEER.pdf

https://www.doanalytics.net/documents/DW-OPCHAIN-SCO-PHARMA.pdf

https://www.doanalytics.net/documents/DW-PPT-OPCHAIN-ESO-Resumen.pdf

https://www.doanalytics.net/documents/DW-PPT-OPCHAIN-ESO-Full.pdf

https://www.doanalytics.net/documents/DW-OPCHAIN-RPO-Regional-Planning.pdf

https://www.doanalytics.net/documents/DW-OPCHAIN-MINES.pdf

6.????The catalogue of OPCHAIN Mathematical Models presents the models made by DW using OPTEX. (https://goo.gl/3EP9j9)

7.????Customers can access the OPCHAIN-SCO mathematical models in the following forms:

• On premise, in this case the software OPCHAIN-SCO is installed and runs on the servers indicated by the customer. The software can be sold or leased to the customer.
• On demand, in this case the customer has access to OPCHAIN-SCO software on a server of DW in the cloud (cloud). The software may also be rented by periods (years, months, semesters, weeks). The databases of the customer may be in a customer server.
• As a service, through a professional services contract in which DW assumes the responsibility to carry out the agreed work.
• Software Factory, the customer delivers to DW the formulation of the mathematical model and test data and DW delivers to the customer a decision-making support system composed of: i) source of the mathematical model in the selected optimization technology (GAMS, IBM CPLEX, MOSSEL, AMPL, AIMMS,...), ii) data model of information system and iii) test run to probe the correct functioning of the model.

8.????DecisionWare Experience (https://goo.gl/RkwdeY). It contains a brief description of the main projects that DW has done.

9.????DW is interested in supporting R+D (Research and Development) in universities, facilitating the know-how accumulated in OPCHAIN-SCO for thesis or for research projects.

10.?DW is looking for business partners, strategic partners and/or technological partners to expand its business around the world.