Dynamic and Stochastic Programming Problems in Logistics and Their Solutions in MATLAB
MAGAZINE №1 (102) - 2021
AUTHORS
SAVENKOVA T.I. - Department of Logistics and Supply Chain Management, St. Petersburg School of Economics and Management, National Research University «Higher School of Economics», Campus in St. Petersburg (Saint-Petersburg, Russia)
CATEGORY Inventory management Optimization and mathematical modelling
ABSTRACT
Dynamic and stochastic programming methods are often used nowadays for optimization problems solutions. Technological progress, computer performance and programs improvement led to expansion of optimization problems and their appearing in new spheres.
A brief review of dynamic and stochastic programming methods for solution of optimization problems in logistics (there are both classic logistic problems and problems from other spheres, however, from spheres where processes are interlinked with logistic functions and operations, given) is provided in the article. There are main features of reviewed optimization problems (whether the stated problem is one-period or multi-period, whether it is one-index or multi-index, main constraints, optimization criteria and solution methods, uncertainties) given.
The article presents multi-period multi-index optimization problem devoted to the search of optimal strategy of computers purchase and selling via retailers. It is required to find optimal correlation between number of bought and sold computers of three types during four months under the changing demand, there is only demand forecast based on marketing research available. Mathematical statement of the problem and statement of this problem in MATLAB are offered as well as this problem solution in MATLAB.
Keywords:
The SCOR Framework as a Basis for the Model of the Company’s Logistics Cost and Service Level Optimization
MAGAZINE №4 (99) August 2020
AUTHORS RYBAKOV D.S.
CATEGORY Logistics service management Optimization and mathematical modelling Supply chain planning
ABSTRACT
The current state of management practice is characterized by the presence of a demand to improve the efficiency and effectiveness of logistics processes, on the one hand, and an insufficient level of application of one of the main tools for achieving this goal – optimization modeling, on the other. One of the main reasons of this phenomenon is the lack of a universal basis of the proposed optimization models that does not allow them to be applied widely enough in companies with different business process structures. The aim of the research was to develop a universal, based on the SCOR framework, integrated model for optimizing the logistics service of an enterprise. During the research process, the overview of the developed models for logistics service optimization, the analysis of the limitations of the logistics system optimization models, the adaptation of the map of SCOR process metrics have been carried out; the influence diagram of the optimization model components has been developed; the models of cost optimization and logistics service optimization have been combined into a single integrated optimization model; an algorithm for the optimal solution search has been elaborated; the implementation of the model and algorithm as a program for the solution search has been introduced. As a result, the integrated optimization model based on the components of the SCOR model has been developed, combining the cost and service level optimization models, using the outputs of one model as inputs for another when searching for an optimal solution. Building the optimization model on the basis of the SCOR model components provides universal character of its application, taking into account the set of costs, arising in a logistics system, including indirect ones, and the set of metrics of logistics service reflects the links between functional departments, the ability to maintain a level of total costs at the efficiency frontier, achieving the goal of the profit maximization at the same time, provides a link between the tactical and operational levels of decision-making, which together leads to an increase in the reasonableness and quality of management decisions, and creates prerequisites for the overall optimal functioning of an enterprise logistics system.
Keywords: SCOR optimization Optimization Models optimization modeling logistics service logistics costs logistics processes business process metrics performance indicators KPI
Comparative analysis of limited stock distribution principles in logistics network
MAGAZINE №6 (95) December 2019
AUTHORS ERMOLINA M.V., ZAKHODYAKIN G.V.
CATEGORY Information technologies in logistics and SCM Inventory management Simulation modelling
ABSTRACT
The article considers the situation when a company needs to distribute limited amount of stock to the regional warehouses in its own two-echelon distribution network. The network consists of a single distribution center and several regional facilities which are serving the company's customers. It is supposed that every warehouse calculates its requirements for the replenishment daily basing on the on-hand inventory, demand forecast, safety stocks and lead-times from the central warehouse. Thus, company's managers are aware of the consumption rate and inventory level at each regional facility. Demand forecasting and final replenishment planning decisions are centralized.
Notion of the "limited stock" refers to such inventory quantity at the central warehouse that is insufficient to satisfy the total volume of all regional warehouses' requirements for the product. Limited stock situation may have varying length in time.
A system of rationing rules or principles should be applied to make a distribution decision in such a situation. These set of rules identify the volume and sequence of the shipments from the central to regional warehouses.
So, in this article authors aim to solve the following problems:
- to identify factors that affect the choice of a certain set of rationing rules for the limited stock;
- to attempt to classify existing rationing principles;
- to identify how the business goals affect the choice of the preferred rationing principle;
- to create an imitation model and check experimentally which rationing principles are the best for each of the business goal
The outcomes gained might be used as a base for the choice of the limited stock rationing principles in companies with own distribution network, and for better tuning of the distribution algorithms in DRP systems or modules.
Keywords: inventory management imitation modeling simulation modeling simulation model inventory planning optimization stock rationing stock DRP
Vehicle Routing Problem: Overview of Models, Methods and Algorithms. Part 1
MAGAZINE №4 (93) August 2019
AUTHORS
Goncharova Y.A. - Cand.of Tech.Sc., Software engineer, Research and Production Center «GeoTek» (Ufa, Russia)
CATEGORY Analytics and reviews Optimization and mathematical modelling
ABSTRACT
The paper reviews well-known routing problems (Vehicle Routing Problem, VRP), that are an essential part of the transport logistics. The mathematical models of various routing problems’ classes are given: with account to a transport vehicle’s carrying capacity (TV); with the time windows; with split delivery; with a given planning time horizon (periodic problem); with backhauls; with satellite facilities. Since the routing problems are the NP-hard objectives of combinatorial optimization, for the sake of their practical application in the sphere of the transportation management the various heuristic algorithms are being developed. The known metaheuristics are expounded in the paper that present the local search algorithms as well as constructive algorithms, namely, the genetic algorithm; the evolutionary strategies; the ant colony algorithms’ series; the alternating neighbourhood search algorithm. Herewith, the attention is paid to the solution coding and to some neighbourhood constructing solution operations. Since in practice the routing problems are closely connected with the goods disposition within the transport vehicles (the 3D packing problem), the approximate algorithms which provide obtaining the goods packing map are described. The given review of various routing problems’ classes and the effective methods of their solution aid in practical problems of the effective routes search for the goods delivery to various customers. So, Part 2 of the paper describes the mathematical model and the methods of one practical task resolving that is processed together with the 3D packing problem of goods inside car transport vehicles.
Keywords:
Providing the Continuity of Main Production in Metallurgy Enterprises under Prepared Materials Supply
MAGAZINE №4 (93) August 2019
AUTHORS NEGOMEDZYANOV Y.A., NEGOMEDZYANOV G.Y.
CATEGORY Supply chain planning Optimization and mathematical modelling
ABSTRACT
The article discusses principles of providing a delivering the prepared materials to metallurgy enterprises for the continuity of the main production oriented to system-wide interests. The conditions for ensuring the continuity of the main production are revealed. It is shown that to perform its core work — reliable, efficient and continuous provision of technological units with prepared materials — functioning on the basis of a technological process interconnected with the main transport and main production, technologically optimal and logistically organized based on the approach to it as a process prepared materials should have an optimal operational stock of prepared materials. It has been determined that it is more expedient to maintain the operational stock of prepared materials in a warehouse on wheels from specialized cars than in bunkers of a calculated capacity. A mathematical model is proposed for optimizing the parameters for ensuring the continuity of the main metallurgical production. The results of the choice of parameters to ensure the continuity of the main production are given.
Keywords:
Choosing the Optimal Supply Chain Contract Model: Features of Multicriteria Analysis with Risk Assessment
MAGAZINE №1(84) February 2018
AUTHORS GUSEV D.A., MAZUNINA О.А., FEL A.V.
CATEGORY Optimization and mathematical modelling Sourcing
ABSTRACT
Consideration of the supply chain from the point of view of objective understanding as a set of individuals and legal entities, interacting specifically and precisely in material, financial and information flows, presupposes the availability of a tool for fixing the rules for interaction of such parties. Such a tool already exists, it is a contract / agreement / agreement of the parties. It is the contract model of the supply chain that is of great importance in the process of value formation of the product, as it can be considered as a legal documental basis for mutual arrangements for the supply chain. Contract management tasks in the supply chain in terms of the optimal contract model choice are formalized it the paper for the first time as decision-making tasks under many criteria. This format of models allows to consider risks that can be formalized in the form of separate individual criteria. It is shown that a dimensionality phenomenon is associated with problems of this type which can be eliminated on the basis of a transition to new formats for the presentation of estimates of particular criteria: 1) the format of generalized selection criteria; 2) to the standardized form of the problem of choice. For both approaches, tasks of multicriteria choice of the contract model are formalized.
Keywords:
Application of Transport Model in Warehouse Logistics
MAGAZINE №1(84) February 2018
AUTHOR Kuznetsov V.O. - Postgraduate student, Department of Logistics and Supply Chain Management, National Research University Higher School of Economics (St.-Petersburg, Russia)
CATEGORY
ABSTRACT
On the one hand, the relevance of this research is determined by an attempt of solving the problem of optimal inventory allocation, which can open the possibilities for increase in stock turnover. On the other hand, there was an attempt to extend the list of problems which can be solved by operations research methods. The potential of application of operations research methods (transport model as a specific case of linear programming, in particular) is underestimated. According to Taha [2011], a transport model is a problem of finding optimal allocation of homogeneous objects from accumulators to receivers with minimizations of costs on displacement or movement. In our opinion, the canonical form of a transport model represents accumulators as points of departures, receivers as clients and cost on displacement as transport costs. The paradigm of using this model is constrained by using the latter in transport logistics only. In fact we can apply this model in much more problems (micro, meso or macro level). This study shows that objects and variables from the canonical transport model can be represented as objects from different fields (beyond logistics) thus helping to find an optimal solution to a certain problem. Our study represents accumulators as nominal cells where work-in-process (WIP) product is in the warehouse, receivers - as production lines and costs on displacements as mileage of loaders. Thus, the cost function Z that we want to optimize is the function of mileage of loaders. Minimizing function Z will enable us to find the optimal allocation of WIP products to production lines (next production stage)
Keywords:
Diversified Optimization of the Supply Strategy Parameters with a Possibility of Vehicles Selecting with Account of Their Cargo Capacity
MAGAZINE №5 (82) October 2017
AUTHORS GERAMI V.D., KOLIK A.V., SHIDLOVSKIY I.G.
CATEGORY Optimization and mathematical modelling Inventory management
ABSTRACT
A new improved algorithm to optimize the parameters of a diversified supply strategy considering the transportation features for the EOQ-models is proposed. When optimizing decisions it will allow for the first time to take into account the following attributes of the simulated supply chain: 1) cargo capacity of the vehicles used; 2) a possibility of selecting their types when delivering goods; 3) the format of paying storage costs (rent or paying only for occupied places at the warehouse); 4) expediency of deliveries using several vehicles if there are discounts on the cost of such deliveries; 5) factor of time value of money taking into account the efficiency of cash flows of the supply chain itself; 6) assessment of the expected return on the working capital of the simulated supply chain; 7) specificity of such a profitability indicator taking into account the utilization of the cargo capacity of the vehicles used at the deliveries. This algorithm was developed with reference to special EOQ-models. Namely, it relates to a class of models interesting and important for business when profit can be made at each reorder interval. The models in question are those where profit during the reordering interval can be used both to cover part of the costs at that interval and to make payment of the next delivery. Therefore, the format of the algorithm will consider necessary and sufficient conditions fulfillment of which allows to ensure the possibility of these payments from the profit during the supply chain operation.
Keywords:
Metal Trading Company Transportation Service Modelling
MAGAZINE №3 (80) June 2017
AUTHORS
KULAGIN P.A. - Postgraduate student, Department of Mathematical Methods in Economics, Plekhanov Russian University of Economics (Moscow, Russia)
CATEGORY Optimization and mathematical modelling Transportation in logistics
ABSTRACT
The article considers the task associated with the analysis and the evaluation of metal trading company business processes. Particularly, these business processes are connected with the shipments from the supplier's warehouse and the optimization of the transport customer service in the most efficient way as the related services for the main activities. The implementation of enterprise services for the provision of transport services and increasing their share in the total volume of shipments of finished products to customers is suggested. In the article the model of transport service organization efficiency estimation in the metal trading company subject taking into account the restrictions on the existing capacity, traffic and intensity of service is suggested. Also, the model takes into account the dynamics of the finished product flow from the production to the trader warehouse inside the considered transportation network to further its implementation, shipment and export. The problem which is stated in the article is solved by means of economic-mathematical modeling.
Keywords:
Analysis of an Applicability of Existing Approaches to the Distribution Network Design for Retail Companies
MAGAZINE №1 (78) February 2017
AUTHOR SVERCHKOV P.A.
CATEGORY Retail companies’ corporate logistics Distribution logistics
ABSTRACT
The article deals with different approaches to the design of the distribution network, developed by a number of Russian and foreign researchers, and the applicability of these approaches to problems of network optimization in retail companies. The relevance of the article creates by the role that logistics plays for businesses in Retail, and the possible effect on the value of logistics costs and service levels that can be achieved with the use of modeling tools and logistics networks optimization. In the first part of the article, the problem statement and the relevance are described in detail. In the second part, the author presents a comparison of the five most wellknown and commonly used approaches to the distribution network design, using a specific set of comparison criteria. In the conclusion, the author analyzes the specifics of the selected approaches and how it can be improved in order to adapt the algorithms to network design problem in Retail. As such, the following areas of improvement are mentioned:
1. Consideration of strategic factors specific to the retail industry, which affect the design of distribution network.
2. Segmentation of the distribution network into regions, product categories, formats of trade and / or distribution channels;
3. The combination in a single algorithm of common sequence of actions for network design with mathematical optimization techniques
Keywords:
