Studying the use of mathematical programming and heuristics in supply chain management

GUILLÉN, GONZALO; MELE, FERNANDO D.; ESPUÑA, ANTONIO; PUIGJANER, LUIS

San Francisco, EEUU

Conferencia; AIChE Annual Meeting 2003; 2003

AIChE

<!-- /* Font Definitions */ @font-face {font-family:TimesNewRoman; panose-1:0 0 0 0 0 0 0 0 0 0; mso-font-charset:0; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:auto; mso-font-signature:3 0 0 0 1 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-GB;} @page Section1 {size:595.3pt 841.9pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> Supply Chain Management (SCM) aims the integration of a plant with its suppliers and its customers, in order to manage in a co-ordinated manner all the input/output flows: materials, information and finances. The SC problem may be considered at different levels depending on the decision variables: strategic, tactical and operational. This work is focused on the operational level related to day-to-day decisions such as scheduling production and truck loading. The aim of the work is the comparison in terms of benefit and risk between the schedules obtained by means of mathematical programming and those derived from the application of heuristic rules in the SC operation. The mathematical optimisation model includes simultaneously two objectives: the benefit and a measure of the associated benefit risk to explicitly consider the uncertainty of the future demand. The problem is modelled as a two-stage stochastic multi-objective program. The variables associated to the schedule are considered as first-stage variables while sales are taken as second-stage variables. There are two ways of solving this problem: by means of a rigorous method, which allows the generation of the most efficient configuration frontier (Pareto solutions), or with the aid of a metaheuristic approach such as a genetic algorithm. Each solution of the problem implies a SC schedule including production, transportation and storing schedules of the embedded nodes of the chain for a given time horizon. To study the performance associated to the use of the heuristic rules, a simulation model is implemented as a demand-driven system where nothing is done if there is not any customer query. Therefore, the SC is simulated reproducing a set of heuristics such as scheduling rules at the plants, replenishment policies at the stores, and transportation scheduling rules for the lorries. For each customer demand and set of heuristic rules the profit and the risk are evaluated. As a motivating example a simple Supply Chain (SC) is considered. It consists on a batch plant that manufactures several products. Final products are stored in the plant and then transported with lorries to a warehouse where they become available to customers. This simple case is studied by means of mathematical programming, and using the simulator to evaluate a set of defined rules. The systematic comparison between both techniques will show how far the schedules derived from the application of heuristic rules are from those calculated by means of mathematical programming (optimal Pareto schedules). In addition, the trade-off between the solution quality and the calculation time in the two mathematical programming approaches (rigorous and metaheuristic solving methods) will be discussed.