Optimization of fresh–food supply chains in uncertain environments: an application to the meat-refrigeration process Fabrizio Dabbene Paolo Gay Nicola Sacco Cristina Tortia Abstract— In this paper we present a novel approach for the optimization of fresh-food supply chain by managing a trade-off between logistics and some index measuring the quality of the food itself. We propose an hybrid model of the chain, with a part constituted by a event–driven dynamics (the supply chain itself) and a part with time–driven dynamics (the dynamics of some parameters characterizing the jobs in the supply chain). The proposed framework is applied to a real–world example relative to the process of beef–carcasses refrigeration and distribution. I. INTRODUCTION The distribution of fresh food products such as meat, vegetables, fruits and dairy from producer to vendor is in general a complex process, owing to the perishable nature of these agricultural products. A distribution (or supply) chain is a sequence of activities performed in order to deliver a product to a destination with the highest possible quality. Any activity has a potential impact on the product due to the interaction between the action environment and the product. In some cases, i.e. when a product is stored into a cell together with other products, not only the interaction between the product and the surrounding environment is important, but also the interactions between the various products. Each product can be seen as an “object” described by a dynamical model which takes into account the physiological processes occurring in the product. These processes are generally affected by the conditions in the immediate environment of the product. On the other hand, the processes may themselves affect the immediate environment. The objective is to describe the product behavior as a collection of interacting processes, such that their combined action describes the observed phenomenon and such that each subprocess can be fully understood in its description. The nature of the subprocess is largely defined by means of fundamental physical laws and the generally accepted rules in a particular discipline. A typical approach, see e.g. [16], consists in separating high–level processes analyzing intrinsic product properties that, in general, correspond to quality attributes in the phe- nomenon under study. As well explained in [8], the first step in the design of a node of a supply chain (e.g. a chiller or a storage cell) is F. Dabbene is with IEIIT-CNR, Politecnico di Torino, 10129 Torino, Italy fabrizio.dabbene@polito.it P. Gay and C. Tortia are with DEIAFA, Facolt` a di Agraria, Universit` a del Studi di Torino, Grugliasco (TO), Italy (paolo.gay,cristina.tortia)@unito.it N. Sacco is with DAUIN, Politecnico di Torino, 10129 Torino, Italy nicola.sacco@polito.it for the user to draw up specifications. In fact, in many cases, poor design in existing networks is mainly due to a mismatch between the purpose the nodes were originally designed for and how they are actually used. A proper sizing of network throughput and node loads could be in fact a difficult task without the aide of ad-hoc simulation tools. In this paper we present a novel approach for the opti- mization of fresh-food supply chain by managing a trade-off between the logistics of the food treatment, for instance the food delivery date against the quality of the food itself. A quite similar approach can be found for instance in [4], where the authors optimize a manufacturing process that performs a sequence of operations on a set of jobs. Such operations modify some physical characteristic of the jobs. However, the focus of this paper is somewhat different, and there are some distinctive features that distinguish the two works. In fact, in our approach, the single nodes can process more than one job at a time and are supposed to have infinite capacity, and therefore we do not consider queues before the single nodes. More importantly, we consider the situation in which not only the operations performed in the nodes modify some physical characteristic of the single job, but the jobs may influence each other and also the way the nodes process the jobs themselves. II. PROBLEM DESCRIPTION AND NOTATION In this section, we present the formulation of the general problem of optimizing a food supply chain. The first step consists in constructing a mathematical model of the chain. The model we propose is an hybrid model, with a part constituted by a event–driven dynamics (i.e., the supply chain itself) and a part with time–driven dynamics (i.e., the dynamics of some parameters characterizing the jobs in the supply chain). We consider a supply-chain configuration depicted in Fig. 1, consisting in a network formed by n successive nodes in which the different jobs are processed in a sequential way. To keep the formalism at a general level, we will use the term node j node st 1 th n node th Fig. 1. General structure of the problem: n sequential nodes. “job” to refer to the generic portion of food to be treated (which can be for example a pallet of fresh-fruits, a meat Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005 MoIC20.6 0-7803-9568-9/05/$20.00 ©2005 IEEE 2077