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An ice cream production scheduling problem

An ice cream production scheduling problem in a hybrid flow shop model, the scheduling problem that comes from an ice cream manufacturing company. This production system can be modelled as a three stage nowait hybrid flow shop with batch dependent setup costs. To contribute reducing the gap between theory and practice we have considered the real constraints and the criteria used by planners. The problem considered has been formulated as a mixed integer programming. Further, two competitive heuristic procedures have been developed and one of them will be proposed to schedule in the ice cream factory.

The first research papers about hybrid flow shop appear in the 70’s. Salvador (1973) was one of the pioneer papers published on hybrid flow shop with more than two stages. The main motivation for this article was to obtain a programming procedure in a nylon polymerization factory. Although some authors, from this moment on, were concerned with the study of such systems, it was at the end of 80’s when hybrid flow shop systems began to have a real interest to researchers. This interest is caused by the increasing use of this configuration in our industry due to its flexibility. Even so, most of the published papers consider the programming problem in this environment from a theoretical point of view, and very few deal with real cases. According to the state of the art from Vignier, Billaut, and Proust (1999), only Narastmhan and Panwalkar (1984), Proust and Grunenberguer (1995), Paul (1979) and Sherali, Sarin and Kodialam (1990) are concerned on industrial applications. Subsequent to the publication to this state of the art, Wong, Chan and Ip (2001) propose a genetic algorithm to schedule spreading cutting and sewing operations in an apparel manufacture. Göthe-Lundgren, Lundgren and Persson (2002) solve the programming problem in an oil refinery company using mixed integer programming. Jin, Ohno, Ito and Elmaghraby (2002) develop a genetic algorithm to schedule orders in a printed circuit board assembly line. Lin and Liao (2003) propose a heuristic procedure to schedule one day’s orders in a label stickers manufacturing company to minimize the weighted maximal tardiness. Bertel and Billaut (2004) treat the processing checks system as a three-stage hybrid flow shop with recirculation and propose a heuristic procedure to minimize the weighted number of tardy jobs. Lee, Kim and Choi (2004) analyze the production scheduling problem in a leadframes manufacturing plant. The authors propose a bottleneck-focused heuristic procedure to minimize total tardiness of a given set of jobs. Ruiz and Maroto (2006) studied the scheduling problem in a ceramic tiles manufacturing and developed a genetic algorithm that performs very competitively. Ruiz, Serifoglu and Urlings (2008) trying to get closer to the real flow shop scheduling environment, investigated the effect of including realistic considerations, characteristic and constraints, on problem difficulty.

Conscious that an important gap between theory and practice still exists, we visited different types of factories in our surroundings to identify what productive systems can be formulated as hybrid flow shop and to detect, not only the most important constraints that have effects on the scheduling problem but also the criteria used by the planners. It has been possible to verify that different types of manufacturing systems, very different to each other, can be formulated as hybrid flow shop to develop efficient scheduling procedures. Between them, we included the manufacturing system on a labels factory, on an acrylic sheets factory, on a cocoa powder form factory, on an active pharmaceutical ingredients (API) factory, on a cold cuts factory or on an ice cream factory. Some special constraints have been detected on each manufacturing system (Ribas, 2007), but also some constraints that are common to all of them, in particular the effect of setup times. In this paper we have considered the characteristics found in the ice cream factory.

The rest of the paper is organized as follows: Section 2 analyzes the ice cream production system; Section 3 develops a mathematical model using mixed integer programming (MIP). Section 4 proposes a heuristic procedure, Section 5 shows the results obtained in the computational experience and Section 6 concludes.

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