**Parallel Sessions**

** Session 4: Manufacturing – Chair: Ivo Adan**

**Kay Peeters (Eindhoven University of Technology) – Smart heuristics for batching in a poultry processing plant
**Poultry processing plants produce batches of products with a fixed minimum target weight, for which they are paid a fixed price. Profit margins of poultry processing plants are small, and since any weight over the target weight (giveaway) is not paid for they wish to minimize the average giveaway per batch. However, since product weights are stochastic this is a challenging task and there is a need for smart allocation of products to batches. The focus of this talk is on equipment known as graders, which are used to create batches of products with a fixed target weight. Allocation decisions of products to batches in graders have to be made online. Such an allocation problem is known as an online bin covering problem in literature. We show that this problem can be formulated as a Markov decision process (MDP). Furthermore, since the MDP formulation suffers from the curse of dimensionality, a heuristic in the form of an index policy is presented that is shown to perform well. Lastly, we show that index policies can be further improved by using a rollout algorithm.

**Teun Janssen (Delft University of Technology) – Scheduling in the photolithography bay**

The production process in a semiconductor factory is a complex one. The wafer, which contains the chips, will visit different production bays multiple times during its production cycle. The expensive photolithography equipment often are the bottleneck of the production line. Hence, the overall performance of the wafer fab can be improved by raising the equipment throughput on these tools. Photolithography is a process to transfer the geometric pattern of a chip-design onto a wafer. This is done by putting light through a reticle (or mask) onto the production wafer. This reticle contains the geometrical pattern of the computer chip. In this talk, we will look at scheduling problems for the photolithography bay. In European factories, this bay contains many different machines and the products are very diverse. Furthermore, there is only one reticle of every kind in the whole factory, thus products that share a reticle cannot be produced at the same time. This translates to a mathematical problem, which is a special case of scheduling with resource constraints. We will look at this problem and its properties and pose the major open questions.

**Nicky van Foreest (University of Groningen) – Surplus capacity is never wasted
**We consider a single-item production-inventory system in which a machine can switch on and off at the expense of a setup cost. When on, it produced items at a constant rate and stores the items to serve demand. Given holding and backlogging cost, the problem is to find a switching rule for the machine such that the average switching costs and inventory costs are minimal. When the demand process is constant, this problem is known as the Economic Production Quantity problem, and has been solved around 1930. However, when the demand process is a mixture of constant and (compound) Poisson demand, the analysis of the production-inventory system becomes much more complicated. Recently we developed a method that allows us to prove the optimality of a certain class of control policies, but also to compute these policies. With these computational tools we can then obtain insight into the trade-offs between production capacity, demand variability, and average inventory level. In the talk we will briefly describe the tools required for the proofs; the focus will be on the insights we can obtain for production-inventory systems. As an anecdotal response to the (simplistic) idea that all `waste’ should be `rooted out’, we analyze the rule: `set the capacity 50% higher than the average demand.’ If this rules makes demand variability irrelevant and leads to low inventory levels, this would be much easier to implement than convincing customers to smooth their demand.