###### Abstract  
This paper addresses the problem of optimal planning for collection, sorting, and recycling operations. The problem arises in industrial waste management, where distinct actors manage the collection and the sorting operations. In a weekly or monthly plan horizon, they usually interact to find a suitable schedule for servicing customers but with a not well-defined scheme. We proposal an improved negotiation-based approach using an auction mechanism for optimizing these operations. Two interdependent models are presented: one for waste collection by a logistics operator and the other for sorting operations at a recycling plant. These models are formulated as mixed-integer linear programs where costs associated with sorting and collection are to be minimized, respectively. We describe the negotiation-based approach involving an auction where the logistics operator bids for collection time slots, and the recycling plant selects the optimal bid based on the integration of sorting and collection costs. This approach aims to achieve an optimization of the entire waste management process. Computational experiments are presented. waste management; optimization; auctions; negotiation approaches +
Footnote †: journal: _Algorithms_  
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determination problem more effectively compared to standard methods, as we will show in the following. The interaction between collection and sorting is crucial for waste management. Here is how they work together. * Waste collection systems need to be well planned and organized to ensure that waste is collected regularly and efficiently. Proper collection routes and schedules are established based on the type of waste, the volume of waste generated, and the specific needs of the area. By implementing effective collection practices, waste can be gathered and transported to sorting facilities in a timely and cost-effective manner. * Sorting plays a vital role in separating recyclable materials from non-recyclable waste. Once waste reaches the sorting facility, trained personnel or automated systems sort through the waste to identify and separate materials such as paper, plastic, glass, metal, and organic waste. This segregation allows for the recycling of valuable materials and prevents them from being disposed of in landfills or incinerators. * By effectively sorting waste, recyclable materials can be diverted from landfills and sent to recycling facilities. Sorting also enables the recovery of valuable resources from waste, promoting a circular economy and reducing the need for raw material extraction. * Not all waste materials can be recycled. Sorting ensures that non-recyclable waste is properly identified and disposed of in appropriate ways, such as landfilling or waste-to-energy facilities. By separating non-recyclable waste, the focus can be placed on maximizing the recycling potential of the remaining materials. In summary, collection and sorting are interconnected steps in waste management. The efficient collection ensures that waste is gathered and transported to sorting facilities, while sorting allows for the separation of recyclables from non-recyclable waste. This collaboration is essential for effective waste management practices that promote recycling, resource conservation, and proper disposal. Negotiation plays an important role in waste management, especially when it comes to addressing the interests of various stakeholders and finding mutually beneficial solutions. Here is how negotiation works in waste management. * The first step in the negotiation process is identifying the relevant stakeholders involved in waste management. This may include government agencies, waste management companies, environmental organizations, local communities, and residents. * Each stakeholder will have different interests, objectives, and concerns when it comes to waste management.