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I am currently working on a storage location assignment problem (SLAP), which involves optimizing the allocation of various items with different dimensions to different storage areas. My model comprises two phases: warehousing, where there is one storage area with a specific number of racks, and manufacturing, which has its storage area and a specific number of racks as well.

In this problem, I aim to determine both the number of supplies for each SKU item and the allocation of storage spaces for each item. These allocations need to adhere to the capacity constraints of each storage area while maximizing the production of final products. Each final product or order is a combination of several items.

While addressing this problem, I've noticed that there are processes in manufacturing and final products that have sequence and timing considerations (there is a timing/sequence of operations to produce one product). This makes the problem somewhat resemble a flexible flow shop scheduling problem. However, unlike traditional flow shop scheduling, I am not looking to minimize makespan. Instead, I want to focus on the allocation of items to space and the supply of each SKU item based on the entire process of warehousing and manufacturing.

Could you please help me identify the specific type of problem or hybrid problem that my model falls under? Additionally, any insights or guidance on how to approach this complex optimization challenge would be very helpful.

Maryam
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I guess, as you correctly mentioned, this problem is too complex as actually many of the SCM problems are complex and I doubt one math formulation can handle all of its aspects. Instead, the problem can be decomposed into at least three separated models with some interchanges between them. (please, be aware it is an initial thought and may extend to more than these three models).

  • First, a lot-sizing or MRP model to capture the optimum number of orders based on the production needs and supplier capacity.
  • Second, a packing and storing model to determine the best package form and the amount of racks needed to store these packages. In both warehouses and also production lines.
  • Third, a sequencing model to represent how the products should be allocated to resources based on the production routes. (specifically, in the mentioned hybrid flow shop).

Based on the above three mentioned models, you will then decide how to develop either a math model, or heuristics, or hybrid solutions.

A.Omidi
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  • For the first part of the model, could you provide further clarification? The number of orders is inherently stochastic, and we can only estimate a range based on market demand. What exactly do we mean by 'optimum' in this context?

    As for the second point, the composition of packages (i.e., how many of each item type is included in an order) is a known variable. However, determining the optimal storage allocation within racks and spaces remains a challenge. To formulate this problem effectively, are there any resources or communities where I can seek guidance?

     – Maryam Sep 24 '23 at 03:38
  • I'm reading books, articles, and trying to work on a simple version of the problem myself, but I was wondering if there's a community or experts I can turn to for guidance? – Maryam Sep 24 '23 at 03:38
  • @Maryam, 1) for the first part pleaes, search lot-sizing or MRP keywords. 2) I meant by optimum was actually based on solving a math model either in deterministic or stochastic form. 3) If you can determine how many of each item type are included in an order and also you know how you can package them, e.g. in a specific carton and then laying them down in the pallet, you only need to determine the number of racks needed based on the simple calculation without having any math model. – A.Omidi Sep 24 '23 at 15:44
  • pleaes, see these links, 1 - 2 - 3. And also by searching the community you absolutely find many related resources.
    • – A.Omidi Sep 24 '23 at 15:44