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September 11th, 2013, 05:09 AM  #1 
Newbie Joined: Sep 2013 Posts: 1 Thanks: 0  Scheduling problem
Hello, I don’t know how to solve the following scheduling problem. A company assembles products (only in 1 step, there are no successor operations) fully performed by human operators. There are 8 timeslots of 1 hour between 9AM and 17PM. Each order is shipped on a pre specified timeslot (due date). The processing time of assembling a product is 2 minutes. There are approximately 1000 orders each day, therefore on average 5 employees are necessary. Decision: allocate order X to time slot Y Number of operators to hire Constraint: order X should start between 9AM and the shipment time for that order (for example 14PM). So there is some space to position the order. The sum of orders in time slot Y should not exceed the capacity (number of operators). Summarized, I want to allocate orders X to a time slot Y such that the number of required human operators (costs) is minimized. This is a ILP problem which I can not solve by a solver. Therefore I am looking for a simple heuristic to smooth production/scheduling. If orders are not positioned smoothly, there are peaks in the workload which results in a higher number of required operators. Who knows a practicle solution approach? 

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