The item dependent stockingcost constraint

Abstract

In a previous work we introduced a global StockingCost constraint to compute the total number of periods between the production periods and the due dates in a multi-order capacitated lot-sizing problem. Here we consider a more general case in which each order can have a different per period stocking cost and the goal is to minimise the total stocking cost. In addition the production capacity, limiting the number of orders produced in a given period, is allowed to vary over time. We propose an efficient filtering algorithm in O(n log n) where n is the number of orders to produce. On a variant of the capacitated lot-sizing problem, we demonstrate experimentally that our new filtering algorithm scales well and is competitive wrt the StockingCost constraint when the stocking cost is the same for all orders.

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Notes

  1. 1.

    in the same way as minimumAssignment [6, 7] generalizes allDifferent [18], cost-gcc [24] generalizes gcc [22, 23], or cost-regular [4] generalizes regular [19], etc.

  2. 2.

    In typical applications of this constraint, assuming that ct is O(1), the number of orders n is on the order of the horizon T: nO(T).

  3. 3.

    A constraint is bound consistent if, for each minimum and maximum values, there exists a solution wrt the constraint by considering the domains of other variables without holes.

  4. 4.

    The monotonicity ensures that if we prune the upper bound of a variable to a given value, all other values greater than this value in the domain of the variable are inconsistent.

  5. 5.

    A reversible variable is a variable that can restore its domain when backtracks occur during the search.

  6. 6.

    item: order type.

  7. 7.

    idle period: period in which there is no production.

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Correspondence to Vinasetan Ratheil Houndji.

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Houndji, V.R., Schaus, P. & Wolsey, L. The item dependent stockingcost constraint. Constraints 24, 183–209 (2019). https://doi.org/10.1007/s10601-018-9300-y

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Keywords

  • StockingCost constraint
  • Production planning
  • Lot-sizing
  • Scheduling
  • Constraint programming
  • Global constraint
  • Optimization contraint
  • Cost-based filtering