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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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: n ∼ O(T).
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.
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.
A reversible variable is a variable that can restore its domain when backtracks occur during the search.
item: order type.
idle period: period in which there is no production.
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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
- StockingCost constraint
- Production planning
- Constraint programming
- Global constraint
- Optimization contraint
- Cost-based filtering