Optimisation of policy parameters in supply chain applications

Abstract

In this paper, three approaches for finding optimal parameters for supply chain systems are described and evaluated. The first approach is based on rigorous mixed integer linear programming concepts. Although using this approach guarantees finding the optimal solution for the policy parameters, the drawback of applying such a model to supply chain networks is the excessive computational requirements. The second approach is to combine a detailed stochastic simulation model with a simulated annealing algorithm. While optimality is no longer guaranteed with this approach, far larger problems should be tractable. Finally, a gradient-based approach is suggested, in which a higher-level optimiser utilises the results from the same detailed stochastic simulation model to obtain the optimal parameters. Results obtained when introducing small deviations to the policy parameters are used to estimate the gradients, which are used by the higher-level model. Two case studies are considered: a simple reorder-point warehouse example and an industrial-scale multi-site production distribution problem. The first example is used to compare the effectiveness of the simulated annealing and gradient-based approaches with the rigorous mixed integer linear programming (MILP) formulation. In the industrial example, only simulated annealing and simple gradient-based methods are applied, as the MILP model becomes intractable. Here, dynamic safety stock levels and order quantities are primarily investigated.

Keywords:

• Enterprise supply chain modelling
• Sampling
• Gradient-based optimisation

Notes

^†Which is used in the simulated annealing and gradient-based approaches.

^†The values of T ₀, α _T and α _N are in the range generally recommended in the literature and have been obtained through testing. The values of P ₀ and Q ₀ are specified to be sufficiently far away from the optima to evaluate critically the simulated annealing properties. The values of Nh are a proportion of the values of P ₀ and Q ₀.