Abstract
We consider a stochastic single item production‐inventory‐routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then, the candidate solutions are tested on a larger sample, and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the first‐stage decision variables is fixed, and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances.
Highlights
We consider a single item stochastic production-inventory-routing (SPIR) problem with a single supplier/producer, multiple retailers/clients and multiple vehicles.A vendor managed inventory approach is followed where the supplier monitors the inventory at the retailers and decides on the replenishment policy for each retailer
The proposed adjustable heuristic approach has several advantages in relation to the classical sample average approximation (SAA) method: i) it does not require solving each sample set to optimality; ii) it does not require the use of large sample sets, and iii) it allows the nal solution to be adjusted to a larger sample set since many rst-stage variables are kept free
In this subsection we describe the adjustable sample average approximation (ASAA) heuristic
Summary
We consider a single item stochastic production-inventory-routing (SPIR) problem with a single supplier/producer, multiple retailers/clients and multiple vehicles. The proposed adjustable heuristic approach has several advantages in relation to the classical SAA method: i) it does not require solving each sample set to optimality; ii) it does not require the use of large sample sets, and iii) it allows the nal solution to be adjusted to a larger sample set since many rst-stage variables are kept free. A very general metaheuristic focused on the exploitation of strategic memory components was proposed by Glover [22] Such a metaheuristic, known as Adaptive Memory Programming (AMP), has been applied over the years to solve several hard combinatorial optimization problems, such as vehicle routing problems [23, 41], stochastic production distribution network design [15] and supplier selection problems [42].
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