Production-routing with price-dependent demand

Our paper (co-authored with Somayeh Torkaman, Mohammad Reza Akbari Jokar and Nevin Mutlu):

Solving a production-routing problem with price-dependent demand using an outer approximation method

is now available online on the Computers & Operations Research website. Use this personalized URL to obtain the following 50 days free access to the article.

we develop a framework to study a manufacturer’s integrated decision-making with respect to marketing (i.e., pricing) and operations decisions. The setting we are considering is an extension of the traditional production routing problem (PRP), which aims to optimize the production, inventory, and routing decisions of a manufacturer who serves multiple retailers with exogenous demand in a multi-period setting. 

Demand follows a general convex, differentiable, continuous and strictly decreasing function in price. The problem is modeled as a mixed integer nonlinear program (MINLP). Two Outer Approximation (OA) based algorithms are developed to solve the PRP-PD. The efficiency of the proposed algorithms in comparison with commercial MINLP solvers is demonstrated. The computational results show that our basic OA algorithm outperforms the commercial solvers both in solution quality and in computational time aspects. On the other hand, our extended (two-phase) OA algorithm provides near-optimal solutions very efficiently, especially for large problem instances. These findings prevail both for linear and for nonlinear demand functions.

Additional sensitivity analyses are conducted to investigate the impact of different problem parameters on the optimal solution. The results show that the manufacturer should give higher priority to the retailer who has lower price sensitivity and who is closer to the manufacturer. Another takeaway is that a larger market size and a lower price sensitivity lead to more profit.

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