## Invited Session Mon.1.H 0111

#### Monday, 10:30 - 12:00 h, Room: H 0111

**Cluster 13: Logistics, traffic, and transportation** [...]

### Supply chain optimization

**Chair: Edwin Romeijn**

**Monday, 10:30 - 10:55 h, Room: H 0111, Talk 1**

**Joseph Geunes**

Multi-period price promotions in a single-supplier, multi-retailer supply chain under asymmetric demand information

**Coauthor: Yiqiang Su**

**Abstract:**

This paper considers a two-level supply chain in which a supplier serves a retail chain. We consider a two-stage Stackelberg game in which the supplier sets price discounts for each period of a finite planning horizon under uncertainty in retail-store demand. To stimulate sales, the supplier offers periodic off-invoice price discounts to the retail chain. Based on the price discounts offered, and after store demand uncertainty is resolved, the retail chain determines store order quantities in each period. The retailer may ship inventory between stores, a practice known as diverting. We demonstrate that, despite the resulting bullwhip effect and associated costs, a carefully designed price promotion scheme can improve the supplier's profit when compared to the case of everyday low pricing (EDLP). We model this problem as a stochastic bilevel optimization problem with a bilinear objective at each level and with linear constraints. We provide an exact solution method based on a Reformulation-Linearization Technique (RLT). In addition, we compare our solution approach with a widely used heuristic and another exact solution method from the literature in order to benchmark its quality.

**Monday, 11:00 - 11:25 h, Room: H 0111, Talk 2**

**Dolores Romero Morales**

A multi-objective economic lot-sizing problem with environmental considerations

**Coauthors: H. Edwin Romeijn, Wilco van den Heuvel**

**Abstract:**

In this talk we study a Multi-Objective Economic Lot-Sizing Problem. This Multi-Objective Economic Lot-Sizing Problem is a generalization of the classical Economic Lot-Sizing Problem, where we are concerned with both the lot-sizing costs, including production and inventory holding costs, as well as the production and inventory emission of pollution. With respect to the emissions, the planning horizon will be split into blocks of the same length (except for possibly the last one), and the total emission in each block will be minimized. This includes the case in which we are interesting in measuring the pollution in each of the planning periods, or across all periods, or more generally, across subsets of periods. We assume fixed-charge production cost and emission functions, and linear inventory holding cost and emission functions. When more than one objective function is optimized, the Pareto efficient frontier is sought. In this talk, we show that the Pareto optimal problem is NP-complete. We then identify classes of problem instances for which Pareto optimal solutions can be obtained in polynomial time. We end with some results on the Pareto efficient frontier of the problem.

**Monday, 11:30 - 11:55 h, Room: H 0111, Talk 3**

**Zohar Strinka**

Approximation algorithms for risk-averse selective newsvendor problems

**Coauthor: H. Edwin Romeijn**

**Abstract:**

We consider a single-item single-period problem of a supplier who faces uncertain demands in a collection of markets and wishes to choose a subset of markets *z* whose demand to satisfy as well as a corresponding overall order quantity *Q*. The supplier faces costs associated with satisfying demands, overage and underage costs, and lost revenues in the markets whose demand is not selected. Moreover, the supplier optimizes a risk measure associated with those random costs. Finally, we assume that the joint distribution of all market demands and revenues is nonnegative with finite mean. We develop an approximation framework that, under certain conditions on the cost structure and risk measure, provides a solution whose objective function value is, with high probability, within a constant factor of the optimal value. This framework depends on two key techniques: (i) rounding the solution to a continuous relaxation of the problem, and (ii) sampling to approximate the true revenue and demand distribution. We provide explicit examples of some cost structures and risk measures for which the algorithm we develop is efficiently implementable.