An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static–dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time. -------------------------------------------------------------------------------

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.Inventory Relaxation Stochastic non-stationary demand Mixed integer programming Service level Static-dynamic uncertainty

Inventory control for a perishable product with non-stationary demand and service level constraints

We study the practical production planning problem of a food producer facing a non-stationary erratic demand for a perishable product with a fixed life time. In meeting the uncertain demand, the food producer uses a FIFO issuing policy. The food producer aims at meeting a certain service level at lowest cost. Every production run a set-up cost is incurred. Moreover, the producer has to deal with unit production cost, unit holding cost and unit cost of waste. The production plan for a finite time horizon specifies in which periods to produce and how much. We formulate this single item – single echelon production planning problem as a stochastic programming model with a chance constraint. We show that an approximate solution can be provided by a MILP model. The generated plan simultaneously specifies the periods to produce and the corresponding order-up-to levels. The order-up-to level for each period is corrected for the expected waste by explicitly considering for every period the expected agedistribution of the products in stock. The model assumes zero lead time and backlogging of shortages. The viability of the approach is illustrated by numerical experiments. Simulation shows that in 95.8% of the periods the service level requirements are met with an error tolerance of 1%

Essays on Retail Management with Emerging Practice and Customer Behavior

This dissertation is motivated by observations of emerging retail practice and the corresponding customer requirements and behavior. Specifically, it includes the following topics: (1) omni-channel and e-commerce logistics, (2) inventory management, and (3) product strategy and pricing analytics. In the first chapter of the dissertation, we study the shipment consolidation policy facing an increasing frequency of orders per customer. Shipment consolidation (i.e., shipping multiple orders together instead of shipping them separately) is commonly used to decrease total shipping costs. However, when the delivery of some orders is delayed so they can be consolidated with future orders, a more expensive expedited shipment may be needed to meet shorter deadlines. In this paper, we study the optimal consolidation policy focusing on the trade-off between economies of scale due to combining orders and expedited shipping costs, in the setting of two warehouses. Our work is motivated by the application of fulfillment consolidation in e-commerce and omni-channel retail, especially with the rise of so-called on-demand logistics services. Sellers have the flexibility to take advantage of consolidation by deciding when to ship the orders and from which warehouse to fulfill the orders, as long as the orders' deadlines are met. The optimal policies and their structures are characterized. Using the insights of these structural properties, we propose two easily implementable heuristics that perform within 1-2% of the optimal solution and outperform other benchmark consolidation methods in numerical tests. In the second chapter of the dissertation, we study the inventory decision when there are explicit high service-level requirements. We consider a stochastic inventory model (under both backorder and lost-sales) with non-stationary demands, positive lead times, and sequential probabilistic service level constraints. This is a notoriously difficult problem to solve and, to date, not much progress has been made in understanding the structure of its optimal control, especially for the lost-sales inventory system. In this paper, we propose a simple order-up-to control, whose parameters can be calculated using the optimal solution of a deterministic approximation of the backorder inventory system, and show that it is asymptotically optimal for both the backorder and lost-sales systems in the regime of high service level requirement. This result contributes to the growing body of inventory literature that show the near-optimality of simple heuristic controls. Moreover, it also gives credence to the use of deterministic approximation for solving complex inventory problems in practice, at least for applications where the targeted service level is sufficiently high. In the third chapter of the dissertation, we study product strategy and pricing analytics, in settings where customers have both positive and negative product network externalities. One unique feature of luxury products is the coexistence of two opposite externalities: snob customers experience negative externalities with product sales while follower customers experience positive externalities. Motivated by several interesting and (perhaps) counter-intuitive practices in the luxury industry, we study the effect of these two opposite externalities with respect to the selling strategies from three perspectives: 1) the product-line strategy in a monopoly setting, 2) the pricing strategy in a competition setting, and 3) the product bundling strategy. We find that these two opposite externalities generally work in the same direction, although through different mechanisms.PHDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155161/1/laiwi_1.pd