Onur A. Kilic

Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop a unified mixed integer linear modelling approach to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under static–dynamic uncertainty strategy. The proposed approach applies to settings in which unmet demand is backordered or lost; and it can accommodate variants of the problem for which the quality of service is captured by means of backorder penalty costs, non-stockout probabilities, or fill rate constraints. This approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the stochastic lot sizing problem, some of which have been previously tackled via ad hoc solution methods and some others that have not yet been addressed in the literature; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds based on piecewise linearisation of the first order loss function. We illustrate the effectiveness and flexibility of the proposed approach by means of a computational study.

A reformulation for the stochastic lot sizing problem with service-level constraints

We study the stochastic lot-sizing problem with service level constraints and propose an efficient mixed integer reformulation thereof. We use the formulation of the problem present in the literature as a benchmark, and prove that the reformulation has a stronger linear relaxation. Also, we numerically illustrate that it yields a superior computational performance. The results of our numerical study reveals that the reformulation can optimally solve problem instances with planning horizons over 200 periods in less than a minute.

Order acceptance in food processing systems with random raw material requirements

This study considers a food production system that processes a single perishable raw material into several products having stochastic demands. In order to process an order, the amount of raw material delivery from storage needs to meet the raw material requirement of the order. However, the amount of raw material required to process an order is not exactly known beforehand as it becomes evident during processing. The problem is to determine the admission decisions for incoming orders so as to maximize the expected total revenue. It is demonstrated that the problem can be modeled as a single resource capacity control problem. The optimal policy is shown to be too complex for practical use. A heuristic approach is proposed which follows rather simple decision rules while providing good results. By means of a numerical study, the cases where it is critical to employ optimal policies are highlighted, the effectiveness of the heuristic approach is investigated, and the effects of the random resource requirements of orders are analyzed.

Intermediate product selection and blending in the food processing industry

This study addresses a capacitated intermediate product selection and blending problem typical for two-stage production systems in the food processing industry. The problem involves the selection of a set of intermediates and end-product recipes characterising how those selected intermediates are blended into end products to minimise the total operational costs under production and storage capacity limitations. A comprehensive mixed-integer linear model is developed for the problem. The model is applied on a data set collected from a real-life case. The trade-offs between capacity limitations and operational costs are analysed, and the effects of different types of cost parameters and capacity limitations on the selection of intermediates and end-product recipes are investigated.

A discrete time formulation for batch processes with storage capacity and storage time limitations

Abstract This paper extends the conventional discrete time mixed integer linear programming (MILP) formulation for scheduling multiproduct/multipurpose batch processes by introducing storage capacity and storage time limitations. For this purpose, storage vessels are explicitly modeled on which material flows are defined, and storage capacity and storage time constraints are expressed. The approach is shown to be effective in modeling the scheduling problem in a variety of storage configurations such as single/multiple dedicated and multipurpose storage vessels. In a numerical study, cases where storage capacity and storage time limitations have significant impacts on scheduling production and storage operations are highlighted.

The stochastic lot sizing problem with piecewise linear concave ordering costs

We address the stochastic lot sizing problem with piecewise linear concave ordering costs. The problem is very common in practice since it relates to a variety of settings involving quantity discounts, economies of scales, and use of multiple suppliers. We herein focus on implementing the ( R , S ) policy for the problem under consideration. This policy is appealing from a practical point of view because it completely eliminates the setup-oriented nervousness - a pervasive issue in inventory control. In this paper, we first introduce a generalized version of the ( R , S ) policy that accounts for piecewise linear concave ordering costs and develop a mixed integer programming formulation thereof. Then, we conduct an extensive numerical study and compare the generalized ( R , S ) policy against the cost-optimal generalized (s,S) policy. The results of the numerical study reveal that the ( R , S ) policy performs very well - yielding an average optimality gap around 1%. HighlightsWe address the stochastic lot sizing with piecewise linear concave ordering costs.We introduce the generalized ( R , S ) policy and present a MIP formulation thereof.The generalized ( R , S ) policy yields an optimality gap around 1%.

Optimal policies for production-clearing systems under continuous-review

In this paper, we consider a production-clearing system with compound Poisson demand under continuous review. The production facility produces one type of item without stopping and at a constant rate, and stores the product into a buffer to meet future demand. To prevent high inventory levels, a clearing operation occasionally removes all or part of the inventory from the buffer. We prove that an (m, q)-policy, i.e., a policy that clears the buffer to level m as soon as the inventory hits a level q, minimizes the long run average holding and clearing cost. We also derive a numerically very efficient approach to compute the optimal parameters of the (m, q)-policy for models with backlogging and models with lost sales. With these numerical methods we show that tuning the clearing levels m and q in concert can lead to substantial cost savings.

A MIP-Based Heuristic for the Stochastic Economic Lot Sizing Problem with Remanufacturing

Abstract We consider the stochastic economic lot sizing problem with remanufacturing under customer service level constraints. The problem is a stochastic extension of the classical lot sizing problem where demand can be met via two alternative sources: manufacturing new products and remanufacturing returned products. It is known that even the deterministic version of this problem is NP-hard. We propose a mixed integer programming based heuristic for the problem building on a static-dynamic uncertainty strategy.

Modeling intermediate product selection under production and storage capacity limitations in food processing

In the food industry products are usually characterized by their recipes, which are specified by various quality attributes. For end products, this is given by customer requirements, but for intermediate products, the recipes can be chosen in such a way that raw material procurement costs and processing costs are minimized. However, this product selection process is bound by production and storage capacity limitations, such as the number and size of storage tanks or silos. In this paper, we present a mathematical programming approach that combines decision making on product selection with production and inventory planning, thereby considering the production and storage capacity limitations. The resulting model can be used to solve an important practical problem typical for many food processing industries.

An Extended Mixed-Integer Programming Formulation and Dynamic Cut Generation Approach for the Stochastic Lot-Sizing Problem

We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function—as is the case in earlier formulations—it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach. The online appendix is available at https://doi.org/10.1287/ijoc.2017.0792.