Single item lot-sizing with non-decreasing capacities

Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms

The single-item lot-sizing problem with two production modes, inventory bounds, and periodic carbon emissions capacity

New mixed integer approach to solve a multi-level capacitated disassembly lot-sizing problem with defective items and backlogging

We consider an economic lot-sizing problem with a special class of piecewise linear ordering costs, which we refer to as the class of modified all-unit discount cost functions. Such an ordering cost function represents transportation costs charged by many less-than truckload carriers. We show that even special cases of the lot-sizing problem are NP-hard and therefore analyze the effectiveness of easily implementable policies. In particular, we demonstrate that there exists a zero-inventory-ordering(ZIO) policy, i.e., a policy in which an order is placed only when the inventory level drops to zero, whose total inventory and ordering cost is no more than 4/3 times the optimal cost. Furthermore, if the ordering cost function does not vary over time, then the cost of the best ZIO policy is no more than 5.6/4.6 times the optimal cost. These results hold for any transportation and holding cost functions that satisfy the following properties: (i) they are non decreasing functions, and (ii) the associated cost per unit is non increasing. Finally, we report on a numerical study that shows the effectiveness of ZIO policies on a set of test problems.

For the single-item capacitated lot-sizing problem with linear costs and no backlogging, we suggest a straightforward time algorithm, which does not need a polymatroid or min-cost flow problem reformulation.

Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches

A lot-sizing problem is considered for a group of items with a common manufacturing setup. These items are aggregated in a group by a technique of group technology. The common setup cost for the group is generally less than the sum of each item's setup costs. The cost reduction is expected when lot-sizing is carried out for the group of items rather than for each item independently. The determination of the lot-size for a group of items sharing a common setup is called "group lot-sizing". It is shown by simulation that the percentage of the total cost reduction (PCR) is different due to the dispersion of time between orders (TBO) and the group setup ratio (GSR), the ratio of the group to the sum of each item's setup costs. A small dispersion of TBO or small GSR brings about an increase of PCR. Lastly, the optimal grouping method using dynamic programming and a numerical example is shown.

In this paper, we consider the lot-sizing problem in a periodic-review inventory system under non-stationary stochastic demand. We propose a heuristic and compare its performance with the optimal solution given by dynamic programming for 90 problem instances. Across all the problem instances the heuristic averages 1.96% error, and is found to be at least 30 times faster than dynamic programming.

NP-hard cases of the single-item capacitated lot-sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known that produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave backlogging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models.

This paper addresses a real-life lot-sizing problem which can be considered a single-item dynamic lot-sizing problem with bounded inventory. The particularity is that the demand of a period can be entirely or partially outsourced with an outsourcing cost. The goal is to minimize the total cost of production, setup, inventory holding, and outsourcing. The cost functions are linear but time-varying. We assume that the unit production cost is constant or nonincreasing over time. The problem is shown to be solvable in a strongly polynomial time with a dynamic-programming approach. The proposed algorithm can solve problems of sizes of up to 400 periods in less than 2 ms on a 1.4-GHz Pentium IV processor.

In this short note, one data driven model predictive control is studied to design the optimal control sequence. The idea of data driven means the actual output value in cost function for model predictive control is identi_ed through input-output observed data in case of unknown but bounded noise and martingale di_erence sequence. After substituting the identi_ed actual output in cost function, the total cost function in model predictive control is reformulated as the other standard form, so that dynamic programming can be applied directly. As dynamic programming is only used in optimization theory, so to extend its advantage in control theory, dynamic programming algorithm is proposed to construct the optimal control sequence. Furthermore, stability analysis for data drive model predictive control is also given based on dynamic programming strategy. Generally, the goal of this short note is to bridge the dynamic programming, system identi_cation and model predictive control. Finally, one simulation example is used to prove the e_ciency of our proposed theory

A polyhedral study of the single-item lot-sizing problem with continuous start-up costs

In recent years, GPU computing has become an increasingly important tool to develop efficient applications in several areas, including optimization. One of the optimization approaches that seems to take most advantage from GPU computing is dynamic programming. In this paper, we investigate the application of GPU computing to the two-dimensional guillotine cutting problem, solved by dynamic programming. We show a possible implementation and we discuss a number of technical issues. Computational results on test instances available in the literature and on new larger instances show the effectiveness of the dynamic programming approach based on GPU computing for this problem. Data, as supplemental material, are available at http://dx.doi.org/10.1287/ijoc.2016.0693 .

A network flow model for the capacitated lot-sizing problem

State-of-charge-constraint-based energy management strategy of plug-in hybrid electric vehicle with bus route