On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures

Chan, Lap Mui Ann; Muriel, Ana; Shen, Zuo‐Jun Max; Simchi‐Levi, David

doi:10.1287/opre.50.6.1058.350

Cited by 74 publications

(35 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As pointed out by Chan et al (2002), DLS models such as ours can help a planner make decisions on production and cycle inventory (based on forecasts of demand over a given planning horizon) that balance the trade-offs between fixed production cost and variable costs of production, inventory, and, in our models, conversion. DLS models are particularly useful in situations where demand is non-stationary, which is frequently encountered in production planning, such as Materials Requirements Planning.…”

Section: Introductionmentioning

confidence: 99%

Dynamic lot size problems with one-way product substitution

Hsu

Xiao

2005

IIE Transactions

View full text Add to dashboard Cite

We consider two multi-product dynamic lot size models with one-way substitution, where the products can be indexed such that a lower-index product may be used to substitute the demand of a higher-index product. In the first model, the product used to meet the demand of another product must be physically transformed into the latter and incur a conversion cost. In the second model, a product can be directly used to satisfy the demand of another product without requiring any physical conversion. Both problems are computationally intractable in general. We develop dynamic programming algorithms that solve the problems in polynomial time when the number of products is fixed. A heuristic is also developed, and computational experiments are conducted to test the effectiveness of the heuristic and the efficiency of the optimal algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamic lot size problems with one-way product substitution

Hsu

Xiao

2005

IIE Transactions

View full text Add to dashboard Cite

show abstract

“…As the lot-sizing problem with modified all units discount studied by Chan et al (2002) is a special case of LS-PC, LS-PC is NP-hard unless the breakpoints are time invariant and the number of breakpoints is bounded above by a constant. Swoveland (1975) presents characteristics of an optimal solution when inventory holding and production cost functions are piecewise concave functions.…”

Section: Figure 2 Examples Of Piecewise Concave Functionsmentioning

confidence: 99%

“…They assume that the production cost function has two pieces and propose dynamic programming algorithms of complexity O n 3 and O n 2 for the problems with all units discount and incremental discount, respectively, where n is the number of periods. Chan et al (2002) consider the modified all units discount depicted in Figure 1(c). They prove that the lot-sizing problem with this cost structure is NP-hard when either the production cost functions vary from period to period or the number of breakpoints is not bounded by a constant.…”

Section: Introductionmentioning

confidence: 99%

Lot Sizing with Piecewise Concave Production Costs

Koca

Yaman

Aktürk

2014

INFORMS Journal on Computing

View full text Add to dashboard Cite

W e study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction-based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch.

show abstract

“…In this case, a set of warehouses coordinates the flow of goods from a number of suppliers to multiple retailers with the objective of reducing costs through consolidation. A number of authors have focused on LTL shipping costs in the Single-Warehouse Multi-Retailer setting, including incremental discounts (e.g., Muriel and Simchi-Levi [19], Balakrishnan and Graves [6], Amiri and Pirkul [2]) and modified all unit discounts (Chan et al [7,8]). …”

Section: Introductionmentioning

confidence: 99%

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Jin¹,

Muriel

2009

Naval Research Logistics

Self Cite

View full text Add to dashboard Cite

Abstract:We consider a multi-stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118-138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system-wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T 2 ) algorithm for the single-stage dynamic lot sizing problem; (2) an O(T 3 ) algorithm for the case of a single-warehouse single-retailer system; and (3) a nested shortest-path algorithm for the single-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single-stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal.

show abstract

On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures

Cited by 74 publications

References 10 publications

Dynamic lot size problems with one-way product substitution

Dynamic lot size problems with one-way product substitution

Lot Sizing with Piecewise Concave Production Costs

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Contact Info

Product

Resources

About