Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs

Alp, Osman; Erkip, Nesim; Güllü, Refık

doi:10.1287/opre.51.1.160.12799

Cited by 31 publications

(26 citation statements)

References 10 publications

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“…In using the concept of monotone costs in a multifacility environment, we require that the truck capacity be the same for all shipping links in the same period, whereas it can still increase from period to period, and that holding goods at the warehouse in a particular period be always no higher than holding them at the retailer. 1 Pochet and Wolsey [20] consider nonstationary fixed plus linear shipping costs and linear inventory costs, and stationary capacity. The monotone cost functions (Lippman [17]) place more restrictions on how costs change over time, but consider more general fixed plus concave shipping costs and general nondecreasing inventory costs, and allow the capacity to possibly increase from period to period.…”

Section: Single-warehouse Multi-retailer Problem: Extended Propertiesmentioning

confidence: 99%

“…For the basic single-stage dynamic lot sizing problem with multiple setups and stationary (or more generally monotone) costs, Lippman [17] shows that there is an optimal solution such that (1) no partially filled trucks are shipped in periods with positive initial inventory, and (2) the inventory in each period is less than the truck capacity. These two properties have been the cornerstone for much of the posterior research, including the present work.…”

Section: Introductionmentioning

confidence: 99%

“…Alp et al [1] characterize optimal policies and develop a dynamic programming algorithm for the problem with stochastic lead times. Li et al [16] consider a very general model that allows for demand backlogging and includes time-varying fixed and practical transportation-related ordering costs representing both fixed costs per full truck dispatched and linear costs associated with Less-than-Truckload (LTL) shipments.…”

Section: Introductionmentioning

confidence: 99%

“…We contribute to this literature by using the structural properties of the problem solutions to develop (1) an O(T 3 ) algorithm for the case of a single-warehouse single-retailer system, (2) a nested shortest-path algorithm for the single-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers, and (3) aggregated and disaggregated Lagrangian decomposition methods for large-scale problems, all under the FTL shipping cost structure described earlier.…”

Section: Introductionmentioning

confidence: 99%

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

Jin¹,

Muriel

2009

Naval Research Logistics

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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.

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Section: Single-warehouse Multi-retailer Problem: Extended Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Jin¹,

Muriel

2009

Naval Research Logistics

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“…Chao and Zhou (2009) consider the multi-echelon full-batch ordering problem with minimum setup time (time between consecutive orders). Alp et al (2003) consider a general version of our problem under deterministic demand settings and show some optimality properties.…”

Section: Introduction and Related Literaturementioning

confidence: 99%

Inventory Control with Multiple Setup Costs

Alp

Huh

Tan³

2014

M&SOM

Self Cite

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We consider an infinite-horizon, periodic-review, single-item production/inventory system with random demand and back-ordering, where multiple set-ups are allowed in any period, and a separate fixed cost is associated for each set-up. Contrary to majority of the literature on this topic, we do not restrict the order quantities to be integer multiples of the exogenously-given batch size and instead allow the possibility of partial batches, in which case the fixed cost for ordering the batch is still fully charged. We build a model that particularly takes the batch ordering cost structure into account. We introduce an alternative cost accounting scheme to analyze the problem, which we use for developing a computationally efficient optimal solution method and several properties of the optimal solution. In addition, we propose two heuristic policies, both of which perform extremely well computationally.

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Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

Toptal

Çetinkaya

2006

Naval Research Logistics

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Abstract:We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single-period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function.For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win-win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor-managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor-managed delivery arrangement that potentially improves the centralized solution.Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single-period setting.

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Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs

Cited by 31 publications

References 10 publications

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

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

Inventory Control with Multiple Setup Costs

Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

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