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The efficiency and responsiveness of supply chains are vitally dependent on inventory replenishment and transportation decisions. In this paper, we study a supply chain consisting of a single retailer ordering seasonal products within the newsvendor framework. The primary objective of the paper is to investigate the retailer's decision-making process, aimed at determining the optimal replenishment quantities and selecting the appropriate mix and size of the truck fleet. Initially, we formulate a mathematical model where the retailer exclusively manages a limited fleet of its own trucks for inbound transportation of a single seasonal product. In this context, we determine a lower breakeven point for the fixed transportation cost than what has been previously proposed in the literature. Subsequently, we examine a commonly encountered transportation scenario where the retailer has the opportunity to expand its fleet size by leasing trucks from the external market. The outcomes of the numerical example indicates that the flexibility resulting from the utilization of different types of trucks can lead to reduced overall costs. We also address the practical transportation problem of efficiently shipping various seasonal products solely with the retailer's own trucks. For this complex problem, we propose an optimal solution procedure based on Lagrangian method. We show that the joint replenishment of multiple products results in cost savings and enhances utilization of the trucks' capacities. [ABSTRACT FROM AUTHOR]

Abstract In response to the rising public concerns on environmental issues and the recently imposed governmental legislations and directives in this regard, companies nowadays ought to constantly adopt sustainable practices in their day-to-day operations. To that end, this paper seeks to optimize the replenishment strategy for a firm (e.g. retailer), who is facing a discrete time-varying demand for a temperature-sensitive (cold) product, while taking into account carbon emissions resulting from transportation and storage activities. In essence, the problem tackled herein is a variant of the classical dynamic lot-sizing problem (DLSP) for cold products with limited shelf life. To better resemble reality, we assume a stepwise cost function that is proportional to the number of fixed-capacity refrigerated trucks and cold stores used. We present three mathematical models, with the first being a cost minimization model, the second a carbon footprint minimization model, and the third a hybrid model that utilizes the carbon tax policy to jointly optimize both economic and environmental measures. We identify several structural properties of the optimal solution to the three models leading to the development of an exact solution algorithm based on the dynamic programming approach. The results of the computational experiments suggest that accounting for environmental aspects induces a change in the cost minimizing lot-sizing policy, resulting in a minor increase in the operational cost where the savings in the CO 2 related costs outweigh this minor increase. The two-way sensitivity analysis, conducted under randomized values of the demand, truck sizes, and cold stores capacities, indicates that higher savings in cost and carbon reductions are realized for increasing values of the carbon tax rate. Furthermore, on average, more cost savings and lower carbon emissions are also achieved when the values of the shelf life, truck size, and cold store capacity are increased. [ABSTRACT FROM AUTHOR]

Highlights • Jointly optimizes procurement, production and shipping decisions for a two-stage closed-loop supply chain system. • Presents two mathematical models for two different raw material (RM) replenishment strategies. • Proposes an efficient iterative search algorithm that guarantees convergence to near optimal solutions. • The Incorporation of RM replenishment strategy greatly impacts production sequencing, lot sizing and shipping decisions. Abstract This paper seeks to jointly optimize the raw material (RM) procurement and shipping decisions as well as those pertaining to the lot sizing and the production sequencing of manufactured and remanufactured products for a centralized two stage closed loop supply chain, wherein the vendor and the buyer operate under consignment stock partnership. Most of the existing closed loop models have overlooked the tradeoffs involved in optimizing RM replenishment strategy in conjunction with the production sequence, and assumed the predetermined sequence of (R, P) where R remanufactured batches are produced first followed by P manufactured batches as this sequence prioritizes the clearance of the accumulated inventory of returned items. As such, we jointly optimize the aforementioned interrelated decisions, alongside others as well, under two RM replenishment strategies; multi-to-one (MTO) and one-to-multi (OTM) where a mathematical model is developed for each strategy. In essence, this work seeks to assess what impact would the incorporation of RM procurement decisions have on the shipping and production policy downstream. Extensive computational experiments, carried out under different settings of the problem parameters, indicate that accounting for RM procurement strategy greatly impacts not only the production sequence, but extends to include the lot sizing and shipping decisions as well. Furthermore, the computational study suggests that it is economically advantageous to synchronize RM orders such that they take place right at the time needed for the production of newly manufactured products. [ABSTRACT FROM AUTHOR]

The elevated level of public and organizations awareness concerning sustainability has necessitated the adoption of environmentally conscious practices in the management of supply chains. As such, classical inventory models wherein the sole measure of performance is cost minimization are no longer appropriate to handle such emerging and pressing issue. This paper assesses the impact of accounting for carbon emissions, resulting from transportation and storage activities of a cold item, in the context of a multi stage supply chain comprised of a plant/warehouse, a distribution center (DC) and a retailer. We present an operational cost minimization model, a carbon footprint minimization model and a hybrid economic and environmental minimization model where all models seek to determine the optimal lot sizing and shipping quantities, alongside the number of trucks to be used in the upstream and downstream directions of the supply chain as well as the number of freezer units utilized at the DC which is owned by a third party logistics provider. The structural properties for the optimal solution of the three models are identified and solution algorithms are also proposed. Upon conducting computational experiments, it turns out that the incorporation of carbon related costs, through carbon tax regulation, may call for adjusting the adopted operational policy which results in a minor increase in the operational cost. However, this increase is outweighed by the savings resulting from the carbon related costs. Numerical results of the sensitivity analysis on the carbon tax policy indicate that as the tax rate increases, substantial reductions in the amount of carbon footprint emitted are realized and cost savings are also achieved when adopting the lot sizing and shipping policy of the third/integrated model over the operational cost minimization model. [ABSTRACT FROM AUTHOR]