3,660 research outputs found

    Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

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    This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model

    Ergonomics as a Social Component of Sustainable Lot-sizing: A Review

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    Lot-sizing has an increased attention in recent years. In the area of production planning and control, this trend has given rise to the development of lot-sizing models that considers sustainability issues besides the optimization of total operational cost. The study is based on tertiary study that is ensured to analyze the total work have been published. The research was conducted by the definition of appropriate keywords for understanding sustainability issues and ergonomics as a social component in lot-sizing. The paper at hand attempts to understand the development of sustainability issues in lot-sizing and ergonomics as a social component in lot-sizing. We observe that studies focusing on all three dimensions of sustainability are comparatively scarce. However, only a few of the studies have been covered the social sustainability aspect. It is observed that studies addressing ergonomics issues are scarce, and more focus is required on the social sustainability impacts along the supply chain and lot-sizing. Most of ergonomic assessment covered relaxation allowance and energy expenditure rate, OWAS, NIOSH and another consideration about ergonomic lot-sizing is the motion types investigated by authors which were picking, storing as a lifting and carrying motions and did not covered pushing, pulling, bending and other hand motions which have positive relationship with work related musculoskeletal disorders. Finally, we propose future directions to extend research on the ergonomics in lot-sizing

    Optimization Models for Cost Efficient and Environmentally Friendly Supply Chain Management

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    This dissertation aims to provide models which will help companies make sustainable logistics management and transportation decisions. These models are extensions of the economic lot sizing model with the availability of multiple replenishment modes. The objective of the models is to minimize total replenishment costs and emissions. The study provides applications of these models on contemporary supply chain problems. Initially, the impact of carbon regulatory mechanisms on the replenishment decisions are analyzed for a biomass supply chain under fixed charge replenishment costs. Then, models are extended to consider multiple-setups replenishment costs for age dependent perishable products. For a cost minimization objective, solution algorithms are proposed to solve cases where one, two or multiple replenishment modes are available. Finally, using a bi-objective model, tradeoffs in costs and emissions are analyzed in a perishable product supply chain

    Programming problems on time scales: Theory and computation

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    In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases in between. Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and dual models have been established using the time scales approach. Third, state-constraints separated linear programming primal and dual models on time scales are considered. Fourth, linear fractional primal and dual models have been constructed on time scales. Fifth, quadratic programming problems are formulated using the time scales technique. Sixth, quadratic fractional programming problems have been constructed using a hybrid of the parametric approach and the time scales technique. In addition, for each class of these programming problems the weak duality theorem and the optimality conditions theorem are established for arbitrary time scales, while the strong duality theorem is given for isolated time scales to ensure that our formulation is indeed a perfect formulation. Furthermore, examples for the most well-known isolated time scales are given to illustrate the main results --Abstract, page iv

    Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

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    Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product’s demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation.The analysis of results helps supply chain managers to take right decision in different demand and service level situations

    Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

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    Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations

    Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

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    Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time

    The trade-off between costs and carbon emissions from lot-sizing decisions

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    Logistics decisions can have a significant impact on carbon emissions, a driver of global warming. One possible way to reduce emissions is by adapting a lower delivery frequency, which enables better vehicle utilization or the usage of relatively effcient large vehicles. We study the situation in which a decision maker decides on the amount to be shipped in each period, where he/she can order items in each period and keep items on inventory. If the shipped quantity is large, vehicle capacity is well utilized, but many products have to be stored. Existing studies in this field of research, called lot-sizing, have introduced models for incorporating carbon emissions in the decision making, but do not focus on realistic values of the emission parameters. Therefore, we conduct a survey of empirical studies in order to establish the possible marginal emissions from holding inventory and performing a shipment with a truck.

    Optimal Lot Sizing for Perishable Products under Strict Carbon Cap Policy considering Stochastic Demand and Energy Usage cost

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    In this paper, we have considered stochastic demand for perishable items under strict carbon cap policy and energy usage. Perishable foods like meat, poultry, fish, dairy products etc. which are likely to spoil if not kept refrigerated. So that we related to the energy usage for maintaining perishable items at certain climate conditions where the inventory is stocked. Due to the nature of perishable product starts to decay at certain time, so that vendor provide a discount for the product in demand rate. We model the system into two stage, On first stage holds fresh items as non-discount period and second stage as older items as discount period nearer to expiration. A mathematical model is developed to determine the optimal order quantity, reorder point and number of shipments in a two-echelon supply chain considering partial backorders. The objective is to minimize the total expected supply chain cost while satisfying the carbon emission constraint. A numerical example is given to illustrate the solution procedure
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