Articles written in Sadhana

    • Trade-credit modeling for deteriorating item inventory system with preservation technology under random planning horizon


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      This paper deals with a stochastic deteriorating item inventory model with preservation technology and trade-credit finance. The planning horizon of many seasonal or fashionable items stochastically varies to some extent. On the other side, the demand of such items increases in initial phase followed by a constant. This type of demand pattern can be modeled as ramp-type demand. Deterioration of such products is a characteristic, which can be reduced by making the investment on latest equipment and technology. Consumption of such itemswithin shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In these regards, this study examines the joint effect of preservation technology investment and trade-credit policy, wherein shortage is allowed and mixture of partial backlog and lost sales. Six cases may arise depending upon three parameters of time μ(demand increases up to μ), T (when on-hand inventory reaches to zero) and M (trade-credit period). The mathematical models are mainly categorized in two cases: (i) μ≤M and (ii) μ>M. The model is illustrated through numerical experiments, sensitivity analysis, and graphical representation.

    • Modelling a type-2 fuzzy inventory system considering items with imperfect quality and shortage backlogging


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      In this paper, an inventory model considering items with imperfect quality is developed in fuzzy environment, wherein shortages are allowed and are backlogged. In order to detect the items with imperfect quality, all items are screened before they are sent for consumption, and all imperfect quality items are sold at discounted price, called salvage value. In view of the fact that demand may not be predicted precisely, because it depends upon many uncertain and perturbing market activities, it is assumed to be a type-2 fuzzy variable.Quantity of imperfect quality items in the received lot may not be predicted precisely; hence percentage of imperfect quality items is also considered as a type-2 fuzzy variable. In this regard, this study developed a defuzzificationmethod of type-2 fuzzy variable pertaining to interval approximation. The mathematical model is analysed to find closed form formulae of order quantity and backlogging quantity. Finally, the proposed methodology and model are testified on numerical examples, and sensitivity of decision variables is examinedand discussed to underline the managerial insights as well as to establish the robustness of the mathematical model.

    • Designing a multi-depot multi-period vehicle routing problem with time window: hybridization of tabu search and variable neighbourhood search algorithm


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      This research formulates a real-life multi-depot and multi-period vehicle routing problem (MDMPVRP) by imposing time window (TW) and many other constraints. A set of customers, spread in different locations, are to be served by a fleet of heterogeneous vehicles over a finite number of periods. Eachcustomer is associated with combinations of routes and vehicles over the period. A customer must be served in one of the allowable combinations. The objective of this MDMPVRP-TW is to minimize the total distance traversed by the fleet over the planning horizon. The proposed MDMPVRP-TW is an extension of vehiclerouting problem (VRP), and is hence an NP-hard problem. In order to optimize it, we propose a hybrid metaheuristic approach by combining tabu search (TS) and variable neighbourhood search (VNS) algorithms. Furthermore, to provide richer insights, the efficacy of the proposed method and mathematical formulation isdemonstrated through numerical experiments for a number of instances varying from small to large scale.

    • Continuous review inventory system for intuitionistic fuzzy random demand under service level constraint


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      An intuitionistic fuzzy random variable (IFRV) handles ambiguous, incomplete and ill-known data or information along with statistical variability, and deals with fuzzy number, grade of membership and nonmembership functions and probability distribution function. So, taking such advantages of IFRV, we extend the classical continuous review inventory system in intuitionistic fuzzy random (IFR) environment by considering demand rate as IFRV. Due to uncertain variability, demand may suddenly increase, consequently, item shortage(stock out) may occur in the inventory system. To minimize the shortage quantity, fuzzy service level constraint and reorder level pertaining to safety stock are considered here. Service level constraint ensures that a certainfraction of demand to be fulfilled by on-hand inventory, whereas safety stock is kept against anticipation of shortage. Furthermore, we develop a methodology to compute the fuzzy expected shortage quantity for IFR inventory system, and determine the order quantity and reorder level. The proposed model is illustrated with numerical example and sensitivity analysis by changing the values of key parameters, which also helps in delineating the managerial insights.

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