Bhaba R. Sarker

Optimal payment time for a retailer under permitted delay of payment by the wholesaler

Abstract The retailer (buyer) is usually allowed a permissible credit period to pay back the dues without paying any interest to the wholesaler (supplier). In this problem the retailer can pay the wholesaler either at the end of credit period or later incurring interest charges on the unpaid balance for the overdue period. This research develops a retailers model for optimal cycle and payment times for a retailer in a deteriorating-item inventory situation where a wholesaler allows a specified credit period to the retailer for payment without penalty. Under these conditions, this wholesaler-and-retailer system is modeled as a cost minimization problem to determine the optimal payment time under various system parameters. The model is solved through an iterative search procedure and the overall findings indicate that the retailer has always an option to pay after the permissible credit period depending on interest rates, unit purchase and selling price, and the deterioration rate of the products.

Supply chain models for perishable products under inflation and permissible delay in payment

Abstract In many inventory situations, purchasers are allowed a period to pay back for the goods bought without paying any interest. Depending on the length of that payment period, the purchaser can earn interest on the sales of the inventory. This paper develops a model to determine an optimal ordering policy for deteriorating items under inflation, permissible delay of payment and allowable shortage. The present value of total cost incurred in this inventory system is developed first, then an optimal order quantity and maximum allowable shortage are obtained by using a search procedure. The effect of inflation and time value of money was investigated under given sets of inflation and discount rates. This study shows that the optimal order quantity and maximum allowable shortage vary with the difference between inflation and time discount. Computational results provide some interesting policy implications. Scope and purpose A significant part of the manufacturing goods are usually kept in the supply chain, especially either in a manufacturer’s/wholesaler’s inventory or in a retailer’s storage. This paper addresses the ordering policy by a retailer of a perishable product, where the decision is influenced by the time value of money and inflation, and the retailer is allowed a delay period to pay back the dues for the products purchased. The purpose of this research is to aid the retailers in economically stocking the inventory (i.e., ascertaining the ordering quantity) under the influence of different decision criteria such as time value of money, inflation rates, purchase price of the product, and deterioration rate.

Optimal manufacturing batch size with rework process at a single-stage production system

Determining an optimal batch quantity in a production system that produces defective items has been the primary focus recently among the researchers. While most of the work has been reported to explore the traditional optimal inventory level in ideal cases, little appears to have been done with rework option. In this paper, models have been developed to determine the optimum batch quantity in a single-stage system in which rework is done under two different operational policies to minimize the total system cost. The first policy deals with rework being completed within the same cycle. The second policy deals with the rework being done after N cycles causing less than the desired quantity of good products in each cycle. The models have been validated with illustrating numerical examples and the sensitivity of optimal batch size and total system cost with respect to the defective proportion have also been performed.

Optimal payment time under permissible delay in payment for products with deterioration

A permissible credit period is usually allowed to a retailer to pay back the dues without paying any interest to the supplier. The retailer can pay the supplier either at the end of the credit period or later incurring interest charges on the unpaid balance for the overdue period. The retailer is expected to settle the account at a time before the end of the inventory cycle time because the payable interest rate is generally higher than the earned interest rate. A model for optimal cycle and payment times is developed here for a retailer in a deteriorating-item inventory situation where a supplier allows a specified credit period to the retailer for payment without penalty. Under these conditions, this supplier-and-retailer system is modelled as a cost minimization problem to determine the optimal payment time under various system parameters. An iterative search procedure is applied to solve the problem, and the overall findings indicate that the retailer always has an option to pay after the permissible credit period depending on unit purchase and selling price, the deterioration rate of the products and the interest rate.

The performance of push and pull systems: a simulation and comparative study†

Ideally the just-in-time (pull system) production system holds no buffer inventory so that the production is ‘just in time’. This is achieved only when the stages operation times are constant and equal; but realistically the variability of operator performance and/or the unequal distribution of task times precludes such an ideal situation. As a result, the production line experiences problems. In this paper we investigate the effects of these variabilities on the performance of push and pull systems and how the manager can decide which production technique to adopt. The implication of the simulation results are reported and openings for future research are identified.

An order-level lot size inventory model with inventory-level dependent demand and deterioration

Abstract Many inventory models have been developed for various deteriorating items with constant demand rate. It is a common experience that, for perishable consumer goods, the age of inventory has a negative impact on the demand due to the loss of consumer confidence on such product. Consumers tend to keep off perishable items which have reached closer to their expiry dates. This paper describes an inventory model in which the demand is considered as a composite function consisting of a constant component, and a variable component which is proportional to the inventory level in the periods when there is a positive inventory buildup. The rate of production is considered finite and the decay rate as exponential. The total cost function is composed of four cost components of all phases of the cycle (backorder replenishment, inventory buildup, inventory depletion and shortage). This cost function is later reduced to a two-variable function using boundary relations to determine iteratively the set of values of the variables that resulted in minimum cost per cycle. The optimum lot-size and order-level were then obtained with relations established previously. Results are demonstrated for an instance of the model.

ECONOMIC MANUFACTURING QUANTITY IN A JUST-IN-TIME DELIVERY SYSTEM

A just-in-time (JIT) buyer demands frequent deliveries of small lots of certain products. However, there is a perception among the suppliers that participation in a JIT delivery system is economically disadvantageous for them. To test this conjecture, a generalized inventory model is developed for a supplier who has to meet a deterministic demand at fixed intervals. The generalized total cost model developed here is found to be a piecewise convex function. A simple algorithm is developed to compute the optimal batch size. When production uptime and cycle time are each equal to an integer multiple of the shipment interval, a perfect matching of shipment size occurs, and for such a situation, the generalized model specializes to more traditional inventory models. The solution approach for such models becomes much easier. It is found that, under certain conditions, the total cost decreases linearly with reduced shipment size and the suppliers benefit from this. Economic impact of ordering and setup costs red...

Optimal batch sizing in a multi-stage production system with rework consideration

In a production system, rework process plays an important role in eliminating waste and effectively controlling the cost of manufacturing. Determining the optimal batch size in a system that allows for rework is, therefore, a worthwhile objective to minimize the inventory cost of work-in-processes and the finished goods. In this paper, models for the optimum batch quantity in a multi-stage system with rework process have been developed for two different operational policies. Policy 1 deals with the rework within the same cycle with no shortage and policy 2 deals with the rework done after N cycles, incurring shortages in each cycle. The major components that play a role in minimizing this cost of the system are manufacturing setups, work-in-processes, storage of finished goods, rework processing, waiting-time, and penalty costs to discourage the generation of defectives. The mathematical structure of this rework processing model falls under a nonlinear convex programming problems for which a closed-form solution has been proposed and results are demonstrated through numerical examples, followed by sensitivity analyses of different important parameters. It is concluded that the total cost in policy 2 tends to be smaller than that in policy 1 at lower proportion of defectives if the in-process carrying cost is low. Policy 2 may be preferred when the work-in-process carrying cost is low and the penalty cost is negligible.

A similarity coefficient measure and machine-parts grouping in cellular manufacturing systems

For more than three decades, similarity coefficient measures one of the important tools for solving group technology problems have gained the attention of the research community in cellular manufacturing systems. A new similarity coefficient measure that uses a set of important characteristic properties for grouping is developed here for use as an intermediate tool to form cohesive cells. A mathematical model that uses this similarity coefficient for optimally solving the cell-formation problems in cellular manufacturing is developed. A heuristic procedure that improves the optimal methodology in term of solution capability of the large instances is devised for an efficient solution. Both the optimal methodology and the heuristic are applied to some well-known problems from literature to compare the grouping efficiencies. The similarity coefficient and the solution methodologies developed are able to solve the cell formation problems efficiently.

Effects of inflation and the time value of money on order quantity and allowable shortage

Abstract This paper investigates the effects of inflation and time value of money on the optimal ordering quantities and the maximum allowable shortage in a finite replenishment inventory system. The present value of total cost incurred in this inventory system is developed first, then an optimal order quantity and maximum allowable shortage are obtained by using a search procedure. The effect of inflation and time value of money was investigated under given sets of values of inflation and discount rates. This study shows that the optimal order quantity and maximum allowable shortage vary with the change in difference between inflation and time discount. Computational results indicate that this effect on the system becomes more significant with the increase of the difference between inflation rate and time discount rate.