The Deterministic, Two-Product, Inventory System with Capacity Constraint

Purpose To examine the effect of order-size dependency on all-unit discount and the trade credit period at two levels, and formulate a total combined profit function for the manufacturer and the supplier. Also, to test this model by taking a numerical example and performing a sensitivity analysis to gain managerial insights and results. Design/methodology/approach This work presents an integrated inventory model with a bi-level trade credit period and an all-unit discount dependent on order size under capacity constraints. To address stockouts, this model uses a partial backorder approach. The concavity of the profit function is shown and an algorithm is developed to find the optimal decision policy for the manufacturer and supplier. Findings The supplier places more frequent orders to take benefit of trade credit whenever demand and interest earned rate increase. Joint profit generated by both the manufacturer and supplier grows, even though the manufacturer offers a price discount to the supplier. The supplier should order an amount of inventory that can be accommodated in their own warehouse instead of renting an additional warehouse. Originality/value Till now, as per our best knowledge, there is no existing literature that has simultaneously considered order size-dependent two-level trade credit, capacity constraint, all-unit discount linked to order purchase price and partial backordering. Combining these factors, this paper derives an integrated inventory model to maximize the total combined profit of the manufacturer and supplier. These unique factors set this paper apart from existing literature, providing distinct advantages.

We consider a single‐item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur. Returned items can be repaired and then used to satisfy future demand, or they can be disposed of. We identify those inventory levels where disposal is the best policy.It is shown that this problem is equivalent to a problem of controlling a single‐server queue. When the return and demand processes are both Poisson, we find the optimal policy exactly. When the demand and return processes are more general, we use diffusion approximations to obtain an approximate model, which is then solved. The approximate model requires only mean and variance data. Besides the optimal policy, the output of the models includes such characteristics as the operating costs, the purchase rate for new items, the disposal rate for returned items and the average inventory level. Several numerical examples are given.An interesting by‐product of our investigation is an approximation for the steady‐state behavior of the bulk GI/G/1 queue with a queue limit.

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We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity (sales quantity) under random yield is more (less) than that under certain yield.

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This paper deals with economic manufacturing quantity (EMQ) models with stochastic machine breakdown and repairs. Under two minimal repair policies to maintain a production machine, the expected cost functions per unit time in the steady state, incurred in the manufacturing operation, are formulated and the optimal policies which minimize them are calculated. As a special case, we consider the case where the machine breakdown time follows the homogeneous Poisson process and calculate the optimal EMQ policies numerically. Also, an approximation method is used to represent the expected cost.

In this paper we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation and trade credit. Demand rate is a linear function of selling price and decreases negative exponentially with time over a finite planning horizon. Shortages are allowed and partially backlogged. Under these conditions, we model the retailer’s inventory system as a profit maximization problem to determine the optimal selling price, optimal order quantity and optimal replenishment time. An easy-to-use algorithm is developed to determine the optimal replenishment policies for the retailer. We also provide optimal present value of profit when shortages are completely backlogged as a special case. Numerical examples are presented to illustrate the algorithm provided to obtain optimal profit. And we also obtain managerial implications from numerical examples to substantiate our model. The results show that there is an improvement in total profit from complete backlogging rather than the items being partially backlogged.

We consider a single‐item, continuous‐review, (s, S) inventory system, under complete backlogging and a constant procurement lead time. Demands occur in independent, identically distributed batches, separated by independent identically distributed intervals. The model also includes a class of periodic review systems as a special case. Of interest are the optimal control policies with respect to a stationary cost rate function, constructed to include ordering, holding and shortage costs. We study the structural properties of the cost rate function and report some new bounds and optimality conditions. An application of these to the computation and approximation of optimal policies is also discussed.

This paper considers the optimal deterministic inventory policy for a monopolist. The novel element concerns the consumers. Each has a time at which he would most prefer to obtain the good; he incurs a shortage cost if he buys it after that time, and a holding cost if he obtains it before. The firm must consider that any change in its policy will affect the quantity of goods it can sell and the maximum price it can charge. We find that the seller's optimal policy can take only one of three possible forms: sell the goods throughout each cycle; sell the goods continuously during an interval that is shorter than an inventory cycle; or sell the goods only at the instant each cycle begins.

Limit Order Books with Stochastic Market Depth

Although many researches have conjectured the optimality of the hedging point policy for the multiple-product stochastic capacitated periodic review problem, it is still a challenge to prove the hypothesis. This paper considers a special case of the capacitated multiple-product periodic review problem where stochastic demand distribution, production rate, unit production cost and periodic expected inventory cost are the same for all different products. For this symmetric problem, we prove an optimal policy where ordering and non-ordering regions for every product are defined. Our research provides significant implications to the characterization of the optimal policy for the general problem.