Narrow Results

In this article, we generalize Lev and Weiss's (1990) finite horizon economic order quantity (EOQ) model with cost change to the inventory system with deterioration. Supplier announces some or all of cost parameters may change after a decided time. Depending on whether the inventory is depleted at the time of the last opportunity to purchase before some or all of the cost parameters may change, there are two types of inventory models to be discussed. The main objective of this paper is to identify the optimal ordering policy of the inventory system by comparing the minimum cost of the two types of models. We suggest a finite horizon EOQ model to combine the above two types and propose a theorem that can quickly identify the optimal policy of the suggested model. In considering temporary price discount problem and discrete-time EOQ problem, in general, there are integer operators in mathematical models, but our approach offers a closed-form solution to these kinds of problems. Numerical examples are presented to demonstrate the results of the proposed properties and theorem.

Firms often utilize promotion (such as coupons, advertisements, recruitment of excellent salespeople, and leafleting etc.) and dynamic adjustment of price to manage customers as well as proper production/inventory plan to satisfy the customers to get maximal profit in a firm. The decision on promotion and pricing and the decision on production/inventory must support each other. This paper addresses coordinated decision on pricing, promotion(non-price promotion) and inventory management. Specifically, we study a single item, periodic review model. The demand function is a linear demand function in which the market scale can be affected by the promotion conducted in that period. Unsatisfied demands are fully backlogged. We characterize the structure of the optimal policy that simultaneously determines the price, the promotion and the ordering quantity to maximize the total discounted profit with finite and infinite period problems. We show that the optimal replenishment policy is the quasi base stock list price target promotion policy, i.e., there exist a critical inventory level, a list price and a target promotion such that it is optimal to order up to the critical level, charge the list price and conduct the target promotion when the initial inventory is below the critical level and order nothing, conduct a higher promotion and charge a proper price to increase the demand otherwise. We also prove that the expected demand and the optimal promotion are increasing in the inventory, and price and promotion are complementary. Then we extend the problem to the case with capacity constraint. We show that the modified quasi base stock list price target promotion policy is optimal. For the joint decision problem on pricing, promotion and inventory control with positive fixed setup cost, we show that the optimal policy is (s, S, p, e) policy. That is, there exist two critical inventory levels s_t and S_t(s_t ≤ S_t), a list price p_t and a target promotion e_t in period t such that order up to S_t, charge price p_t and conduct promotion e_t when the initial inventory is less than s_t and order nothing, charge a proper price and conduct a proper promotion otherwise.

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete-time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous-time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs; we allow cash dividends on the risky asset. The allocation shifts toward the riskless asset relative to diffusion in varying degrees depending on parameter values. It is sensitive to the proportion of the jump component to total volatility, but also to the expected amplitude for a given proportion. The shift becomes small when the relative risk aversion increases, but it becomes major when the solvency constraint is active in the presence of jumps. We derive utility losses and risk premia due to jumps under realistic parameter values, and show that even when the no transaction region is very similar between pure diffusion and the mixed process the latter corresponds to lower utility because of higher portfolio restructuring costs.