Asia-Pacific Journal of Operational Research

In this study, we have applied optimal control theory to determine the optimum value of tax revenues accruing to a state given the range of budgeted expenditure on enforcing tax laws and awareness creation on the payment of the correct tax. This is achieved by maximizing the state's net tax revenue over a fixed time interval subject to certain constraints. By assuming that the satisfaction derived by the Federal Government of Nigeria on the ability of the individual states to generate tax revenue which is as near as the optimum tax revenue (via the state's control problem) is described by the logarithmic form of the Cobb–Douglas utility function, a formula for horizontal revenue allocation in Nigeria in its raw form is derived. Afterwards, we illustrate the use of the proposed horizontal revenue allocation formula using hypothetical data.

Tramway transit has an important place within the public transportation system of Belgrade. However, due to the very unfavorable age structure, the bad condition of tramway tracks and infrastructure, as well as the maintenance system that require significant advancement, Belgrade tramways are in very bad repair, so the transport requirements are not properly met. The principal task of the analysis presented in this paper is to recognize and estimate the justifiability of investment into various solutions for revitalization of Belgrade tramway rolling stock. We have chosen a somewhat different from usual approach to decision making, that is, applied a combination of cost-benefit, life-cycle cost and multi-criteria analysis.

The "trade-offs Data envelopment analysis (DEA)" model is built by adding an extra axiom to the traditional production possibility set. The axiom introduces some replacement relations as production rules between inputs and outputs and leads to some extensions to the production possibility set. It provides more discriminatory power of decision-making units (DMUs) in DEA models, and the results are more adaptable to real conditions. In this paper, these variations are defined in proportional forms, which make the variation proportionate to DMUs' sizes. So we call them proportional trade-offs, and they offer some advantages in comparison with simple trade-off vectors, which depend on input or output units of measurements. First of all, the proportional trade-offs vectors can fairly consider the DMUs' abilities and their strengths in adapting to the proposed changes. Secondly, it will be seen that proportional trade-off vectors can be used as a generalization of usual returns to scales (RTS), and finally the proportional trade-offs models cover the basic DEA models and their related production possibility set (PPSs) as special cases.

This study considers the supplier's warranty return and the buyer's rebate policy as business-return policy in the supplier–buyer supply chain. The policy as well as the displayed stock level influences the behavior of the buyer. Distinct from the traditional single-stage inventory model, we investigate a two-stage replenishment policy model for deteriorating item considering the effect of imperfect production process, product design, stock level and business-return. A mathematical model utilizing the time weighted inventory (TWI) approach and two-variables fixed point optimization technique is developed to derive the optimal inspection starting time, the number of deliveries, the optimal delivery-time interval and the optimal business-return period. A numerical example is presented to illustrate the model developed. The result shows that the fixed demand rate, the unit holding cost and the unit inspection cost are the critical factors affecting the scheduling and performance of the two-stage supply chain.

In this paper, we consider an inventory model in which a firm uses the spot market for procurement in order to accomplish the minimization of total discounted costs. The model can be formulated as impulse control problem where the demand and spot price follow diffusion stochastic processes. We explore sufficient conditions under which an optimal policy exists. Furthermore, we derive an optimal policy as an (s, S) policy where s and S are uniquely determined as a solution of simultaneous equation. Finally, we show some analytical properties of the optimal policy. Some numerical examples are also presented.

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.

For a periodic-review inventory system with stochastic and continuous demands and without setup costs, it is known that there exists a base-stock policy to be optimal. For a finite-horizon system with non-stationary parameters, it is essential to find approximate optimal policies because of the computational intractability of finding the optimal policy. This paper provides an approach, by which an analytical bound of the error between the costs of the approximate optimal policy and the optimal policy is given. It is shown that the approximate optimal policy converges to the optimal policy as the size of the computational grid decreases. Numerical results are presented to illustrate the methodology.