Hon-Shiang Lau

The Newsboy Problem With Price-Dependent Demand Distribution

Abstract This paper considers an extension of the classical newsboy problem where a stochastic price-demand relationship exists for the product. First presented is a versatile approach capable of modeling price-demand relationships of various levels of complexities. Solution procedures are then presented for different optimization objectives. For the simplest price-demand relationship, analytical solutions are obtainable. For other cases, very efficient numerical procedures are developed.

Effects of a demand-curve's shape on the optimal solutions of a multi-echelon inventory/pricing model

Abstract When a price–demand relationship is needed in inventory/pricing models, very often a convenient (typically linear) function is arbitrarily chosen. The common-wisdom implication is that any downward-sloping demand curve would lead to similar conclusions. This paper applies different demand-curve functions to a simple inventory/pricing model, and shows that while the common-wisdom implication is valid for a single-echelon system, assuming different demand-curve functions can lead to very different results in a multi-echelon system. In some situations, a very small change in the demand-curve appearance leads to very large changes in the model’s optimal solutions. Other significant but counter-intuitive effects of the demand-curve form are also revealed. This paper does not completely resolve the difficulties revealed by the counter-intuitive effects reported here, but establishing the existence of these effects represents a first step towards developing procedures to handle such effects; these procedures will be necessary to ensure the reliability of many multi-echelon models for products having price-sensitive demands.

The newsstand problem: A capacitated multiple-product single-period inventory problem

Abstract Practically all of the many earlier papers on the newsboy problem consider a single newsboy product with no capacity constraint. This paper presents formulations and solution procedures for handling multiple newsboy-type products under two cases: (A) one resource-capacity constraint; and (B) multiple resource constraints. For case A, we present a necessary extension to the classical Hadley-Whitin result for handling general demand distributions. For case B we present a solution procedure that can efficiently handle the common situation where a very large number of products are involved.

Some two-echelon supply-chain games: Improving from deterministic-symmetric-information to stochastic-asymmetric-information models

Abstract Many supply-chain and inventory models use the following two-echelon symmetric-information and deterministic gaming structure: a “manufacturer” wholesales a product to a “retailer,” who in turn retails it to the consumer. The retail market demand varies with the retail price according to a deterministic “demand function” that is known to both the manufacturer and the retailer. It is then assumed that the “players” (the manufacturer and the retailer) arrive at their pricing and batch-size decisions through a Stackelberg game or a “fixed markup percentage” game. The first part of this paper reveals many implausible effects of demand-curve forms on the behavior of these gaming models. However, we do not merely conclude that two-echelon gaming results obtained via assuming one convenient demand-curve form can often become invalid under other demand-curve forms. More importantly, we argue in the second part of the paper that the various implausible effects revealed here suggest a different but more fundamental conclusion: the assumed non-cooperative games are themselves flawed, because “gaming” is meaningless and logically circular in a deterministic-and-symmetrical-information system. We then present an introductory illustration on how the introduction of stochasticity and information- a symmetry leads to more plausible two-echelon supply-chain gaming models. Together, the two parts demonstrate the necessity and practicality of using a stochastic-and-asymmetric-information instead of the prevalent deterministic-symmetric-information approach in many supply-chain models.

The multi-product multi-constraint newsboy problem: Applications, formulation and solution

Abstract Practically all of the many earlier papers on the newsboy problem consider a single newsboy product with no capacity constraint. This paper points out the real-world prevalence of the “multiple-product multiple-constraint newsboy problem”, i.e., the “newstand problem”. We present a formulation and a solution procedure for this newsstand problem. Our solutions procedure has been designed to efficiently handle the common situation where a large number of products are involved; this solution procedure is shown to be necessary for the practical solution of realistic newsstand problems.

Reordering strategies for a newsboy-type product

Abstract This paper considers the very common situation in which a single-period ‘newsboy’ type product may be ordered or produced twice during a season/period. We show that the explicit consideration of this reorder opportunity makes the newsboy problem very much richer. The specific version considered in this paper allows a reorder during mid-season after the early-season demand has been observed, and this reorder arrives after a given lead time. The demand distributions during the various portions of the season may have very general distribution forms; also, the late-season and early-season demands may be dependent. Solution procedures are developed to find the best way to exploit this reorder opportunity, and our numerical solutions indicate that this reorder opportunity can improve profits considerably as long as the products profit margin is not very high. Other real-world variations of this two-order newsboy problem are briefly discussed.

Evaluating the impact of operating conditions on the performance of appointment scheduling rules in service systems

Abstract The general practice in implementing an appointment scheduling rule (ASR) is to enforce a certain rule, such as “block appointment”, to schedule customer arrivals in service systems. The operating environments of service systems are expected to affect considerably the performance of a selected ASR. The objective of this paper is to evaluate the impact of the environmental factors which include probability of no-show ( ρ ), the coefficient of variation ( C ν ) of service times, and the number of customers per service session ( N ). The extent to which a certain environmental factor affects the performance of ASR is examined to see if there is any ASR that performs well under most operating conditions. Under situations characterized by 27 different combinations of the factors ρ , C ν , and N , the performance of nine scheduling rules are evaluated by a simulation study. The simulation results show that an ASR designed to reduce customer waiting time performs very well in most operating environments considered. One commonly used ASR in real-world service systems, which schedules several customers to arrive at the start of each service session, tends to induce long customer waiting time.

A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain

Abstract Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at

A fast procedure for computing the total system cost of an appointment schedule for medical and kindred facilities

p/unit. The retail-market demand volume varies with p according to a given demand curve. This basic system is commonly modeled as a manufacturer-Stackelberg ([mS]) game under a “deterministic and symmetric-information” (“det-sym-i”) framework. We first explain the logical flaws of this framework, which are (i) the dominant manufacturer-leader will have a lower profit than the retailer under an iso-elastic demand curve; (ii) in some situations the system’s “correct solution” can be hyper-sensitive to minute changes in the demand curve; (iii) applying volume discounting while keeping the original [mS] profit-maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel. We then present an extension of the “stochastic and asymmetric-information” (“sto-asy-i”) framework proposed in Lau and Lau [Lau, A., Lau, H.-S., 2005. Some two-echelon supply-chain games: Improving from deterministic–symmetric-information to stochastic-asymmetric-information models. European Journal of Operational Research 161 (1), 203–223], coupled with the notion that a profit-maximizing dominant manufacturer may implement not only [mS] but also “[pm]”—i.e., using a manufacturer-imposed maximum retail price. We show that this new framework resolves all the logical flaws stated above. Along the way, we also present a procedure for the dominant manufacturer to design a profit-maximizing volume-discount scheme using stochastic and asymmetric demand information. Using our sto-asy-i framework to resolve the logical flaws of the det-sym-i framework also reveals two noteworthy points: (i) the attractiveness of the perfectly legal but overlooked channel-coordination mechanism [pm]; and (ii) volume discounting as a means for the dominant manufacturer to benefit from information known only to the retailer.

Pricing and volume discounting for a dominant retailer with uncertain manufacturing cost information

Scheduling outpatients and medical operation rooms has the following structure: N users are given appointment times to use a facility, the duration required by the facility to service each user is stochastic. The system incurs a “user idle cost” if a user arriving at the appointed time finds the facility still engaged by preceding users, while a “facility idle cost” is incurred if the facility becomes free before the next user arrives. We develop an accurate procedure to compute the expected total system costs for any given appointment schedule. Compared to earlier related procedures, ours is much faster and can handle larger problems as well as very general service-time distributions. We then show that this fast computation procedure enables one to determine easily the “lowest-cost appointment schedule” for any given “job” (i.e., “user”) sequence. This in turn will enable one to search for the optimal job sequence that has the best “lowest-cost appointment schedule”.