Public.kenan-flagler.unc.edu

The Kenan-Flagler Business School, University of North Carolina, Chapel Hill, North Carolina 27599-3490 The 1998 settlement of a lawsuit by the state of California required 19 pharmaceutical firmsto provide $150 million worth of drugs free of charge to more than 150 California clinics andhospitals over a three-year period. We developed a decision-support system that utilizes amultiobjective optimization model and a heuristic solution taking into account the efficiency,effectiveness, and equity of the drug-allocation process. As of November 2002, 90 percent ofthe total budget has been distributed to the various clinics with the help of this decision-support system.
(Health care: pharmaceutical. Decision analysis: systems.) T he1998settlementofalawsuitbythestateofCali- Over 150 clinics and hospitals have participated in fornia required 19 pharmaceutical firms to pro- the project through October 2002. These medical fa- vide $150 million worth of drugs free of charge to more cilities range in size from very large clinics and hos- than 150 California clinics and hospitals over a three- pital networks, such as that of Los Angeles County, to year period. In July 2001, six other pharmaceutical very small specialized clinics. The clinics also vary in firms were added to this lawsuit, and they brought an their expertise: some are general purpose, while others additional $20 million worth of products to distribute.
are specialized, such as mental health clinics. Based on The Public Health Institute ͗www.phi.org͘, an inde- the settlement, each clinic was assigned a maximum pendent, nonprofit organization that promotes health dollar value of drugs that it could receive. Because all for people throughout California and the United the drugs were to be provided free of charge, the Pub- States, was given the responsibility of distributing lic Health Institute expected the clinics to order pri- these drugs in a fair and equitable manner. They called marily the most critical drugs and to order up to their this large-scale project the Drug Distribution Project maximum dollar-value allocations. This posed a prob- lem in allocation: because there was an overall dollar- The DDP was to distribute 125 drugs in more than value cap on the amount of each drug available for 20 drug categories. These drugs ranged from routine distribution, there was every likelihood that orders for antibiotic drugs, such as Amoxil and Ceftin, to com- certain critical drugs would exceed the quantities plex drugs, such as Artane (for the nervous system) available. To resolve those situations, the Public Health and Epivir (for HIV). Further, each pharmaceutical Institute sought my help in developing an allocation firm restricted the wholesale value (in total, by drug heuristic that could be used in a decision-support sys- category, and by individual drug) of the products it tem to allocate the drugs equitably to the clinics.
could provide in a given period. The pharmaceutical Several previous research studies in health-care firms imposed additional restrictions on the clinics in management and optimization models for nonprofit terms of minimum order amounts per period, in dol- environments are related to this work. Folland et al.
(1997) discuss the prevalence and the relevance of Vol. 33, No. 2, March–April 2003, pp. 1–11 SWAMINATHAN
nonprofit organizations in the health sector. They also Savas (1978) defines efficiency as the ratio of service highlight the difficulties associated with managing outputs to service inputs. In this case, service inputs activities with a nonprofit purpose. Several other re- are fixed and are based on the dollar amount and searchers have adopted and adapted optimization quantity of drugs that the pharmaceutical firms are ob- models for the public-sector environment (Bodily 1978, ligated to donate. Therefore, allocational efficiency is Heiner et al. 1981, and Mandell 1991). Brill (1979) dis- measured by the extent to which the DDP distributes cusses the limitations of using traditional optimization all resources available. Our objective to minimize the models for generating alternatives and facilitating total dollar value of the drug budget left over, which their evaluation. He also discusses the role of heuristics is equivalent to maximizing the dollar value of drugs and computer algorithms. Savas (1978) identifies three allocated in a given period, accomplishes the goal of measures of performance in a nonprofit environ- ment—efficiency, effectiveness, and equity. He defines We measured allocational effectiveness by the extent efficiency as the ratio of service inputs to service out- to which clinics receive the drugs they needed. To puts; effectiveness as how well the need for services is maximize effectiveness, we used a weight matrix pik satisfied and adverse consequences are prevented; and that determines the importance of drug k for clinic i.
equity as the fairness, impartiality, or equality of ser- The DDP managers based the weight matrix on several Problem Description
The three-year drug distribution was subdivided into several ordering intervals (that occurred typically once every three months). The sequence of operations forordering drugs in any order period was as follows.
factors. For example, it gives mental-health clinics First, the DDP provided the clinics their drug budgets higher priority for mental-health drugs; it gives small for the order period. The state of California had estab- clinics priority over large clinics in certain cases; and lished rules for determining the drug budgets for clin- it gives high priority to clinics participating for the first ics based on such characteristics as location, popula- time in Public Health Institute programs to encourage tion served, and financial condition. Clinics then had further participation. To some extent, effectiveness is a two-week window in which to place their drug or- also affected by the budget limit that the state deter- ders with the DDP. Using the online decision-support tool, the DDP also provided the clinics with informa- We measured equity of allocation by the extent to tion on drug availability for the ordering period. A which allocations are fair with respect to clinic char- clinic could work on its order, finalize it, and then send acteristics, such as financial resources, geographical re- it at any point during this time. Once the clinic sent moteness, and medical specialization. Folland et al.
the order to the DDP, it was considered final and could (1997) discuss the notion of need-based allocation and not be changed. After the two-week order-placement the ambiguities involved in discerning the need of con- window expired, the decision-support system consid- stituents that makes this measure difficult to optimize.
ered all orders as final and began the allocation pro- In this case, for example, large organizations and hos- cess. We (I along with the DDP managers) decided that pitals need more drugs but also have more resources it was reasonable to optimize drug allocation for only with which to buy those drugs in the open market.
one ordering period at a time. This allocation process Similarly, specialized clinics need drugs related to will be repeated once every quarter over three years.
their specialties more acutely than other clinics. Along The decision-support tool took into account effi- the same lines, some of the small clinics need drugs ciency, effectiveness, and equity while allocating drugs allocated to them even though their orders may be for very small amounts. To achieve equity, we designed SWAMINATHAN
the allocation heuristic such that each clinic gets a frac- The allocation constraints relate the requested quan- tion that is proportional to the requested amount tities and the allocated quantities. Constraint (5) en- (weighted by pik) of any drug in short supply.
sures that the dollar value of a drug delivered to a For example, if clinic 1 has a weight of 5 for drug i clinic is less than or equal to the requested amount.
and clinic 2 has a weight of 4 and their orders are 50 Constraint (6) ensures that the DDP meets the mini- and 100 respectively and the budget for this drug is mum order quantity for each drug and clinic. Con- 100, we allocate $38.46 to clinic 1 and $61.54 to clinic 2 straint (7) is the nonnegativity constraint.
to make an overall allocation that reflects the order The allocation problem has multiple objectives, is sizes and the clinics’ respective weights nonlinear, and has integer variables. The size of the real problem (more than 150 clinics, 25 pharmaceutical firms, 125 drugs, and 20 drug categories) makes opti-mal allocation very difficult to achieve in a reasonable Such an allocation may not be always feasible because time. Because the optimization model was to be used of limits on minimum orders. However, it is an attempt regularly for decision support and the priority weight to equalize the distribution of drugs among the clinics, matrix would be somewhat subjective, we focused our taking into account their orders and their priorities attention on developing a fast heuristic solution that for the drugs. The ability to change allocations based addressed the efficiency, effectiveness, and equity on the priority weights allows the DDP managers to study the impact of priority weights on allocationsmade by the decision-support system.
Given the above measures, we formulate the prob- Allocation Heuristic
lem (Appendix) with two objectives, to minimize theleftover budget (Objective O1, the equivalent of max- The allocation heuristic develops a solution that takes imizing the dollar value of the drug allocation) in any care of the performance measures and keeps the pro- given period, which addresses efficiency, and to min- cedure simple enough for the DDP managers to use it imize the difference between the ratio of the allocations for decision support. The basic idea in the allocation and the weighted orders from the clinics, thereby ad-dressing the effectiveness and equity measures (Objec- tive O2). The allocation also needed to take into ac- count the following constraints on participating clinics and pharmaceutical firms (Appendix).
The DDP allocated each clinic a budget Bi for the total dollar value of drugs it could obtain per order heuristic is to identify scarce drugs (those for which period based on a formula determined by the state of demand is greater than supply) and to find a fair al- California. This clinic constraint (1) ensures that clinics location among clinics while taking all the constraints do not exceed their budgets. Although the budget alone should normally be sufficient to restrict the The heuristic starts by allocating to all clinics the amount allocated to a clinic, we added a constraint that quantities requested for all the drugs (Step 0). Then, it limits orders as well to discourage clinics from order- checks whether any constraints have been violated; if ing irrational or exorbitant amounts.
not, the heuristic ends. Otherwise, the heuristic iden- Each pharmaceutical firm categorizes its products.
tifies all the scarce drugs, the drug categories, and the For example, they put all mental-health drugs to- pharmaceutical firms (Steps 1–3). The heuristic then gether. Constraints (2), (3), and (4) ensure that in any starts at the scarce drug level and identifies the maxi- given period the dollar values of total disbursement, mum number of clinics that can be served subject to category-level disbursement, and drug-level disburse- the minimum-order constraint (Step 3a). If this number ment, do not exceed the limits set in the settlement turns out to be less than the number of clinics that placed an order for a given drug, the heuristic selects InterfacesVol. 33, No. 2, March–April 2003 SWAMINATHAN
the clinics with the highest priority for the drug (Step performance of this heuristic depends to a great extent 3b). This step addresses the effectiveness criterion.
on the priority weight matrix pik, provided by the de- Next, the heuristic allocates the existing budget for this scarce drug to the high-priority clinics to optimize ob-jective O2 for the drug (Steps 3c–3f). Doing this means Illustrative Example
splitting the existing budget to allocate drugs to clinicsbased on their order size and their priority. These steps Let us consider two firms that manufacture five drugs in the heuristic are introduced to achieve equity of al- (N1, N2, N3, MH, HIV) which are distributed to five location. Whenever a surplus is created, the heuristic clinics (C1, C2, C3, CMH, CHIV) that differ in size and immediately redistributes it among the clinics to main- speciality. Each drug comes in only one package, and tain the efficiency of the allocation. The heuristic also firms have no separate budgets for various categories.
adjusts the amount going to the different clinics to sat- The input parameters are Dj, the set of drugs manu- isfy the minimum-order constraint (Steps 3g–3i(3)).
factured by firm j ; Bi, the budget allocation for clinic i; This adjustment may take several iterations and occa- dtj, the maximum disbursement from firm j ; ddjk, the sionally may even lead to a reduction in the number maximum disbursement for drug k; and ek, the mini- of clinics that are allocated the scarce drug (Step 3i(3)).
This is repeated for each of the scarce drugs in the cate- Once the heuristic allocates all the drugs in a cate- gory, it evaluates the constraint for the drug category (Step 2a). If the constraint has been violated, the heu- ristic reduces the budget for all the drugs in that cate-gory to meet the constraint (Step 2b). While there are alternative ways to artificially reduce the budgets as- sociated with the different drugs, we used this method to treat all the drugs equally. With the budgets for thedrugs in the category reallocated, the heuristic begins Table 1 shows the priority weight matrix for the ex- the entire process of drug allocation again with the ample, and Table 2 shows the orders from the five clin- scarce drugs in the category. The heuristic repeats this procedure for all the scarce drug categories for a given Here is how the heuristic determines the allocation: manufacturer (Step 2c). Once the heuristic has allo- Step 0: is to allocate R ס Oik for all i, k. Because N3 cated all the drugs in all the categories established by is a scarce drug (demand is 400 while the drug budget one manufacturer, it checks the manufacturer’s overall budget constraint (Step 1a); if that constraint has been Step 1: is to identify the manufacturer of the scarce violated, the heuristic reduces the budgets for all of drug; manufacturer 2 produces drug N3.
that manufacturer’s drugs by an equal fraction and re- Step 3: for scarce drug N3: peats the whole process of allocation (Step 1b). Theheuristic ends when allocations have been computed for all the manufacturers (Step 1c).
By maximizing the allocation of drugs, the heuristic accomplishes the first objective O1. Minimum orders, however, introduce inefficiency into the system, and a small amount of money is often left over after alloca- tion. By explicitly incorporating objective O2, the heu- ristic produces an equitable allocation. Like the per-formance of any decision-support algorithm, the Table 1: This is the priority weight matrix p in the illustrative example.
ik
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Table 2: These are the dollar values of orders from the clinics for the
different drugs (O ) in the illustrative example.
Table 3: This is the dollar value allocation of drugs for the clinics (R ) in
ik
ik
the illustrative example.
—Step 3a: Determine the maximum number of clin- ics whose demand can be satisfied; Z ס min{dd for the first ordering period. The online ordering and distribution system consisted of three main compo- —Step 3b: Because Z ס 5, fill the orders for all five nents: the order-entry system, the order-processing system, and the order-distribution system (Figure 1).
—Step 3c: Because the sum of clinic orders exceeds The order-entry system allowed clinics to enter their (͚iס1Rik Ͼ ddjk), go to orders using the Internet. Each clinic was provided with a user name and a password. Clinics could pre- —Step 3d: Compute the total weight of the orders pare, modify, and submit orders during each ordering across all the remaining clinics: W ס ͚ —Step 3e: Allocate drug N3 to each clinic based on —Step 3f: Because that allocation gives C3 more than period. Further, the system automatically checked that clinics met minimum-order constraints and did not ex- —Step 3g: Because all the clinics have been allocated ceed their drug budgets. While placing their orders, more than the minimum quantity, split the sur- the clinics saw a running total of their orders and the plus equally among clinics C1, C2, CMH, CHIV. So, remaining budget, and the system accepted only or- ders that were within the budget and greater than or equal to the minimum order quantity. The clinics could Table 3 shows the final allocation as determined by sort drugs by category and by pharmaceutical firm.
Educating clinic employees about the ordering processwas challenging because many were unfamiliar with Implementation
computer-based ordering using the Internet. Also, the Beginning in May 2000, the DDP implemented the al- DDP managers had to make them understand that location heuristic in a real-time decision-support- they might not get exactly what they ordered because system environment, namely the DDP’s custom- designed, online order system. A software firm called At the end of each ordering period, the order- Choice Systems implemented the DDP online order processing system took all the orders and computed system. About 166 safety-net clinics and county hos- the allocations based on the above heuristic using the pitals in California used this system to place orders for priority weight matrix pik provided by the DDP man- $40.6 million of pharmaceutical products in May 2000 agers. This system also produced reports on scarce InterfacesVol. 33, No. 2, March–April 2003 SWAMINATHAN
Figure 1: These architectural details reflect the product and information flow in the online drug-ordering and
distribution system.
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drugs, including degree of scarcity, and the clinics that $802.50 of a drug that was available in three package might be responsible for creating the scarcity.
sizes: (1) 100 capsules for $300.00; (2) 50 capsules for The third component of the system, order distribu- $175.00; and (3) 25 capsules for $90.00. If the clinic or- tion, was not under the control of the Public Health dered three packets of 100 each, the heuristic would Institute. Once the DDP managers were comfortable first allocate two packets with 100 and then allocate with all the allocations, they sent an electronic data one packet with 50 (Steps 6a–6b). At this point, the interchange (EDI) or fax message to the pharmaceuti- remaining budget for this clinic would be $802.50— cal firms with the orders to be distributed to the dif- ($600 ם $175.00) ס $27.50. The heuristic would then ferent clinics and updated the ordering system to re- note the minimum amount the clinic would have to flect the allocation of drugs so that the clinics knew pay to get one more package (in this case it is $90.00) what to expect from the different firms. The pharma- and add the $27.50 remaining budget to a surplus ac- ceutical firms contacted the clinics and informed them count (Step 6c). After processing all the orders for the about the actual deliveries of the drugs.
drug in the above manner, the heuristic would distrib- A number of issues arose during implementation ute the surplus amount among the clinics in order of that prompted modifications to the original heuristic their priority weight pik so that each clinic that was and priority weight matrices. One issue was that some short by at least the minimum package amount would drugs were available in several package sizes. For ex- get the minimum amount for one more package ample, Monopril could be ordered in packages of 30 ($90.00 for the clinic in this example) until the surplus or 90. Clinics placed orders for different sized pack- budget was exhausted or dropped below $90.00, the ages. The decision-support system computed their to- lowest package unit value (Steps 7–8b).
tal cost based on wholesale prices for the packages.
Another important issue that came up during im- After determining the clinic’s overall allocation using plementation concerned the size of the clinics. The the allocation heuristic, the decision-support tool had DDP managers had expected to receive orders from to calculate how many packages of the different types both big clinics and small clinics; however, they did the clinic would receive. We determined package-level not anticipate that some regions would have central- allocations using another heuristic called the package ized procurement for the different clinics. Los Angeles heuristic (Appendix). Once the dollar amount R County, for example, was one of these regions; it pre- drug k that was to be allocated to clinic i was deter- sented orders that were much higher than those pre-sented by other clinics. We changed the priority- weight matrix to prevent such large customers fromovershadowing the other clinics in the allocation pro- cess. To achieve this, we normalized the base weights have been filled as part of the DDP.
for all the clinics with respect to Los Angeles County.
For example, if the Los Angeles County hospitals’ bud- mined, the package heuristic had to determine how get was 100 times that of a small Native American many of each package size to give to a clinic so as to clinic, we adjusted their base priority weights approx- match the allocation as closely as possible to the re- quest, and at the same time distribute the maximum Yet another issue related to the size of the priority- amount of drugs. This problem has characteristics weight matrix (pik): With over 150 clinics and 125 similar to the integer knapsack problem. The package drugs, the full matrix would contain 18,750 values. To heuristic adopted a greedy approach for each drug by simplify the priority-weight determination, we as- starting from the largest package size, providing the signed priority weight for each clinic consisting of a maximum possible amount of the drug in that package base value (determined by the size of the clinic) and a and then going down to the next package size, one size drug-specific value (which would be added to the base value) for certain crucial drug categories, such as men- For example, suppose that a clinic was allocated tal health and HIV. For the remaining drugs, we used InterfacesVol. 33, No. 2, March–April 2003 SWAMINATHAN
the clinic’s base value as the priority weight. The DDP k: index that represents the different drugs (k ס 1 managers could then input different base values and drug-specific weights to the allocation heuristics to ob- tain allocations that were reasonable and realistic.
Dj: set of drugs manufactured by pharmaceutical Although we expected a number of glitches to show up in the allocation heuristic during the first period of Cjl: set of drugs manufactured by firm j that are clas- execution (May 2000), they were very minor, and the sified under drug category l.
order processing went smoothly. As expected, a small percentage of drugs was extremely popular and, as a Mk: total number of packages in which drug k is sold.
result, very scarce; however, the allocation heuristic qkm: size of one package of drug k (by quantity con- handled the allocation of these scarce drugs well, as it tained) in package size m (m ס 1 . . . Mk).
had been designed to do. More details about the actual km: negotiated price of one package of drug k in ordering process can be found at ͗www.medpin.org/ i: total budget allowed for clinic i.
dtj: maximum disbursement of drugs in the period Conclusions
ddjk: maximum disbursement of drug k in the period The DDP managers have used the decision-support system since May 2000 when they received the first set jl: maximum disbursement of all drugs in the cate- gory l in the period by firm j (in dollars).
of orders. As of November 2002, 90 percent of the total ek: minimum order for drug k from any clinic in a $170 million budget has been distributed to the various clinics with the help of the decision-support system.
Oik: dollar value of drug k requested by clinic i.
Despite the need for a few changes to the heuristic, the OPikm: number of packages of size m of drug k or- DDP managers judge the allocation heuristic to be very successful at providing an efficient, effective, and eq- pik: priority weight of drug k for clinic i.
uitable method for determining drug allocations as part of the DDP’s order-processing system. A large Rik: dollar value of drug k received by clinic i.
number of uninsured patients who would otherwise Yik: 0–1 variable that represents whether clinic i ob- have had difficult or no access to medication have re- tained any allocation of drug k.
ceived their prescribed drugs. Although an accurate count of the number of patients affected is not avail- able, it is estimated that approximately 2.4 million 30- day drug prescriptions have been filled as part of the DDP. Further, many pharmaceutical firms are explor- ing use of the DDP’s decision-support system to ensure more efficient and equitable operation of the charitable (Rik * pnk * Onk מ Rnk * pik * O ) Appendix
The Model
i: index that represents the different clinics (i ס 1 . . .
j : index that represents the pharmaceutical firms ( j SWAMINATHAN
– Step 3h. If the clinics can be brought to the min- imum level with the surplus money, do so; then ex- haust the remaining surplus by dividing it equally and go to Step 3j; else go to Step 3i.
– Step 3i. Go to Step 3i(1).
• Step 3i(1). Sort the clinics that have more than the minimum quantity by the ratio of allocation toactual order.
Oik • Yik מ Rik Ն 0 ∀i, k, • Step 3i(2). Reduce the allocation of the first clinic (while maintaining at least the minimum order) so ik מ Yik • ek Ն 0 that the first and second clinics have the same ratio Rik ʦ R , Yik ʦ {0, 1}.
of allocation to order. Reallocate the extra from thefirst clinic to the clinics with shortfalls so that theymeet the minimum order. If the surplus generated Allocation Heuristic
is insufficient to bring all clinics with shortfalls up Oik for each clinic and drug.
to the minimum-order amount, go to Step 3i(3); else, Check whether all constraints are valid. If yes, then go if all clinics have met the minimum order, allocate the remaining surplus equally among the clinics Step 1. For each scarce manufacturer j (such that from which the surplus was created and go to Step j or ∃k ʦ Dj s.t.
iס1Rik Ͼ ddjk or ∃l s.t.
• Step 3i(3). Reduce the allocations of the top two Step 2. For each scarce drug category l (such that clinics so that they have the same ratio of allocation to order as the third clinic. Then reallocate the extra jl or ∃k ʦ Cjl s.t.
Step 3. For scarce drug k in C from the first two clinics to bring all clinics with shortfalls up to the minimum order. If all clinics are – Step 3a. Determine the maximum number of clin- brought up to the minimum order amount, allocate ics Z that can be supported with the minimum order the remaining surplus equally among those clinics requirement, i.e., Z ס largest integer less than or from which the surplus was generated and go to equal to min((djk/ek), I).
Step 3j; else repeat Step 3i(3), first with the top three – Step 3b. Select the top Z clinics (based on pik) to clinics, then with the top four clinics, and so on as needed to bring all clinics with shortfalls up to the – Step 3c. Check whether I ͚iס1Rik Ն ddjk. If not, go minimum order. If no more clinics remain from which to generate a surplus and some clinics still – Step 3d. Compute the total weight of orders have not met the minimum order amount, reduce Z across all the remaining clinics (Iˆ where i ʦ Iˆ implies 0) and W ס ͚iʦIˆ pikOik.
– Step 3j. If all scarce drugs in the category have – Step 3e. Allocate drug to each clinic based on its been exhausted, go to Step 2a; else go to Step 3 with the next scarce drug in the category.
– Step 3f. If any clinic is allocated more than re- Oik), add this amount to the surplus bank and set Rik to Oik.
Step 2b. Reduce the budget for all drugs in this cate- – Step 3g. Check whether allocations meet mini- have been allocated a positive dollar amount. If yes, allocate any surplus equally among all the clinics, and then go to Step 3j; else go to Step 3h.
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Identify all the scarce drugs in the category; start with the first drug k in the category, and go to Step 3.
val is the minimum value of a package size, cpkm ) Step 2c. If all the drug categories for the manufac- and surplus Ͼ Minval, then increase RPikm turer have been checked, go to Step 1a; else go to Step 2 with the next drug category for the manufacturer.
Step 8b. If surplus Ͻ Minval and scarce drugs still remain, go to Step 4 with the next drug; else go to Step 8 with the next clinic. If no scarce drugs remain, Step 1b. Reduce the budget for all drugs by this man- Acknowledgments
I thank Kathryn Duke, Maurice Ashe, and Leon Wilder from the Drug Distribution Project at the Public Health Institute, Oakland, California for introducing this problem, sharing information about the drugs, pharmaceutical firms, and clinics in the state of Californiainvolved in this project, and implementing the allocation scheme in Identify all the scarce drugs in the category, and go to their ordering and distribution system. I also thank an anonymous area editor and two referees whose comments improved the expo- Step 1c. If the drugs from all the manufacturers have been allocated, end; else go to Step 1 with the next References
Bodily, S. E. 1978. Police sector design incorporating preferences of interest groups for equality and efficiency. Management Sci. Package Heuristic
24(12) 1301–1312.
Brill, E. D., Jr. 1979. The use of optimization models in public-sector This heuristic is used after the dollar budgets have planning. Management Sci. 25(5) 413–421.
been allocated only when a drug comes in multiple Folland, S., A. C. Goodman, M. Stano. 1997. The Economics of Health and Health Care. Macmillan Publishing, New York.
Heiner, K., W. A. Wallace, K. Young. 1981. A resource allocation and represents the number of packages of mth size of drug evaluation model for providing services to the mentally re- k that are allocated to clinic i.
tarded. Management Sci. 27(7) 769–784.
Step 4. For each scarce drug (identified in the allo- Mandell, M. B. 1991. Modeling effectiveness-equity trade-offs in cation heuristic above) k, set the surplus budget to 0.
public service delivery systems. Management Sci. 37(4) 467–481.
Step 5. For each clinic i, set the remaining budget Savas, E. S. 1978. On equity in providing public services. Management Sci. 24(8) 800–806.
Step 6. For package size m, starting with the biggest Kathryn S. Duke, JD, MPH, Program Director of Medpin, 505 14th Street, Suite 810, Oakland, California94612, writes: “Under the California litigation settle- ment, we are distributing nineteen pharmaceutical companies’ products, totaling $148 million in value, to“safety net” clinics and hospitals throughout Califor- where integer(x) is the largest integer less than or nia over a three year period. In December 1999, we approached Professor Swaminathan to help us with Step 6b. Reduce RM by RPikm * cpkm.
Step 6c. If RP designing a fair and efficient mechanism to distribute biggest package size; else add RM to the surplus and these drugs. This problem is very difficult and al- go to Step 5 with the next clinic. If no clinics remain, though we understood the pros and cons of allocating drugs and had a good idea on the constraints on drug Step 7. Sort the clinics according to p budgets that we faced, we had limited experience and knowledge on how to develop a rational model and a SWAMINATHAN
decision-support solution that could help us in allo- then operationalizing the unique approach we are tak- ing to implement a litigation settlement. The decision- “Professor Swaminathan modeled the problem cap- support tool helped us gain very useful insights on the turing all the constraints associated with drug alloca- ordering of drugs and their allocations. When we tion and developed an efficient methodology to deter- started our work on DDP we were concerned about mine drug allocations once clinics had placed orders our ability to design an allocation system that would with us. We benefited a great deal from this thorough meet all of our project’s goals in a cost-efficient man- analysis and solution development. He also mediated ner. We also knew that doing the allocation manually with the software provider, ChoiceSystems Inc., the would have been extremely cumbersome if at all pos- company that created a custom-designed Internet- sible. We are pleased to report that the basic concept based ordering system for the DDP, to integrate of the DDP continues to work well as we continue to this allocation approach into the drug distribution disburse drugs under this project, thanks to the prac- tical experience and conceptual assistance that Profes- “Professor Swaminathan’s analysis and allocation heuristic was very helpful to us in conceptualizing and InterfacesVol. 33, No. 2, March–April 2003

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