### Table 1. Technical Coefficient Matrix and Stochastic Final Demand of a Hypothetical Economy Technical Coefficient Matrix Final Demand

### Table 1. Stochastic Features in Selected Robust Supply Chain Models

in Abstract

2003

"... In PAGE 7: ... 2.4 Literature Summary Table1 defines the stochastic features included in the papers discussed in this paper. Almost all of the papers consider stochastic demand, while a few consider stochastic demands and costs together.... ..."

### Table 4 : The evolution of effective adaptive supply chain management policies when facing stochastic customer

2002

"... In PAGE 16: ... This is much less than 7463 obtained using the 1 - 1 policy. Table4 shows the evolution of effective adaptive supply chain management policies when facing stochastic customer demand and stoch astic lead - time in the context of our experiments. We further tested the stability of these strategies discovered by agents, and found that they are stable, thus constitute an apparent Nash equilibrium.... ..."

Cited by 12

### Table 1: Weekly demand and its uncertainties. Weekly demand Uncertainty

2002

"... In PAGE 2: ...ertain. The selling price is sp cents per paper. For a speci c problem, whose weekly demand is shown below, the cost of each paper is c = 20 cents and the selling price is sp = 25 cents. Solve the problem, if the news vendor knows the demand uncertainties but does not know the demand curve for the com- ing week a-priori ( Table1 ). Assume no salvage value s = 0, so that any papers bought in excess of demand are simply discarded with no return.... In PAGE 2: ... Our rst instinct to solve this problem is to nd the average demand and nd the optimal sup- ply x corresponding this demand. Since the average demand from the Table1 is 70 papers, x = 70 should be the solution. Let us see if this represents the op- timal solution for the problem.... In PAGE 3: ... Therefore, the value of stochastic solution, VSS, is 1750 ( 50) = 1800 cents per week. Now consider the case where the vendor knows the exact demand ( Table1 ) a-priori. This is the perfect information problem where we want to nd the solution xi for each day i.... In PAGE 12: ... For instance, for k = 1, uk = 0 ( rst discrete value), then problem (20) would become: z = Min v+ 11 + v+ 12 + v 11 + v 12 s: t: v11 + v12 v13 + v14 + v+ 11 v 11 = 2:5 v11 + v12 + v13 v14 + v+ 12 v 12 = 2:25 v11; v12; v13; v14 gt;0 v+ 11; v+ 12; v 11; v 12 gt;0 (21) The solution to (21) is z = 0. The results of all of the problems (k = 1 11) are summarized in Table1 . Variables not shown are equal to zero.... In PAGE 13: ...13 Table1 : Determining feasibility of the second stage. k uk zk vk2 vk4 1 0 0 2.... In PAGE 16: ... A new variant of stochastic an- nealing, HSTA (Hammersley stochastic annealing), therefore, incorporates (i) HSS for the generation probability Gij, (ii) HSS in the inner sampling loop for Nsamp determination, and (iii) the HSS-speci c error bandwidth ( HSS) in the penalty term. Table1 : E ciency improvements. Stochastic algorithm Total moves SA + xed Nsamp 274,200 ESA + xed Nsamp 170,000 STA 5,670 ESTA 3,265 HSTA 1,793 Test function : z = P10 i=1 ui xi i 10 2 + P10 i=1 ui y2 i Q10 i=1 cos(4 ui yi) Table 1 shows total number of con gurational moves of di erent stochastic optimization methods.... In PAGE 16: ... Table 1: E ciency improvements. Stochastic algorithm Total moves SA + xed Nsamp 274,200 ESA + xed Nsamp 170,000 STA 5,670 ESTA 3,265 HSTA 1,793 Test function : z = P10 i=1 ui xi i 10 2 + P10 i=1 ui y2 i Q10 i=1 cos(4 ui yi) Table1 shows total number of con gurational moves of di erent stochastic optimization methods. The rst two algorithms are (conventional) stochas- tic optimization algorithms with a xed Nsamp while the last three algorithms are stochastic annealing al- gorithms with a varying Nsamp.... In PAGE 20: ...SIAG/OPT Views-and-News Table1 : Base sample. Sample No.... ..."

### Table 4. Sampling Experiments for the Stochastic Volatility Model

2001

"... In PAGE 14: ... Due to the computational demands, we limit the posterior draws to 20,000. Each experiment was repeated 200 times, and the resulting parameter estimates are summarized in Table4 . Also, , which posterior distri- bution requires an extensive number of draws to estimate accurately, is xed to 1 2 in the simulation study.... In PAGE 14: ... For the parameter measuring the reversion in the log-volatility process, z, the estimates are also slightly downward biased, while the estimate of the di usion coe cient for the log-volatility process, z, is virtually unbiased using a sample size of 2000. When interpreting the results in Table4 , it should be kept in mind that the reversion coe cients can be inter- preted as approximately quot;autocorrelation - 1 quot;. This, cou- pled with the well-known fact that sample autocorrelation coe cients are downward biased for processes with near unit roots may explain, at least partially, the direction of the bias in the sampling experiments.... In PAGE 14: ... It does, however, in uence the dispersion of the posterior means, as measured by the RMSE. Hence, the results in Table4 are likely to underestimate the e ciency of the MCMC estimator. Overall, the performance of the MCMC method for es- timating the parameters in the stochastic volatility model is di cult to assess.... ..."

Cited by 30

### Table 1: E ciency improvements. Stochastic algorithm Total moves

2002

"... In PAGE 2: ...ertain. The selling price is sp cents per paper. For a speci c problem, whose weekly demand is shown below, the cost of each paper is c = 20 cents and the selling price is sp = 25 cents. Solve the problem, if the news vendor knows the demand uncertainties but does not know the demand curve for the com- ing week a-priori ( Table1 ). Assume no salvage value s = 0, so that any papers bought in excess of demand are simply discarded with no return.... In PAGE 2: ... Assume no salvage value s = 0, so that any papers bought in excess of demand are simply discarded with no return. Table1 : Weekly demand and its uncertainties. Weekly demand Uncertainty i Day Demand j Demand Probability (di) (dj) (pj) 1 Monday 50 1 50 5/7 2 Tuesday 50 2 100 1/7 3 Wednesday 50 3 140 1/7 4 Thursday 50 5 Friday 50 6 Saturday 100 7 Sunday 140 Solution: In this problem, we want to nd how many papers the vendor must buy (x) to maximize the pro t.... In PAGE 2: ... Our rst instinct to solve this problem is to nd the average demand and nd the optimal sup- ply x corresponding this demand. Since the average demand from the Table1 is 70 papers, x = 70 should be the solution. Let us see if this represents the op- timal solution for the problem.... In PAGE 3: ... Therefore, the value of stochastic solution, VSS, is 1750 ( 50) = 1800 cents per week. Now consider the case where the vendor knows the exact demand ( Table1 ) a-priori. This is the perfect information problem where we want to nd the solution xi for each day i.... In PAGE 12: ... For instance, for k = 1, uk = 0 ( rst discrete value), then problem (20) would become: z = Min v+ 11 + v+ 12 + v 11 + v 12 s: t: v11 + v12 v13 + v14 + v+ 11 v 11 = 2:5 v11 + v12 + v13 v14 + v+ 12 v 12 = 2:25 v11; v12; v13; v14 gt;0 v+ 11; v+ 12; v 11; v 12 gt;0 (21) The solution to (21) is z = 0. The results of all of the problems (k = 1 11) are summarized in Table1 . Variables not shown are equal to zero.... In PAGE 13: ...13 Table1 : Determining feasibility of the second stage. k uk zk vk2 vk4 1 0 0 2.... In PAGE 16: ... Table1 shows total number of con gurational moves of di erent stochastic optimization methods. The rst two algorithms are (conventional) stochas- tic optimization algorithms with a xed Nsamp while the last three algorithms are stochastic annealing al- gorithms with a varying Nsamp.... In PAGE 20: ...SIAG/OPT Views-and-News Table1 : Base sample. Sample No.... ..."

### Table 1. Input parameters for the PRP demand simulator, PRPsym

"... In PAGE 5: ... The sensors are assumed to provide error and noise free readings of the actual concentrations. The parameter values for residential water demand simulations done herein are listed in Table1 . Two types of output are produced by the PRPsym software for each node: (i) water demand time series and (ii) water demand simulation statistics.... In PAGE 5: ...5, 1, 2, 4, 6, 12 and 24 hour time step lengths. The base case simulation used as the ground truth in this work simulates instantaneous demands using the parameters in Table1 and then aggregates these demands over 30 minute time steps. These aggregated demands are used in EPANET for simulation of the transport from node 435.... In PAGE 5: ... The concentrations observed at the nodes with sensors are then recorded as the observed concentrations. The same demand generation parameters, Table1 , are then used to generate demands aggregated over 1, 2, 4, 6, 12 and 24 hour time steps. The base demand at each node ... In PAGE 9: ... One way to examine the uniqueness of these results with respect to the aggregated demands will be to generate multiple stochastic demand patterns for each time step size and characterize the range of objective function, mass fraction and entropy values across all simulated demands. Other simulations that can be done to assess the sensitivity of the results presented here include varying the parameters used in PRPsym ( Table1 ) to generate the demands and to vary the number of sensors within the network. Rapid assessment of these additional simulations is feasible due to the minimal computational burden that can be achieved by the inversion approach used herein.... ..."

### Table 5 Adjustment Cost Function (Linear Approximation)--Stochastic Variation Log(7 ) = N + N *10 U + e i01 ii 3

1996

"... In PAGE 19: ... Stochastic volatility appears somewhat less important in explaining the variation in adjustment costs. Table5 reports the estimates of the parameters of the inverse adjustment cost function when the independent variables are the variance of the stochastic component of labor demand--defined as the variance of the residuals in the regression of the percentage change in employment on monthly dummy variables. The OLS and WLS estimates of N are 1 significantly negative in five and three of the two-digit industries, respectively.... ..."

### Table 2: Unit Shipping Costs and Demands

2006

"... In PAGE 117: ...COMPUTATIONAL RESULTS FOR LP MODEL Table2 0: Performance of Three Policies and Bound Gap between Proposition 11 and Optimal Values Set Instance Our Smallest Fit Multi-criteria Bound Policy Max Min Avg Max Min Avg Gap 1 1.00 1.... In PAGE 118: ...Table2 1: Performance of Three Policies and Bound Gap, Cont. Set Instance Our Smallest Fit Multi-criteria Bound Policy Max Min Avg Max Min Avg Gap 1 1.... In PAGE 120: ...Table2 2: Performance on Small Location Problems Inst- All a Priori Benders Cuts When Needed ance TC TIM TC DC TIM TC AC IT TIM 1 1 0.15 1 0 0.... In PAGE 121: ...Table2 3: Performance on Medium Location Problems Inst- All a Priori Benders Cuts When Needed ance TC TIM TC DC TIM TC AC IT TIM 1 5 9.09 5 2 11.... In PAGE 122: ...Table2 4: Performance on Large Location Problems Inst- All a Priori Benders Cuts When Needed ance TC TIM TC DC TIM TC AC IT TIM 1 21 4473 9 4 4999 5 2.5 2 4418 2 16 2956 1 0 4746 4 4 1 2794 3 14 523 15 11 640 3 1.... In PAGE 124: ...Table2 5: Performance of Algorithms for Small Stochastic Problems Instance Single-Cut Method Double-Cut Method L-shaped All Fea Fea When L-shaped All Fea Fea When Set Fea a priori Needed Fea a priori Needed 1 12.26 2.... In PAGE 125: ...Table2 6: Performance of Algorithms for Medium Stochastic Problems Instance Single-Cut Method Double-Cut Method L-shaped All Fea Fea When L-shaped All Fea Fea When Set Fea a priori Needed Fea a priori Needed 1 369.15 186.... In PAGE 126: ...Table2 7: Performance of Algorithms for Large Stochastic Problems Instance Single-Cut Method Double-Cut Method L-shaped All Fea Fea When L-shaped All Fea Fea When Set Fea a priori Needed Fea a priori Needed 1 6734.97 1411.... ..."

### Table 5: Results for manufacturer for different demand patterns The aggregation of order data into larger time units leads to significantly lower safety stocks for all demand patterns. A maximum reduction of approximately 58% can be achieved also for the manufacturer if demand contains trends.

2007

"... In PAGE 11: ...2. Results for the Manufacturer As can be seen in Table5 , inefficiencies of applying traditional stochastic inventory policies based on order data can be observed also for the manufacturer. The benefits obtained from information sharing are even more striking for the manufacturer than for the distributor in terms of lower mean inventories and safety stocks for constant demand.... ..."