1. 1 1 Exam 1 John H. Vande Vate Spring, 2007

2. 2 2 Process 80+ exams to grade Certainly errors, misunderstanding, … Happy to re-grade BUT –Only respond to WRITTEN requests –Simply explain what you think was mis- graded identifying specific questions and sections and give it to me with the exam. –It may take a while.

3. 3 3 Grades ~20 point curve >~70 A >~50+ B >40 C

4. 4 4 Answers Question 1: A full truck load of pillows weighs 0.9 lbs/cu ft * 3,900 cu ft = 3,510 lbs so we clearly “cube out” long before we reach the 50,000 lbs limit. A full truck load is 3,510 lbs/ 3lbs = 1170 pillows Guess a full truck load is less than the EOQ. Compute Inventory –If we ship full truck loads t he average inventory at each customer location will be half a truckload or 585 units, worth about $17,550 –Carrying cost $3510 at each customer Compute Transportation Conclusion? MilesUnits (Thousands)Loads/yearTransport/year 3501,000 854.70 $ 448,718 2400500 427.35 $ 1,538,462 900400 341.88 $ 461,538

5. 5 5 Working Capital Total working capital required for these customers will be Inventory at customer DCs: 3*$17,550 = $52,650 Pipeline Inventory to Customer 1: 1 million units/yr/ 365 days/year = 2,740 units/day 350 miles/500 miles/day = 0.7 days in transit Pipeline inventory = 0.7*2740 = 1,918 units Working Capital = $30*1918 = $57,534 Pipeline Inventory to Customer 2: 500,000 units/yr/ 365 days/year = 1,370 units/day 2400 miles/500 miles/day = 4.8 days in transit Pipeline inventory = 4.8*1370 = 6,576 units Working Capital = $30*6576 = $197,280 Pipeline Inventory to Customer 3: 400,000 units/yr/ 365 days/year = 1,096 units/day 900 miles/500 miles/day = 1.8 days in transit Pipeline inventory = 1.8*1096 = 1,973 units Working Capital = $30*1,973 = $59,184 Working Capital at the Plant in Inventory for these customers A bit less than half a truckload. In fact, since these customers represent 80% of our capacity, it will be 0.8*(Q/2) = 0.8*17,550 Or $14,040 Total Working Capital: $380,688

6. 6 6 Question 2 The model is clearly missing Flow Conservation at the DCS. These should ensure flow in = flow out for each product at each DC s.t. FlowConservation{dc in DCS, prod in PRODUCTS}: sum{(orig, dc) in LANES} Flow[orig, dc, prod] – sum{(dc, dest) in LANES} Flow[dc, dest, prod] = 0; For each dc in DCS and prod in PRODUCTS

7. 7 7 Question 2 Constraints ensuring the Trucks on a lane are sufficient to handle the weight s.t. HandleWeight{(orig, dest) in LANES}: sum{prod in PRODUCTS} Weight[prod]*Flow[orig, dest, prod] <= TruckWeight*Trucks[orig, dest]; For each (orig, dest) in LANES

8. 8 8 Question 2 Constraints ensuring the Trucks on a lane are sufficient to handle the cube s.t. HandleCube{(orig, dest) in LANES}: sum{prod in PRODUCTS} Cube[prod]*Flow[orig, dest, prod] <= TruckCube*Trucks[orig, dest]; For each (orig, dest) in LANES

9. 9 9 Question 3 Answer: Several answers make sense. Priority 1: The EOQ quantity from Indianapolis to the stores weighs less than 10,000 lbs, so we can serve 3 stores with a single truckload. Build routes that serve several stores. This will reduce transportation costs with only a small increase in inventory in Indianapolis and perhaps, because of timing, at the stores. I list this as the first priority because I estimate it will have the greatest impact with little complication in operations.

10. 10 Question 3 Priority 2: Since the company is already shipping less-than-full trucks, the next step would be to compute the separate EOQ quantities for stores at different distances from Indianapolis. This will have a mixed effect. In some cases (where the stores are less than 1,000 miles from Indianapolis) it will reduce the shipment quantity and so reduce inventory costs while increasing transportation costs. In other cases (where stores are more than 1,000 miles from Indianapolis) it will increase the shipment quantity and so increase inventory while decreasing transportation costs. Naturally, this should be done in conjunction with Priority 1. I list this as the second priority because I estimate its impact will be smaller.

11. 11 Question 3 Priority 3: Explore opening other distribution centers, e.g., at the other plants, or as pool points. This has the potential to reduce transportation costs without significantly increasing inventory. Priority 4: Explore serving stores directly from plants they are close to. This has the potential to reduce transportation costs without significantly increasing inventory costs if it is implemented appropriately. I put this as a last priority as I suspect it has the smallest impact on cost, but will significantly complicate our operations.

12. 12 Models /* Whether or not each DC serves each pool */ Var UseEdge{DCS, POOLS} binary; /* Shipments of each product we supply from each dc to each pool in units/year */ Var Ship{PRODUCTS, DCS, POOLS} >=0; /* Deliveries of each product from each pool to each store in units/year */ Var Deliver{PRODUCTS, ASSIGNMENTS}>=0; /* Minimize (Outbound) Transportation Costs: DCs to Pools + Pools to Stores (You will need to add this part) */ Minimize OutBoundTransport: Sum{prod in PRODUCTS, dc in DCS, pool in POOLS} (InBoundCost[prod, dc]+OutBoundCost[prod, dc, pool])* Ship[prod, dc, pool]+ Sum{prod in PRODUCTS, (pool, store) in ASSIGNMENTS} DeliverCost[prod, pool, store]*Deliver[prod,pool,store];

13. 13 Question 4 /* Flow conservation for each product at each pool */ s.t. PoolFlowConservation{prod in PRODUCTS, pool in POOLS}: sum{dc in DCS}Ship[prod, dc, pool] = sum{(pool, store) in ASSIGNMENTS} Deliver[prod, pool, store]; /* Meet demand for each product at each store */ s.t. MeetDemand{prod in PRODUCTS, store in STORES}: sum{(pool, store) in ASSIGNMENTS} Deliver[prod, pool, store] >= Demand[prod, store];