INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN STUDENT: HUYNH MINH TRI ID: St THESIS ADVISOR: ASSISTANT PROFESSOR HUYNH TRUNG LUONG PROGRAM COMMITTEE: DR. HUYNH TRUNG LUONG (CHAIRPERSON) DR. VORATAS KACHITVICHYANUKUL DR. PISUT KOOMSAP

CONTENTS: - THE OBJECTIVES & THE SCOPES OF THIS THESIS - MULTI DELIVERY IN JUST IN TIME ENVIROMENT - ASPESTS CONSIDERED IN CHOOSING DELIVERY POLICIES - MODELINGS & RESULTS OF THIS STUDY - CONCLUSIONS AND RECOMMENDATIONS INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

Objectives of the study  Determine the optimal order lot size Q* for an integrated production and inventory system  In particular, the models developed in this research will take into consideration decisions of where to hold the inventory (upstream or downstream echelon) and when to ship the product between them

The following assumptions are used in the development of the two-echelon inventory model in this thesis:  Demand rate is constant.  Two manufacturers with one product are considered  Production rates are constants  Lead-time to deliver products from one echelon to another echelon is negligible.  No deterioration occurs in the stock. INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

THE CONFIGURATION OF THE SYSTEM Transfer q i, n j, Tr i Manufacturer i q i, p i, h i,A i Manufacturer j q j, p j, h j Demand D Outgoing inventory of manufacturer i Incoming inventory of manufacturer j INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN Figure 1: Two-echelon Inventory-Production System Lot size Q*=q i n j

NOTATIONS: Q: lot size D: demand rate of the customer (product/unit time) q i : production batch size (product) p i : production rate of manufacturer i (product/unit time) p j : using rate of manufacturer j (product/unit time) n j :the number of batch needed for one lot of size h i : outgoing inventory holding cost of manufacturer i ($/period) h j : incoming inventory holding cost of manufacturer j($/period) Tr i : transportation cost per batch from manufacturer i to manufacturer j ($/ batch) INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

I. Case 1.1: p i > p j, h i >h j Figure 2: Outgoing inventory of manufacturer i (Upper graph) Incoming Inventory of manufacturer j (Lower graph)

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN II. Case 1.2: p i > p j, h i <h j Figure 3: Outgoing inventory of manufacturer i (Upper graph) Incoming Inventory of manufacturer j (Lower graph)

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN Figure 4: Outgoing inventory of manufacturer i (Upper graph) Incoming Inventory of manufacturer j (Lower graph) III. Case 2.1: p i >p j, h i >h j

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN Figure 5: Outgoing inventory of manufacturer i (Upper graph) Incoming Inventory of manufacturer j (Lower graph) IV. Case 2.2: p i <p j, h i <h j

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN Develop the joint total cost case After the (k+1) th shipment, manufacturer i may or may not need to produce, and it should stop before the (k+2) th shipment. - After the (k+1) th shipment, manufacturer j needs (n j -k-1) shipments more in order to fulfill the lot size Q.

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN Figure 3: Outgoing inventory of manufacturer i (Upper graph) Incoming Inventory of manufacturer j (Lower graph)

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN The outgoing inventory cost of manufacturer i is Joint total cost per unit time Simplify the above expression, we have The accumulated outgoing inventory level at manufacturer i IL i =S OHA +k*S AMN +S ALK +S KLPT +S PQST +S DSE

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN 2. Determine the solution Take the first partial derivative of TC(q i,n j ) with respect to q i, n j and let them equal to zero Solve the above equations, we obtain the exact solution

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

NUMERICAL EXPERIMENT

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN NUMERICAL EXPERIMENT

Conclusions This thesis achieved all the objectives proposed. 1. Exact mathematical models, based on the analytical technique have been developed to help find the optimum solution. 2. Exact solution expressions for all considered cases are obtained. 3. Numerical experiments and sensitivity analysis have been conducted to illustrated the applicability of the proposed models. 4. It is also noted that although the models are developed under the assumption that transportation time is negligible, we also can apply these results if there exists a constant lead time for transportation between two manufacturers by shifting the inventory graphs by an amount of time equals to the lead time. INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

Recommendations Although this research gains satisfactory results, the solution expressions are simple and easy to be employed. There are still some limitations exist that need to be addressed in future researches. 1. The models are developed under an implicit assumption of unlimited capacity of the transport facility 2. The results here are applicable for a two-stage supply chain with two manufacturers and one product. Further researches should be conducted so that the models developed here can be expensed for a general supply chain with more than two manufacturers INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

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INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN SENSITIVITY ANALYSIS I. Preliminary analysis - Decision variables are independent of demand - q i is independent of production setup cost A i II. Parameters - Variation of higher production rate and variation of lower production rate - Variation of higher inventory holding cost and lower inventory holding cost - Other parameters used in the numerical examples are kept intact

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN 1. Sensitivity analysis of the model with respect to small variation of higher production rate

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN